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Waves

The document contains a series of physics questions related to interference patterns, wave properties, and optical phenomena. It includes calculations and discussions on the effects of changes in experimental setups on the results. The questions cover various topics such as the behavior of light, wave mechanics, and the properties of optical fibers.

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0% found this document useful (0 votes)

126 views108 pages

Waves

Uploaded by

nilenamikaze69

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as PDF, TXT or read online on Scribd

You are on page 1/ 108

Q1.

The figure below shows a diagram of apparatus used to demonstrate the formation
of interference fringes using a white light source in a darkened room. Light from the
source passes through a single slit and then through two narrow slits S1 and S2.

(a) Describe the interference pattern that is seen on the white screen.

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(b) A filter transmits only green light of wavelength λ and red light of wavelength
1.2λ
This filter is placed between the light source and the single slit.

Describe the interference pattern now seen on the white screen.

Use a calculation to support your answer.

______________________________________________________________
_____

______________________________________________________________
_____
(4)

(c) A student decides to use the apparatus shown in the figure to determine the
wavelength of red light using a filter that transmits only red light.

The student suggests the following changes:

• decrease slit separation s

• decrease D, the distance between the slits and the screen.

The student decides to make each change independently.

Discuss the effects each independent change has on the interference pattern,
and whether this change is likely to reduce uncertainty in the determination of
the wavelength.

______________________________________________________________
_____

______________________________________________________________
_____
(6)
(Total 12 marks)

Q2.
(a) Figure 1 shows an incident ray of light being partially reflected at the boundary
between glass A and glass B. The refractive index nA of glass A is 1.461

The speed of light in glass B is 3.252% less than the speed of light in glass A.

Figure 1

Calculate the refractive index nB of glass B.

Give your answer to an appropriate number of significant figures.

speed of light in a vacuum = 2.998 × 108 m s–1

nB = ____________________
(3)

(b) Figure 2 shows a cross-sectional view of an optical fibre strain gauge.

Figure 2

A maximum intensity of the reflected light is produced due to superposition of

the light reflected from each of the regions with increased refractive index in
the core.

This maximum intensity occurs at a particular wavelength λR.

Figure 3 shows the relationship between λR and the strain in the optical fibre.

Figure 3

A cable is used to raise and lower a lift. An engineer fixes the optical fibre
strain gauge to the cable to monitor changes of the strain in the cable.

The lift is initially at rest and then accelerates downwards for a short time
before reaching a constant velocity.

Discuss how the value of λR changes.

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(3)

(c) Figure 4 shows the relationship between λR and the strain in two optical fibre
strain gauges P and Q. The engineer wishes to measure small accelerations in
another lift. She can choose to fix either optical fibre strain gauge P or optical
fibre strain gauge Q to the lift’s cable.

Figure 4
Explain which gauge the engineer should select.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 8 marks)

Q3.
A ray of light is incident on a glass–air boundary of a rectangular block as shown.

The refractive index of this glass is 1.5

The refractive index of air is 1.0
The angle of incidence of the light at the first glass–air boundary is 44°

What is the path of the ray of light?

(Total 1 mark)

Q4.
Rays of light are incident at the same angle θ on the core–cladding boundary of
optical fibres P and Q.
The cores of P and Q have the same refractive index n.
P and Q are the same length L.
The core diameter of P is half that of Q.

The time for the ray to travel along optical fibre P is

where c is the speed of light in a vacuum.

What is the time for the ray to travel along optical fibre Q?

(Total 1 mark)

Q5.
The fundamental frequency f is the lowest frequency heard when a stretched string
is vibrating.

The string is now lightly touched one third of the way along its length.

What is the lowest frequency heard?

C f

D 3f

(Total 1 mark)

Q6.
A diffraction grating is illuminated normally with light of wavelength 6.5 × 10–7 m
When a screen is 1.5 m from the grating, the distance between the zero and
first-order maxima on the screen is 0.30 m

What is the number of lines per mm of the diffraction grating?

A 3.3 × 10–6

B 3.3 × 10–3

C 3.0 × 102

D 3.0 × 105

(Total 1 mark)

Q7.
Two points on a progressive wave have a phase difference of rad
The speed of the wave is 340 m s–1

What is the frequency of the wave when the minimum distance between the two
points is 0.12 m?

A 240 Hz

B 470 Hz

C 1400 Hz

D 2800 Hz

(Total 1 mark)

Q8.
The table shows results of an experiment to investigate how the de Broglie
wavelength λ of an electron varies with its velocity v.

v / 107 m s–1 λ / 10–11 m

1.5 4.9

2.5 2.9

3.5 2.1
(a) Show that the data in the table are consistent with the relationship

______________________________________________________________
_____
(2)

(b) Calculate a value for the Planck constant suggested by the data in the table.

Planck constant = ____________________ J s

(2)

Figure 1

An electron beam is incident on a thin graphite target that behaves like the slits
in a diffraction grating experiment. After passing through the graphite target
the electrons strike a fluorescent screen.

Figure 2 shows the appearance of the fluorescent screen when the electrons
are incident on it.

Figure 2

Explain how the pattern produced on the screen supports the idea that the
electron beam is behaving as a wave rather than as a stream of particles.

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(3)

(d) Explain how the emission of light from the fluorescent screen shows that the
electrons incident on it are behaving as particles.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 10 marks)

Q9.
Figure 1 shows the structure of a violin and Figure 2 shows a close-up image of the
tuning pegs.

Figure 1 Figure 2

The strings are fixed at end A. The strings pass over a bridge and the other ends of
the strings are wound around tuning pegs that have a circular cross-section. The
tension in the strings can be increased or decreased by rotating the tuning pegs.

(a) Explain how a stationary wave is produced when a stretched string is plucked.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____
(3)

(b) The vibrating length of one of the strings of a violin is 0.33 m

When the tension in the string is 25 N, the string vibrates with a first-harmonic
frequency of 370 Hz

Show that the mass of a 1.0 m length of the string is about 4 × 10–4 kg

(2)

(c) Determine the speed at which waves travel along the string in question (b)
when it vibrates with a first-harmonic frequency of 370 Hz

speed of waves = ____________________ m s–1

(1)

(d) Figure 3 shows how the tension in the string in question (b) varies with the
extension of the string.

Figure 3

The string with its initial tension of 25 N is vibrating at a frequency of 370 Hz

The diameter of the circular peg is 7.02 mm

Determine the higher frequency that is produced when the string is stretched
by rotating the tuning peg through an angle of 75°

Assume that there is no change in the diameter of the string.

frequency = ____________________ Hz
(4)
(Total 10 marks)

Q10.
In the diagram, P is the source of a wave of frequency 50 Hz

The wave travels to R by two routes, P → Q → R and P → R. The speed of the

wave is 30 m s−1

What is the path difference between the two waves at R in terms of the wavelength λ
of the waves?

A 4.8λ

B 8.0λ

C 13.3λ

D 20.0λ

(Total 1 mark)

Q11.
Light from a point source passes through a single slit and is then incident on a
double-slit arrangement. An interference pattern is observed on the screen.

What will increase the fringe spacing?

A increasing the separation of the single slit and the

double slit

B increasing the width of the single slit

C decreasing the distance between the double slits and

the screen
D decreasing the separation of the double slits

(Total 1 mark)

Q12.
(a) Describe the links between galaxies, black holes and quasars.

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(b) At a distance of 5.81 × 108 light year, Markarian-231 is the closest known
quasar to the Earth. The red shift z of Markarian-231 is 0.0415

Use these data to estimate an age, in seconds, of the Universe.

age = ____________________ s
(4)

(c) A typical quasar is believed to be approximately the size of the solar system,
with a power output similar to that of a thousand galaxies.

Estimate, with reference to the inverse-square law, how much further the most
distant visible quasar is likely to be compared to the most distant visible
galaxy.

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 9 marks)

Q13.
Figure 1 shows a diagram of the Michelson-Morley interferometer that was used to
try to detect the absolute motion of the Earth through the ether (æther).

Light from the monochromatic source passes through the semi-silvered glass block
and takes two different paths to the viewing telescope. The two paths, PM1 and PM2,
are the same length. Interference fringes are observed through the viewing
telescope.

Figure 1

It was predicted that when the interferometer was rotated through 90° the fringe
pattern would shift by 0.4 of the fringe spacing.

(a) Explain how the experiment provided a means of testing the idea that the
Earth had an absolute motion relative to the ether.

Your answer should include:

• an explanation of why a shift of the fringe pattern was predicted

• a comparison of the results of the experiment to the prediction
• the conclusion about the Earth’s absolute motion through the ether.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(6)

(b) The Michelson-Morley experiment provides evidence for one of the postulates
of Einstein’s theory of special relativity.

State this postulate.

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(c) State the other postulate of Einstein’s theory of special relativity.

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(d) One consequence of the special theory of relativity is length contraction.

Experimental evidence for length contraction is provided by the decay of
muons produced in the atmosphere by cosmic rays.

Figure 2 shows how the percentage of the number of muons remaining in a

sample changes with time as measured by an observer in a frame of reference
that is stationary relative to the muons.

Figure 2

In a particular experiment, muons moving with a velocity 0.990c travel a

distance of 1310 m through the atmosphere to a detector.

Determine the percentage of muons that reach the detector.

percentage = ____________________ %
(4)
(Total 12 marks)

Q14.
Figure 1 shows an arrangement used to investigate double slit interference using
microwaves. Figure 2 shows the view from above.

Figure 1

Figure 2

The microwaves from the transmitter are polarised. These waves are detected by
the aerial in the microwave receiver (probe). The aerial is a vertical metal rod.
The receiver is moved along the dotted line AE. As it is moved, maximum and
minimum signals are detected. Maximum signals are first detected at points B and
C. The next maximum signal is detected at the position D shown in Figure 2.

Figure 2 shows the distances between each of the two slits, S1 and S2, and the
microwave receiver when the aerial is in position D.
S1D is 0.723 m and S2D is 0.667 m.

(a) Explain why the signal strength falls to a minimum between B and C, and
between C and D.

______________________________________________________________
_____

______________________________________________________________
_____
(3)

(b) Determine the frequency of the microwaves that are transmitted.

frequency = ____________________________ Hz
(3)

Explain why the minimum intensity between C and D is not zero.

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(d) The vertical aerial is placed at position B and is rotated slowly through 90° until
it lies along the direction AE.

State and explain the effect on the signal strength as it is rotated.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 11 marks)

Q15.
Figure 1 shows a structure that supports a horizontal copper aerial wire W used for
transmitting radio signals.

Figure 1

The copper aerial wire is 12 m long and its area of cross-section is 1.6 × 10–5 m2.
The tension in the copper aerial wire is 5.0 × 102 N.

Young modulus of copper = 1.2 × 1011 Pa

(a) Show that the extension produced in a 12 m length of the aerial wire when the
tension is 5.0 × 102 N is less than 4 mm.
(2)

(b) The cables that support each mast are at an angle of 65° to the horizontal.

Calculate the tension in each supporting cable so that there is no resultant

horizontal force on either mast.

tension = ____________________________ N
(1)

(c) When wind blows, stationary waves can be formed on the aerial wire.
Explain how stationary waves are produced and why only waves of specific
frequencies can form on the aerial wire.

______________________________________________________________
_____

______________________________________________________________
_____
(4)

(d) Calculate the mass of a 1.0 m length of the aerial wire.

Density of copper = 8900 kg m–3

mass = ____________________________ kg
(1)

(e) Calculate the frequency of the wave when the third harmonic is formed on the
aerial wire.
frequency = ____________________________ Hz
(2)

(f) Sketch, on Figure 2, the standing wave on the wire when the third harmonic is
formed.

Figure 2

(1)

(g) High winds produce large amplitudes of vibration of the aerial wire.

Explain why the wire may sag when the high wind stops.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 13 marks)

Q16.
A gravimeter is an instrument used to measure the acceleration due to gravity. The
gravimeter measures the distance fallen by a free-falling mirror in a known time.

To do this, monochromatic light is reflected normally off the mirror, creating

interference between the incident and reflected waves. The mirror is released from
rest and falls, causing a change in the phase difference between the incident and
reflected waves at a detector.

At the point of release of the mirror, the waves are in phase, resulting in a maximum
intensity at the detector. The next maximum is produced at the detector when the
mirror has fallen through a distance equal to half a wavelength of the light. The
gravimeter records the number of maxima detected in a known time as the mirror
falls. These data are used by the gravimeter to compute the acceleration of the
free-falling mirror.

Figure 1 illustrates the phase relationship between the incident and reflected waves
at the detector for one position of the mirror.

Figure 1

(a) Show that the wavelength of the light is 600 nm.

(3)

(b) Determine the phase difference, in rad, between the incident and reflected
waves shown in Figure 1.

phase difference = ____________________________ rad

(2)

In one measurement 2.37 × 105 maxima are recorded as the mirror is released
from rest and falls for 0.120 s.

Using an appropriate equation of motion, calculate the acceleration due to

gravity that the gravimeter computes from these data.
State your answer to 3 significant figures.

wavelength of the light = 600 nm

acceleration due to gravity = ____________________________ m s–2

(3)

(d) Figure 2 is a graph that the gravimeter could produce to show how the
distance travelled by the mirror varies with time as it falls.

Figure 2

Determine the gradient of the line when the time is 0.12 s.

gradient = ____________________________
(2)

(e) State what this gradient represents.

______________________________________________________________
_____
(1)
(Total 11 marks)

Q17.
The diagram shows an arrangement used by a student to investigate vibrations in a
stretched nylon string of fixed length l. He measures how the frequency f of
first-harmonic vibrations for the string varies with the mass m suspended from it.

The table shows the results of the experiment.

m / kg f / Hz
0.50 110

0.80 140

1.20 170

(a) Show that the data in the table are consistent with the relationship

f ∝ √T

where T is the tension in the nylon string.

(2)

(b) The nylon string used has a density of 1150 kg m–3 and a uniform
diameter of 5.0 × 10–4 m.

Determine the length l of the string used.

l = ____________________ m
(3)

(c) The student uses the relationship in question (a) to predict frequencies for
tensions that are much larger than those used in the original experiment.

Explain how the actual frequencies produced would be different from those
that the student predicts.

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 7 marks)

Q18.
Figure 1 shows a ray of monochromatic green light incident normally on the curved
surface of a semicircular glass block.

Figure 1

(a) The angle of refraction of the ray at the plane surface is 90°.

Refractive index of the glass used = 1.6

Calculate the angle of incidence of the ray on the flat surface of the block.

angle of incidence = ____________________ degrees

(1)

(b) A thin film of liquid is placed on the flat surface of the glass block
as shown in Figure 2.

Figure 2

The angle of incidence is changed so that the angle of refraction of the green
light ray at the glass-liquid interface is again 90°. The angle of incidence is
now 58°.

Calculate the refractive index of the liquid.

refractive index = ____________________
(2)

(c) The source of green light is changed for one that contains only red and blue
light. For any material red light has a lower refractive index than green light,
and blue light has a higher refractive index than green light. The angle of
incidence at the glass-liquid interface remains at 58°.

Describe and explain the paths followed by the red and blue rays immediately
after the light is incident on the glass-liquid interface.

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 6 marks)

Q19.
This question is about an experiment to measure the wavelength of microwaves.

A microwave transmitter T and a receiver R are arranged on a line marked on the

bench.

A metal sheet M is placed on the marked line perpendicular to the bench surface.

Figure 1 shows side and plan views of the arrangement.

The circuit connected to T and the ammeter connected to R are only shown in the
plan view.

Figure 1

The distance y between T and R is recorded.

T is switched on and the output from T is adjusted so a reading is produced on the

ammeter as shown in Figure 2.

Figure 2

M is kept parallel to the marked line and moved slowly away as shown in Figure 3.

Figure 3

The reading decreases to a minimum reading which is not zero.

The perpendicular distance x between the marked line and M is recorded.

(a) The ammeter reading depends on the superposition of waves travelling directly
to R and other waves that reach R after reflection from M.

State the phase difference between the sets of waves superposing at R when
the ammeter reading is a minimum.
Give a suitable unit with your answer.

______________________________________________________________
_____
(1)

(b) Explain why the minimum reading is not zero when the distance x is
measured.

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(c) When M is moved further away the reading increases to a maximum then
decreases to a minimum.
At the first minimum position, a student labels the minimum n = 1 and records
the value of x.
The next minimum position is labelled n = 2 and the new value of x is
recorded.
Several positions of maxima and minima are produced.

Describe a procedure that the student could use to make sure that M is
parallel to the marked line before measuring each value of x.
You may wish to include a sketch with your answer.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(d) It can be shown that

where λ is the wavelength of the microwaves and y is the distance defined in

Figure 1.

The student plots the graph shown in Figure 4.

The student estimates the uncertainty in each value of to be 0.025 m and adds
error bars to the graph.

Determine
• the maximum gradient Gmax of a line that passes through all the error
bars
• the minimum gradient Gmin of a line that passes through all the error
bars.

Gmax = ____________________

Gmin = ____________________
(3)

(e) Determine λ using your results for Gmax and Gmin.

λ = ____________________ m
(2)

Figure 4

(f) Determine the percentage uncertainty in your result for λ.

percentage uncertainty in λ = ____________________ %

(3)

(g) Explain how the graph in Figure 4 can be used to obtain the value of y.
You are not required to determine y.

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(h) Suppose that the data for n = 13 had not been plotted on Figure 4.

Add a tick (✔) in each row of the table to identify the effect, if any, on the
results you would obtain for Gmax, Gmin, λ and y.

Result Reduced Not affected increased

Gmax

Gmin
λ

y
(4)
(Total 18 marks)

Q20.
A signal generator is connected to an oscilloscope, as shown in Figure 1.

Figure 1

The Y-voltage gain and time-base settings of the oscilloscope are shown in Figure
2.

Figure 2

When switch S is open (off) the oscilloscope displays the waveform shown in Figure
3.

When S is closed (on) the oscilloscope displays the waveform shown in Figure 4.

(a) Determine the peak-to-peak voltage V of the waveform shown in Figure 4.

V = ____________________ V
(1)

(b) Determine the frequency f of the waveform shown in Figure 4.

f = ____________________ Hz
(2)

Figure 3

Figure 4
(c) Figure 5 shows the signal generator connected in series with a resistor R and
a capacitor C.

Figure 5

The oscilloscope is connected across the capacitor.

The Y-voltage gain and time-base settings are still the same as shown in
Figure 2.

When S is closed (on) the oscilloscope displays the waveform shown in

Figure 6.

Figure 6

Determine the time constant of the circuit in Figure 5.

time constant = ____________________ s

(2)

(d) A student suggests that setting the time-base to 0.2 ms division–1 might reduce
uncertainty in the determination of the time constant.

State and explain any possible advantage or disadvantage in making this

suggested adjustment.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(3)

(e) The student connects an identical resistor in parallel with R and uses the
oscilloscope to display the waveform across C.

Draw on Figure 7 the waveform you expect the student to see.

The waveform of Figure 6 is shown as a dashed line to help you show how
the waveform changes.

Figure 7

Explain the change in the waveform.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(f) Figure 8a is a graph of voltage against time showing the output of the signal
generator. Figure 8b shows the voltage across C during the same time
interval.

The student interchanges the positions of R and C and connects the

oscilloscope across R.

Complete Figure 8c to draw the voltage across R during the time interval.

Figure 8a

Figure 8b

Figure 8c
(2)

(g) State and explain what changes, if any, the student needs to make to the
settings of the oscilloscope so the waveform across R is fully displayed.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 14 marks)
Q21.
(a) Figure 1 shows an ECG trace for a healthy person.

Complete Figure 1 by adding a suitable unit and scale to the potential axis,
and a suitable scale to the time axis.

Figure 1
(2)

(b) Figure 2 shows a faulty ECG trace which was obtained for another healthy
person.

Figure 2

Discuss three possible reasons why this faulty trace was obtained.

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 5 marks)

Q22.
(a) A student models a spacecraft journey that takes one year. The spacecraft
travels directly away from an observer at a speed of 1.2 × 107 m s–1. The
student predicts that a clock stationary relative to the observer will record a
time several days longer than an identical clock on the spacecraft.

Comment on the student’s prediction. Support your answer with a time dilation
calculation.

______________________________________________________________
_____

______________________________________________________________
_____
(4)

(b) In practice, the gravitational field of the Sun affects the motion of the
spacecraft and it does not travel directly away from the Earth throughout the
journey.

Explain why this means that the theory of special relativity cannot be applied to
the journey.

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 6 marks)

Q23.
Figure 1 shows the first-stage filter circuit for a simple AM receiver. The circuit can
be adjusted to resonate at 910 kHz so that it can receive a particular radio station.

Figure 1

(a) Calculate the value of the capacitance when the circuit resonates at a
frequency of 910 kHz.

capacitance = ____________________ pF
(2)

(b) Draw on Figure 2 an ideal response curve for the resonant circuit, labelling all
relevant frequency values based upon a 10 kHz bandwidth.

Figure 2
(3)

Discuss the changes the listener might notice when tuning to this station due
to the practical Q-factor being smaller.
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 7 marks)

Q24.
A photodiode forms part of a light meter used for checking light levels in an office.
Figure 1 shows the circuit diagram for the light meter.

Figure 1

(a) State the mode in which the photodiode is being used in Figure 1.

______________________________________________________________
_____
(1)

(b) In which mode is the operational amplifier being used in Figure 1?

Tick (✔) the correct box.

Non-inverting amplifier

Comparator

Summing amplifier

Difference amplifier
(1)

(c) Figure 2 shows an extract from a data sheet of the characteristics for a
photodiode under different light levels measured in lux.

Figure 2

For a particular lighting condition, the current through the photodiode in Figure
1 was 0.10 mA.

Estimate, using the information in Figure 2, the light level needed to cause this
reverse current through the photodiode.

light level = ____________________ lux

(1)

(d) Calculate the voltage at point X in the circuit shown in Figure 1 for the light
level in question (c).

voltage = ____________________ V
(1)

(e) The 10kΩ linear potential divider shown in Figure 1 is set to give 1.75 V at
point Y.

Assume that the operational amplifier has ideal characteristics.

Deduce whether the output LED would be switched ON or OFF when the
current through the photodiode is 0.10 mA.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 6 marks)

Q25.
Cosmic rays are high-energy particles coming from Space. They collide with the air
molecules in the Earth’s atmosphere to produce pions and kaons.

(a) Pions and kaons are mesons. Identify the quark–antiquark composition for a
meson.

Tick (✔) the correct answer in the right-hand column.

✔ if correct

qqq

qq̄q̄

qq̄

qq
(1)

(b) A positron with a kinetic energy of 2.0 keV collides with an electron at rest,
creating two photons that have equal energy.

Show that the energy of each photon is 8.2 × 10−14 J.

(3)

(c) Calculate the wavelength of a photon of energy 8.2 × 10−14 J.

wavelength = _______________________ m
(2)

(d) Show that the speed of the positron before the collision was about 2.7 × 107 m
s−1.

(3)

(e) Calculate the de Broglie wavelength of the positron travelling at a speed of

2.7 × 107 m s−1.

wavelength = _______________________ m
(2)

(f) The separation between the carbon atoms in graphite is about 0.15 nm.

Discuss whether electrons travelling at 2.7 × 107 m s−1 can be can be used to
demonstrate diffraction as they pass through a sample of graphite.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(4)
(Total 15 marks)

Q26.
The diagram below shows one position of a guitar string stretched between points X
and Y.
The string vibrates at a frequency of 330 Hz.

(a) State the phase relationship between points A and B on the string.

______________________________________________________________
_____
(1)

(b) Points X and Y are 0.66 m apart.

Calculate the speed of the wave along the string.

speed = _________________ m s−1

(2)
(c) The total mass of the string is 3.1 g and the total length of the string is 0.91 m.

Show that the tension in the string when it is sounding the harmonic shown in
the diagram above is about 70 N.

(3)

(d) The string is fixed at one end and wrapped around a tuning peg of radius 3.0
mm at the other. The tuning peg needs to be turned through 3 complete
rotations to increase the tension in the string from 0 to 70 N in part (c).

Discuss, by estimating the energy stored in the string, whether there is a

significant risk to the guitar player when the string breaks.

______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 9 marks)

Q27.
(a) Distinguish between longitudinal and transverse waves.
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(b) A piano repairer replaces the wire that produces the highest note on a piano.
The wire has a vibrating length of 0.050 m. He uses a wire with the following
properties:

diameter = 3.5 × 10−4 m

density = 7.8 × 103 kg m−3
breaking stress = 3.0 × 109 N m−2

Calculate the tension required for the vibrating wire to produce its correct
frequency of 4.1 kHz.

tension = _______________ N
(2)

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(d) The repairer uses faulty wire so that the diameter of the wire increases linearly
with distance along its length. The profile of the vibration produced when the
wire sounds its second harmonic is shown in the diagram below.

The speed c of a transverse progressive wave travelling along a string of

mass per unit length µ and under tension T is given by

Explain which end of the wire, A or B, has the greater diameter and why the
profile of the stationary wave has the shape shown in the diagram above.

______________________________________________________________
_____

______________________________________________________________
_____
(4)
(Total 10 marks)

Q28.
An α particle with an initial kinetic energy of 4.9 MeV is directed towards the centre
of a gold nucleus of radius R which contains 79 protons. The α particle is brought to
rest at point S, a distance r from the centre of the nucleus as shown in the diagram
below.

(a) Calculate the electric potential energy, in J, of the α particle at point S.

electric potential energy = ___________________ J

(2)

(b) Calculate r, the distance of closest approach of the α particle to the nucleus.

r = ___________________ m
(3)

(c) Determine the number of nucleons in the gold nucleus.

R, radius of the gold nucleus = 7.16 × 10−15 m

R0 = 1.23 × 10−15 m
number of nucleons = ________________
(3)

(d) The target nucleus is changed to one that has fewer protons. The α particle is
given the same initial kinetic energy.

Explain, without further calculation, any changes that occur to the distance r.
Ignore any recoil effects.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 10 marks)

Q29.
Figure 1 and Figure 2 show a version of Quincke’s tube, which is used to
demonstrate interference of sound waves.

Figure 1 Figure 2

A loudspeaker at X produces sound waves of one frequency. The sound waves

enter the tube and the sound energy is divided equally before travelling along the
fixed and movable tubes. The two waves superpose and are detected by a
microphone at Y.

(a) The movable tube is adjusted so that d1 = d2 and the waves travel the same
distance from X to Y, as shown in Figure 1. As the movable tube is slowly
pulled out as shown in Figure 2, the sound detected at Y gets quieter and
then louder.
Explain the variation in the loudness of the sound at Y as the movable tube is
slowly pulled out.

______________________________________________________________
_____

______________________________________________________________
_____
(4)

(b) The tube starts in the position shown in Figure 1.

Calculate the minimum distance moved by the movable tube for the sound
detected at Y to be at its quietest.

frequency of sound from loud speaker = 800 Hz

speed of sound in air = 340 m s–1

minimum distance moved = ____________________ m

(3)

(c) Quincke’s tube can be used to determine the speed of sound.

State and explain the measurements you would make to obtain a value for the
speed of sound using Quincke’s tube and a sound source of known frequency.

______________________________________________________________
_____

______________________________________________________________
_____
(4)
(Total 11 marks)

Q30.
Figure 1 shows a circuit including a thermistor T in series with a variable resistor R.
The battery has negligible internal resistance.

Figure 1

The resistance–temperature (R−θ) characteristic for T is shown in Figure 2.

Figure 2
(a) The resistor and thermistor in Figure 1 make up a potential divider.

Explain what is meant by a potential divider.

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(b) State and explain what happens to the voltmeter reading when the resistance
of R is increased while the temperature is kept constant.

______________________________________________________________
_____

______________________________________________________________
_____
(3)

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(d) The battery has an emf of 12.0 V. At a temperature of 0 °C the resistance of

the thermistor is 2.5 103 Ω.

The voltmeter is replaced by an alarm that sounds when the voltage across it
exceeds 3.0 V.

Calculate the resistance of R that would cause the alarm to sound when the
temperature of the thermistor is lowered to 0 °C.

resistance = ____________________ Ω
(2)

(e) State one change that you would make to the circuit so that instead of the
alarm coming on when the temperature falls, it comes on when the
temperature rises above a certain value.

______________________________________________________________
_____

______________________________________________________________
_____
(1)
(Total 9 marks)

Q31.
A student has a diffraction grating that is marked 3.5 × 103 lines per m.

(a) Calculate the percentage uncertainty in the number of lines per metre
suggested by this marking.

percentage uncertainty = ____________________ %

(1)

(b) Determine the grating spacing.

grating spacing = ____________________ mm

(2)

(c) State the absolute uncertainty in the value of the spacing.

absolute uncertainty = ____________________ mm

(1)

(d) The student sets up the apparatus shown in Figure 1 in an experiment to

confirm the value marked on the diffraction grating.

Figure 1

The laser has a wavelength of 628 nm. Figure 2 shows part of the interference
pattern that appears on the screen. A ruler gives the scale.

Figure 2

Use Figure 2 to determine the spacing between two adjacent maxima in the
interference pattern. Show all your working clearly.

spacing = ____________________ mm
(1)

(e) Calculate the number of lines per metre on the grating.

number of lines = ____________________

(2)

(f) State and explain whether the value for the number of lines per m obtained in
part (e) is in agreement with the value stated on the grating.
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(g) State one safety precaution that you would take if you were to carry out the
experiment that was performed by the student.

______________________________________________________________
_____

______________________________________________________________
_____
(1)
(Total 10 marks)

Q32.
The term ultrasound refers to vibrations in a material that occur at frequencies too
high to be detected by a human ear. When ultrasound waves move through a solid,
both longitudinal and transverse vibrations may be involved. For the longitudinal
vibrations in a solid, the speed c of the ultrasound wave is given by

where E is the Young modulus of the material and ρ is the density. Values for c and
ρ are given in the table below.

Substance c / m s−1 ρ / kg m−3

glass 5100 2500

sea water 1400 1000

Ultrasound waves, like electromagnetic radiation, can travel through the surface
between two materials. When all the energy is transmitted from one material to the
other, the materials are said to be acoustically matched. This happens when ρc is
the same for both materials.

(a) Calculate the magnitude of the Young modulus for glass.

Young modulus = ____________________

(1)

(b) State your answer to (a) in terms of SI fundamental units.

(1)

(c) The passage states that ’when ultrasound waves move through a solid both
longitudinal and transverse vibrations may be involved’.

State the difference between longitudinal and transverse waves.

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(d) Show that when two materials are acoustically matched, the ratio of their
Young moduli is equal to the ratio of their speeds of the ultrasound waves.
(2)

(e) The wave speed in a material X is twice that in material Y. X and Y are
acoustically matched.

Determine the ratio of the densities of X and Y.

X = ____________________ Y = ____________________
(1)

(f) Ultrasound waves obey the same laws of reflection and refraction as
electromagnetic waves.

Using data from Table 1, discuss the conditions for which total internal
reflection can occur when ultrasound waves travel between glass and sea
water.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____
(3)
(Total 10 marks)

Q33.
(a) Describe the structure of a step-index optical fibre outlining the purpose of the
core and the cladding.

______________________________________________________________
_____

______________________________________________________________
_____
______________________________________________________________
_____

______________________________________________________________
_____
(3)

(b) A signal is to be transmitted along an optical fibre of length 1200 m. The signal
consists of a square pulse of white light and this is transmitted along the centre
of a fibre. The maximum and minimum wavelengths of the light are shown in
the table below.

Colour Refractive index of fibre Wavelength / nm

Blue 1.467 425

Red 1.459 660

Explain how the difference in refractive index results in a change in the pulse
of white light by the time it leaves the fibre.

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(c) Discuss two changes that could be made to reduce the effect described in part
(b).

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 7 marks)

Q34.
Read through the following passage and answer the questions that follow it.

Measuring the speed of sound in air

After the wave nature of sound had been identified, many attempts were made to
measure its speed in air. The earliest known attempt was made by the French
scientist Gassendi in the 17th century. The procedure involved timing the interval
between seeing the flash of a gun and hearing the bang from some distance away.
5 Gassendi assumed that, compared with the speed of sound, the speed of light is
infinite. The value he obtained for the speed of sound was 480 m s–1. He also
realised that the speed of sound does not depend on frequency.
A much better value of 350 m s–1 was obtained by the Italian physicists Borelli and
Viviani using the same procedure. In 1740 another Italian, Bianconi, showed that
10 sound travels faster when the temperature of the air is greater.
In 1738 a value of 332 m s–1 was obtained by scientists in Paris. This is remarkably
close to the currently accepted value considering the measuring equipment
available to the scientists at that time. Since 1986 the accepted value has been
331.29 m s–1 at 0 °C.

(a) Suggest an experiment that will demonstrate the wave nature of sound (line 1).

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(b) Using Gassendi’s value for the speed of sound (line 6), calculate the time
between seeing the flash of a gun and hearing its bang over a distance of 2.5
km.

time = ____________________ s
(1)

(c) Explain why it was necessary to assume that ‘compared with the speed of
sound, the speed of light is infinite’ (line 5).

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(d) Explain one observation that could have led Gassendi to conclude that ‘the
speed of sound does not depend on frequency’ (line 7).
______________________________________________________________
_____

______________________________________________________________
_____

______________________________________________________________
_____
(2)

(e) Explain how the value obtained by Borelli and Viviani was ‘much better’ than
that obtained by Gassendi (line 8).

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(f) The speed of sound c in dry air is given by

where θ is the temperature in °C, and k is a constant.

Calculate a value for k using data from the passage.

k = ____________________ m s–1 K–½

(2)
(g) State the steps taken by the scientific community for the value of a quantity to
be ‘accepted’ (line 13).

______________________________________________________________
_____

______________________________________________________________
_____
(2)
(Total 10 marks)

Q35.
One of the two postulates of Einstein’s theory of special relativity is that the speed of
light in free space is invariant.

(a) Explain what is meant by this postulate.

______________________________________________________________
_____

______________________________________________________________
_____
(1)

(b) State the other postulate.

______________________________________________________________
_____

______________________________________________________________
_____
(1)
(c) Two detectors are measured to be 34 m apart by an observer in a stationary
frame of reference. A beam of π mesons travel in a straight line at a speed of
0.95 c past the two detectors, as shown in the figure below.

Calculate the time taken, in the frame of reference of the observer, for a π
meson to travel between the two detectors.

time = ____________________
(1)

(d) π mesons are unstable and decay with a half-life of 18 ns.

It is found in experiments that approximately 75% of the π mesons that pass
the first detector decay before reaching the second detector.

Show how this provides evidence to support the theory of special relativity. In
your answer compare the percentage expected by the laboratory observer with
and without application of the theory of special relativity.
(5)
(Total 8 marks)

Mark schemes

Q1.
(a) TWO FROM:
central white fringe ✔
(fringes either side) showing range of colours/spectrum ✔
with red furthest and blue/violet closest to centre ✔
Allow rainbow for spectrum
Reject different colour fringes
If colours mentioned for last mark must be in right order
i.e. red last
1
1
(MAX 2)

(b) FOUR FROM:

central fringe is a mixture of red and green light/two wavelengths ✔
EITHER (1 marks)
(separate) red and green fringes are seen (on either side) ✔
OR (for 2 marks)
spacing of green fringes is less than spacing of red fringe / green fringes
closer to middle than red ✔ ✔
OR (for 3 marks)
spacing of red fringes is 20% (or 1.2 times)greater than green fringes ✔ ✔ ✔
6th green fringe overlaps with 5th red fringe ✔
Allow orange/yellow for central fringe
If w used must be identified as fringe spacing for third
alternative
1
1
1
1
(MAX 4)

(c) The mark scheme gives some guidance as to what statements are
expected to be seen in a 1 or 2 mark (L1), 3 or 4 mark (L2) and 5 or 6
mark (L3) answer. Guidance provided in section 3.10 of the ‘Mark
Scheme Instructions’ document should be used to assist in marking this
question.

Mark
Criteria
QoWC
>
Explains how (%) uncertainties combine to determine uncertainty in wavelength OR identify %
uncertainty s as being the largest
The student presents relevant information coherently, employing structure, style and sp&g to
render meaning clear.
The text is legible.
>
Explain how wavelength is determined using
>
Explains how second change affects fringe spacing
AND
Comments on how change in fringe spacing affects (%)uncertainty / change in s OR D affects
(%)uncertainty
The student presents relevant information and in a way which assists communication of
meaning. The text is legible. Sp&g are sufficiently accurate not to obscure meaning.
>
Explains how second change affects fringe spacing
OR
Comments on how change in fringe spacing affects (%)uncertainty / change in s OR D affects
(%)uncertainty
>
States how one of the changes affects fringe separation (decrease s increases fringe separation
/ decrease D decrease fringe separation
The student presents some relevant information in a simple form. The text is usually legible.
Sp&g allow meaning to be derived although errors are sometimes obstructive.
>
States that one of the changes alters fringe separation
>
No correct change identified
The student’s presentation, spelling and grammar seriously obstruct understanding.
The following statements may be present for
decreasing slit separation s:

Fringe separation increases

Uncertainty in measuring fringe separation will
decrease
and as this is needed to measure wavelength,
uncertainty in wavelength
measurement will decrease

The following statements may be present for smaller D:

Uncertainty in measuring D would increase

Fringe separation would also decrease
so uncertainty in measuring fringe separation would
increase
Both are required to find wavelength so uncertainty in
finding wavelength would increase

FOR Middle Band one of these considered:

Decrease s
Larger fringe separation so smaller (%) uncertainty (in
w)
Smaller s so higher (%) uncertainty in s
Decrease D
Smaller fringe separation so larger (%) uncertainty (in
w)
Smaller D so higher (%) uncertainty in D

If explain reverse change correctly (s increase D

increase) no penalty
6
[12]

Q2.
(a) Use of to make cA the subject of the equation
Condone truncation without appropriate rounding
mid-calculation
OR

speed in glass A = 2.05(2) × 108 ms–1 1✔

Speed in glass B = 1.985(3) × 108

Condone use of c = 3 × 108
But must see answer to 4 sf answer

their speed in glass A × 0.96748 (or equivalent) 2✔

Values obtained using c = 3×108:
• speed in glass A = 2.05(3)× 108 ms–1
• speed in glass B = 1.98(7) × 108
• n = 1.510

Alternative 1st and 2nd marks

Use of nA/nB = cB/cA by substitution for nA 1✔

Use of nA/nB = cB/cA by substitution for nA and cB = cA × 0.96748 2✔

nB = 1.461 / 0.96748 1✔2✔

Watch for maths errors:
Dividing by 1.03252 ≠ multiplying by 0.96748
Multiplying by 1.03252 ≠ dividing by 0.96748

1.510 cao to 4 sf only 3✔

Correct answer to 4 sf obtains all 3 marks
Penalise any unit on final answer
3

(b) Relationship:

Increase in tension (or stress) in cable produces increase in strain resulting in

increase in λR

OR
Decrease in tension (or stress) causes decrease in strain resulting in decrease
in λR 1✔

Variation due to motion:

As the lift accelerates downwards, (the tension is less than the weight in the
cable, a decrease in tension results) in λR decreasing 2✔

At constant velocity (the tension again equals the weight and) λR returns to the
initial, at rest value 3✔
Allow a correct comment on the directional relationship
between tension, strain and λR independent of the
motion of the lift for first mark
3

P because it has a larger gradient (must be a sense of larger increase in λR for

the (same) increase in strain) ✔

Hence smaller accelerations (which produce small changes in strain) can

produce measurable changes in λR

Hence gauge P will have a higher resolution ✔

Selecting Q gains zero marks
Linking steeper gradient to being able to withstand a
larger force negates this mark
Allow more accurate measurement of acceleration
Allow more readings of acceleration can be taken (over
the range)
More sensitive treat as neutral
2
[8]

Q3.
D
[1]

Q4.
A
[1]

Q5.
D
[1]

Q6.
C
[1]

Q7.
A
[1]

Q8.
(a) Clear indication of correct process

two correct values for λv from working plus conclusion

(7.35; 7.25; 7.35) ✔

three correct values plus conclusion ✔

Condone no or misuse of powers of 10
Allow use of value of h as the constant to show that v
values in table are consistent with the λ values
1

....................................................................................

ratio approach v1/v2= λ2/λ1 shown for 2 sets of data ✔

shown for two other sets of data + conclusion ✔

May predict one of the values assuming inverse
proportionality and compare with table value
(once for 1 mark; twice for 2 marks)
1

(b) h =λmv or substitution of correct data in any form ✔

May determine average value using mean constant
from 2.1 or average 3 calculations in this part
1

6.7(0) × 10–34 from first and third data set; 6.6(0) × 10–34 from second ✔
1

(c) Particle behaviour would only produce a patch/circle of light /small spot of light
or Particles would scatter randomly ✔

Wave property shown by diffraction/ interference ✔

Graphite causes (electron)waves/beam to spread out /electrons to travel in

particular directions ✔

Bright rings/maximum intensity occurs where waves

interfere constructively/ are in phase ✔

for a diffraction grating maxima when sinθ = nλ/d ✔

Marks are essentially for
1. Explaining appearance of screen if particle
2. Identifying explicitly a wave property
3. Explaining what happens when diffraction occurs
4. Explaining cause of bright rings
5. Similar to diffraction grating formula (although not
same)
NB Not expected: For graphite target maxima occur
when sinθ =λ/2d (d =spacing of atomic layers in
crystal)
1
1
1

(d) Electrons must provide enough (kinetic) energy

‘instantly’ to cause the excitation

OR
the atom or energy transfer in 1 to 1 interaction

electron can provide the energy in discrete amounts

energy cannot be provided over time as it would be in a wave

Description of Photoelectric effect = 0
Not allowed: any idea that wave cannot pass on
energy, e.g. waves pass through the screen
1

Any 2 from

Idea of light emission due to excitation and de-excitation of electrons/atoms ✔

Idea of collisions by incident electrons moving electrons in atoms between

energy levels/shells/orbits ✔

Light/photon emitted when atoms de-excite or electrons move to lower energy

levels ✔
1
1
[10]

Q9.
(a) Waves travel to the boundaries and are reflected ✔
Not bounce off ...
1

two waves travelling in opposite directions interfere/superpose ✔

Not superimpose or interferes with itself
1

Fixed boundaries (cannot move so) are nodes ✔

creates nodes and antinodes bland = 0

In some positions the waves always cancel /interfere destructively to give zero
amplitude/no vibration/nodes)
OR
interfere constructively to produce positions of maximum amplitude/maximum
vibration/antinodes ✔
1
Max 3

(b) Use of ✔
Either rearranges for μ without substitution or
substitutes correctly in the formula
1

4.2 (4.19) × 10–4 (kg) ✔

(c) 240 (244) (m s–1)

(d) 1 rotation of the peg = 22 mm ✔

Or Reads increase in tension produced by the extra
extension (about 10 N) from graph and adds to 25
1

extra extension = 22 × 75/360 = 4.6 mm

(ecf for incorrect circumference) ✔

πd × 75/360 not evaluated =1
1

Total extension = 11 + 4.6 (15.6 mm) so tension 35 - 36N ✔

Inspect their length and their tension in the substitution
1

Calculates frequency for their tension

T must be greater than the original 25N
Condone adding or subtracting extra extension to 0.33
m
If 4.0 × 10–4 kg used then answer will be in range 448
Hz to 455 Hz
If 4.19 × 10–4 used 438 to 444 Hz
1
[10]

Q10.
C
[1]
Q11.
D
[1]

Q12.
(a) Quasars are produced by (supermassive) black holes. ✔

These black holes are at the centre of (active) galaxies (active galactic nuclei.)
✔
2

(b) Using v = cz gives

v = 3 × 108 × 0.0415 ✔ = 1.25 × 107 = 1.25 × 104 kms–1

Using 1pc = 3.26 lyr

d = 5.81 × 108 lyr = 5.81 × 108/3.26 ✔ = 1.78 × 108 pc

= 1.78 × 102 Mpc (= 5.5 × 1024 m)

Using v = Hd

(H = v/d = 1.25 × 104/1.78 × 102 = 70 kms–1 Mpc–1)

Age of Universe = 1/H = d/v ✔

= 5.81 × 108 × 9.47 × 1015/1.25 × 107 = 4.42 × 1017 s ✔

The first mark is for use of zc.
The second mark is for a calculation of d.
The third mark is for using the idea that the age of the
Universe is 1/H.
The fourth mark is for the answer.
Allow own H for 3rd and 4th marks.
4

Use of Inverse square law eg

Power of quasar/(distance to quasar)2 = power of galaxy / (distance to galaxy)2

✔
Or 1000/d2 = 1/1

So distance to quasar = (1000)½ = about 30 times greater than distance to

galaxy ✔
The first mark is for relating the similar “brightness”.
Accept intensity. Accept in form of equation linking
quasar and galaxy.
The second mark is for applying the inverse square
law. Simply quoting it does not get this mark.
The final mark is for coming to a valid conclusion
related to the distance to the quasar compared to the
distance to the galaxy.
Do not accept answers involving square roots.
These are standalone marks.
1
2
[9]

Q13.
(a) The mark scheme gives some guidance as to what statements are
expected to be seen in a 1 or 2 mark (L1), 3 or 4 mark (L2) and 5 or 6
mark (L3) answer.

Level Criteria QoWC

6 marks A thorough and well The student presents
communicated relevant information
discussion using most of coherently, employing
the statements in bullets 1 structure, style and SP&G
2 and 3 to render meaning clear.
The text is legible.
5 marks A explanation that includes
discussion using most of
the statements in bullets 1 ,
2 and 3 but may contain
minor errors or omissions
4 The response includes The student presents
a well presented discussion relevant information and in
of two from bullets 1 and a way which assists the
two from bullet 3 and one communication of meaning.
from bullet 2 The text is legible. SP&G
are sufficiently accurate not
to obscure meaning.
3 The response includes
a discussion of one
comment from each bullet
2 The response The student presents some
makes comments about relevant information in a
two bullet points simple form. The text is
(This is likely to be from usually legible. SP&G allow
bullets 2 and 3) meaning to be derived
although errors are
sometimes obstructive.
1 Makes relevant comment
from the list
0 No relevant coverage of the The student’s presentation,
likely statements. SP&G seriously obstruct
understanding.
The following statements are likely to be present:
Bullet point 1 in question
(Explanation of how shift expected)
1. PM2 lies in the direction of the Earth's velocity
2. Speed of light different in the two directions
3. The time taken for light to travel from P to M2 and
back to P would be greater than the time taken from P
to M1 and back to P
4. If the speed of light depends on the Earth's velocity
through the ether
5. Rotating the apparatus through 90° would cause the
time difference to reverse/change
6. When rotated there would be a change in the phase
difference between the waves (at each point in the
fringe pattern)
Bullet point 2 in the question
(Results compared with prediction)
7. The apparatus was capable of detecting shifts of
0.05 fringe
8. No shift was detected then or in later experiments
when apparatus rotated
Bullet point 3 in the question (Conclusions)
9. The experiment showed that there is no absolute
motion
10. Ether did not exist so light travels without the need
for a material medium
11. The Earth was dragging the ether with it
Many responses fail to demonstrate an understanding
that the shift pattern is there in the first place and the
shift occurs due to rotation of the apparatus
They often imply that the shift is due to differences in
the distance travelled
6

(b) Correct postulate

Invariance of the speed of light in free space/vacuum

Speed of light the same in free space

Laws of physics unchanged from one inertial frame to another

The same laws of physics are obeyed/apply/hold in
(all) inertial frames of reference/non accelerating
frames of reference/frames moving at a constant
velocity
Not Allowed
All laws of physics
Laws of physics are the same
Laws of physics are constant...
Mention of Newton’s laws being obeyed
Allow 1 here if both (b) and (c) are correct but reversed
1

(d) Time of flight is found to be 4.41 × 10–6 s ✔

OR t0 = 4.41 × 10–6 ✔

(Proper time t0 is) 6.22 × 10–7 s ✔

Percentage remaining is (found from the graph) 82 +/– 1

In muon reference frame

L = 1310 ✔

185 m✔

s✔ allow ecf for incorrect length calculation

82 +/– 1%✔
May do
Number of half lives = 6.22 × 10–7/2.2 × 10–6
fraction remaining = 0.50.283 = 0.82
185 m seen scores 2
Must see this stage with speed = 0.99 × 3 × 108
Final answer in range can be awarded even if 0.99
omitted in MP3
Allow minor differences in time (3rd sf) due to rounding
in processing
4
[12]

Q14.
(a) path difference for two waves ✔
Allow ‘waves travel different distances’
Condone out of phase

gives rise to a phase difference ✔

if phase and path confused only give 1 for first 2 marks

Destructive interference occurs ✔

allow explanation of interference
3
(b) (Path difference =) 0.056 m ✔

Path difference = 2λ or wavelength = 0.028 m ✔e

Use of f=c/λ so f = 11(10.7) × 109 Hz ✔

Allow 2 max for 5.4 × 109 Hz or 2.7 × 109 Hz
Allow ecf
3

(c) Intensity decreases with distance ✔

One wave travels further than the other ✔

Amplitudes/intensities of the waves at the minimum

points are not equal ✔
Or “do not cancel out”
max 2

(d) The signal decreases/becomes zero ✔

The waves transmitted are polarised ✔

zero when detector at 90° to the transmitting

aerial/direction of polarisation of wave ✔
max 3
[11]

Q15.
(a) Substitution of data in

3.1 × 10–3 (m) ✔

2 marks can be awarded if 4mm used to show T>500 N
provided an explanation is provided, otherwise award
zero.
2

(b) (500 = Tcos 65)

T = 1200 N ✔
1

(c) Wind produces a wave / disturbance that travels along

the wire ✔
Wave is reflected at each end / waves travel in
opposite directions✔

(Incident and reflected) waves interfere / superpose ✔

Only certain frequencies since fixed ends have to be

nodes. ✔
4

(d) Mass per m of the wire = 0.14(2) kg ✔

(e) Use of to find fundamental

Third harmonic = 7.4 (Hz) ✔

The second mark is for multiplying the fundamental
frequency by 3 – allow ecf
2

(f) Diagram showing three approximately equally spaced loops

Condone single line
1

(g) Copper may be stretched beyond elastic limit / may

deform plastically ✔

Permenant deformation / Does not return to original

length ✔
Allow 'will remain longer than original' or 'will be
permenantly deformed'
2
[13]

Q16.
(a) Period = 0.2 × 10–14 (s) read off

Recognisable T substituted into T = 1 / f ✔

An acceptable subject (period, time for one cycle, one
cycle, T, etc.)
Allow non-standard symbol with unit seen on time.
Allow this subtraction of two times seen in f = 1/T
Use of T = 1 / f and c = f λ ✔

Use of λ = cT
Use of here is:
Subject must be seen with substitutions or rearranged
equations with f = 1/T and λ = c/f
Condone power 10 error here
Condone lack of subject in vertical working where
rearranged equation with appropriate subject seen at
heading of column

6(.0) × 10–7 (m) ✔

Number must be expressed as 6 × 10–7 or 600 × 10–9
or equivalent not enough to see only nano prefix.
3

(b) (Determines a fraction of cycle)

✔
Condone their fraction × 2π or their decimal × 2π
For 1st mark

2π/5 OR 0.4 π

1.26 or 1.3 ✔
Allow 8π/5 OR 1.6 π
OR
5.03 or 5.0
2

(c) (Distance =) 3 × 10–7 × 2.37 × 105 seen

(Distance =) 0.07(11) (m) seen ✔

Subs into s = at2 ✔

Condone error in sub for s where formula has been
otherwise correctly manipulated with a (or g) as
subject

9.88 (3 sf only) ✔
Alternative:
1st mark average speed =
2nd mark
3rd mark 9.88
3

(d) Draws a tangent to the curve at approximately

t = 120 ms and attempts a gradient calculation ✔

Tangent must be a straight line that touches curve and
divergent from curve before 90 ms and after 150 ms

(Gradient =) 1.2 (range 1.1 to 1.3) ✔

Allow 1.2 × 10–3 (range 1.1 × 10–3 to 1.3 × 10–3 ) ✔
Ignore units on answer line
2nd mark is dependent on 1st mark
Max 1 mark for correct answer in range where tangent
satisfies above conditions but doesn’t quite touch curve
(half-square tolerance)
First alternative:
1st mark
Use of v = u +at with sub for a = 9.88 or 9.875 and
t=0.12
2nd mark
1.2 or 1.19 or 1.185 only
Second alternative:
1st mark
Use of s = 1/2at2 and ds/dt = at with sub for a = 9.88 or
9.875 and t = 0.12
2nd mark
1.2 or 1.19 or 1.185 only
4
(e) (instantaneous) Velocity (of the mirror) or
(instantaneous) speed (of the mirror) ✔
Ignore any units quoted
Do not allow:
Average speed / constant speed
4
[8]

Q17.
(a) EITHER

calculate value for constant using two calculations ✔

calculate value for constant using three calculations

and make a comment that they have same value ✔
need to see table to look for any working

calculate ratio between masses and √T for one pair of

values ✔

calculate ratio between masses and √T for two pairs of

values and make comment about same value ✔
e.g. 0.5/0.8 = √110/√140

work out constant and use to predict one other

frequency or mass ✔

work out constant and use to predict two other

frequencies or mass ✔
no comment needed with this alternative
2

(b) μ = ρA = 1150 × π(5.0 × 10–4/2)2

μ = 2.258 × 10–4 (kg m–1) ✔

use of consistent m and f Substituted in including g but

condone powers of 10 error ✔
Award second mark if T and f substituted correctly
(ignore μ)

0.67 m ✔
If used diameter for radius incorrectly then lose first
mark but can get third mark (answer 0.335 m)
3

(c) appreciation of reducing diameter when string is

stretched. ✔

lower mass per unit length so (constant of

proportionality and hence) frequency is higher (than
would be predicted) ✔
2
[7]

Q18.
(a) i = sin–1 (1/1.6) = 39° ✔
1

(b) sin 58 = n/1.6 ✔

n = 1.4 (1.36) ✔
1
1

(c) blue light undergoes TIR ✔

red light refracted ✔
reason i.e. critical angle for red light is more OR critical
angle for blue light is less ✔
Allow correct description of refraction. Ignore
statements about towards/away from normal
OR
if refractive indices change by same factor ✔
critical angle stays constant ✔
so path followed by red and blue light is the same ✔
OR
don’t know if refractive indices change by same factor
✔
so can’t predict the effect on critical angle ✔
so can’t predict paths of red and blue light ✔
For second two alternatives third mark (i.e. about paths
of red and blue) dependent on first mark (i.e. factor of
refractive index change)
1
1
1
[6]

Q19.
(a) 180 degrees
accept ° for degrees

π radians ✔
condone c or ‘rad’ for radian
reject ‘half a cycle’
treat ‘π radians in phase’ as talk out
1

(b) (idea that) sets of combining waves do not have the

same amplitude ✔
condone ‘waves do not have same intensity’ or ‘same
energy’ or ‘some energy is absorbed on reflection’ or
‘same power’ or ‘same strength’ or idea that non point
source or non point receiver would lead to imperfect
cancellation
condone the idea that the waves may not be
monochromatic
ignore ‘some waves travel further’ or ‘waves do not
perfectly cancel out’
reject ‘waves may not be 180° out of phase’
1

(c) valid use of a set square or protractor against TR (to

ensure perpendicular) 1 ✔

measure x at two different points [at each end of M]

and adjust until [make sure] both distances are the
same 2 ✔

OR
use of set square to align M with the perpendicular line
earns 2 ✔

if method used does not allow continuous variation in x

then award maximum 1 mark

align graph paper with TR 1 ✔

align M with grid lines on graph paper 2 ✔

both marks can be earned for suitable sketch showing
a viable procedure involving one or more recognisable
set squares or protractors; the sketch may also show a
recognisable ruler, eg

allow use of scale on set square to measure the

perpendicular distances don’t penalise incorrect
reference to the set square, eg as ‘triangular ruler’, as
long as the sketch shows a recognisable set square
2

(d) Gmax line ruled through bottom of n = 3 error bar and

through top of n = 11 error bar 1✔

Gmin line ruled through top of n = 5 error bar and

through bottom of n = 13 error bar 2 ✔

Gmax and Gmin calculated from valid y step divided by

valid x step; both n steps ≥ 6 3 ✔
allow 1 mm tolerance when judging intersection of
gradient lines with error bars
ignore any unit given with Gmax or Gmin; penalise power
of ten error in 01.5

12✔= 1 MAX if (either) line is thicker than half a grid

square or of variable width or not continuous;
expect Gmax = 3.2(1) × 10–2 and Gmin = 2.5 (2.49) × 10–2
3

(e)

AND
result in range 2.8(0) to 2.9(0) × 10–2 (m) 1 ✔ 2 ✔

award one mark for

2.7(0) to 3.0(0) × 10–2 (m) 12 ✔

penalise 1 mark for a power of ten error
reject 1 sf 3 × 10–2 (m)
if a best fit line is drawn between the Gmax and Gmin lines
and the gradient of this is calculated award 1 mark for
λ in range 2.8(0) to 3.0(0) × 10–2(m)
2

(f) uncertainty in λ = Gmax – λ

λ – Gmin

1 ✔

percentage uncertainty = (uncertainty/λ)×100 2 ✔

result in range 11(.0) % to 14(.0) % 3 ✔

1 ✔ can be earned by showing a valid uncertainty then
dividing by λ
ecf their λ, Gmax and Gmin for 1 ✔ and 2 ✔
allow λ found from best fit line
12 ✔
allow × 100 where ∆λ is any plausible uncertainty for 2
✔
numerical answer without valid working can only earn 3
✔
3

(g) (states) calculate the (vertical) intercept 1 ✔

OR
outlines a valid calculation method to calculate y 1 ✔

determine the intercept for both lines and calculate

average value 2 ✔

determine the (vertical) intercept of the line of best fit

(between Gmax and Gmin) 2 ✔
draw the line of best fit (between Gmax and Gmin);
perform calculation to find intercept earns 12 ✔
2

(h)
result reduced not affected increased
Gmax ✔
Gmin ✔
λ ✔
y ✔
general marker question
allow any distinguishing mark as long as only one per
row
for ✔ and X in same row ignore X
for ✔ and ✔ in same row give no mark
ignore any crossed-out response
4

alternative approach: single best fit line drawn on Figure 4

(d) G calculated from y step divided by x step;

n step ≥ 6 3 ✔
MAX 1

(e) λ in range 2.8(0) to 2.9(0) × 10–2 ✔

MAX 1

(f) percentage uncertainty in λ = × 100

AND

result in range 11(.0) % to 14(.0) % ✔

MAX 1
(g) calculate intercept

outlines a valid calculation method to find y ✔

MAX 1

(h) as main scheme

no ecf possible
4

alternative approach: non-crossing lines for Gmax and Gmin on

Figure 4: includes lines that meet but do not cross

(d) Gmax and Gmin calculated from y step divided by x step;

both n steps ≥ 6 3 ✔
MAX 1

(e) to (h) as main scheme

1
[18]

Q20.
(a) peak (to peak) voltage = 6.3(0) (V) ✔
accept any answer that rounds to 6.3 V
do not allow power of ten errors, eg 0.0063 V
1

(b) period = 8 divisions

(= 8 × 0.5 × 10–3 (s))

= 4 ms 1 ✔

= 250 (Hz) 2 ✔
award both marks if 250 Hz seen
accept 4.0(0) ms for 1 ✔ but reject 4.05, 3.95 etc
ecf2 ✔ for wrong period
2

(c) any valid approach leading to RC in range

2.1 ×10–4 to 3.4 ×10–4 or 3 ×10–4 (s)

their T in 02.2 × 0.069 ± 10 % 12 ✔ ✔

1 mark can be awarded for use of any valid

approach in which RC is seen with
substitutions or with rearranged equations, eg

1.75 × 10–4 = RC × ln 2

valid approaches;
reads off t when C starts to discharge and t at a lower
value of V:
rearranges to calculate RC
for ecf 2 ✔ ∆t used must correspond to interpretation of
time base used in determining the frequency in (b);
there is no ecf for misinterpretation of the voltage scale
OR
reads off t when C starts to charge and t at a higher
value of V:
rearranges to calculate RC etc
OR
determines half-life t0.5 and finds RC from
for ecf 2 ✔ t0.5 used must correspond to etc
OR
uses idea that during discharge V falls to 0.37V0 in one
time constant: determines suitable V and reads off RC
directly
for ecf 2 ✔ time interval used must correspond to etc
OR
uses idea that during charging V rises to 0.63V0 in one
time constant: determines suitable V and reads off RC
directly
reject idea that V falls to zero in 5RC
2

(d) qualitative comment

idea that the waveform will stretch horizontally 1 ✔

quantitative comment

by a factor of ✔

half a cycle now covers 10 (horizontal) divisions on the

screen 2 ✔ (and also earns 1 ✔ )

(so the) resolution of the time axis has increased 3 ✔

(and also earns 1 ✔ )

measuring larger distance / across more divisions from

the screen reduces (percentage) uncertainty in reading
the time (constant / interval / half life) 4 ✔
for 1 ✔ look for reference to time axis or direction
waveform is re-scaled
accept ‘graph is longer/stretched’ or ‘will not see whole
cycle’ or ‘fewer cycles shown’ or ‘period takes more
space’ or ‘distance being measured is larger’ or ‘time
per division is less’ or ‘larger in x direction’ or ‘time is
stretched’
reject ‘waveform becomes larger’ or ‘may not see
whole cycle’ or ‘measuring larger time’
for 2 ✔ there needs to be valid quantitative detail
award 12 ✔ ✔ for ‘half a cycle now fills the screen’ or
‘half a cycle is displayed’ as these clearly recognise the
stretching is along the time axis and ‘half’ is
quantitative
accept ‘new distance (on screen corresponding to half
life or time constant) is 2.5 × answer shown in working
for (c)’
the candidate who realises that half a wave now covers
the complete width of the screen cannot claim this is a
disadvantage; they would still be able to bring either
half cycle into view by using the X-shift and find RC for
3 ✔ uses technical language correctly

ignore (but do not penalise) ‘times are more precise’ or

‘more accurate’
reject ‘smaller resolution’ or ‘lower resolution’
for 4 ✔ there needs to be a qualifying explanation for
the comment about uncertainty
reject ‘advantage because the (time) scale is easier to
read’
3 MAX

(e) valid sketch on Figure 7 showing discharge time to 0 V reduced and charging
time to peak voltage reduced (see below) 1 ✔

connecting resistor in parallel with R halves [reduces

by 50%] circuit [total] resistance [time constant] 2 ✔

do not insist on seeing second discharge although if

shown this must look correct
2

(f) amendment to Figure 8 showing waveform across R with approximately the

correct shape, amplitude ± V and the correct phase

correct waveform shown while signal generator output

is low (0 V): only the complete negative half cycle
needs to be shown but if second negative half cycle is
included it must be correct 1 ✔

correct waveform shown while voltage across signal

generator output is high; condone no signal or signal =
0 V before going to –V for the first time 2 ✔

don’t insist on seeing vertical lines

(g) reduce the (sensitivity of) (Y-voltage)) gain 1 ✔

(change) to 2 V division–1 2 ✔ (and earns 1 ✔ )

adjust the Y (vertical) shift 3 ✔
‘make (Y-) gain smaller’ or ‘increase the volts per
division’ or ‘reduce the Y-resolution’ are acceptable
substitutes for ‘reduce the (Y-)gain’
increase the (Y-) gain to 2 V division–1 2 ✔ not 1 ✔
reduce the (Y-) gain to 0.5 V division–1 1 ✔ not 2 ✔
ignore any comment about time base or ‘X-gain’
if all positive waveform is given for (f) allow sensible
comment about triggering/stability control, eg
waveform may not be stable 1 ✔ ; adjust triggering 2 ✔
2 MAX
[14]

Q21.
(a) potential axis: unit mV and suitable labelling of 0 and 1
for scale ✔

time axis suitable use of numbers from 0 to 0.6 / 1 ✔

(b) Possible answers to include:

electrodes are not non-reactive ✔

electrodes are not securely taped in place ✔

the patient is not relaxed or does not remain still ✔

the amplifier is not low noise ✔

the amplifier has damaged shielded leads /

interference from other AC sources ✔
Any 3 points with reason and some extension to
explain.
Be aware of the section 3.1 in the instructions to
examiners.
If more than 3 answers given remember
‘right + wrong = wrong’
3
[5]
Q22.
(a) (for Proper time, t0 = 31,536,000 s / 365 days)
Dilated time, t = 31,561,259 s ✔

Time dilation is 25,259 s / 421 minutes / 7.0 hours /

0.29 days ✔

The recorded time will be longer (as predicted) ✔

The recorded time will be less than several days longer
(as predicted) ✔
Accept answers in other units (e.g. 365.3 days)
Accept an answer of 31582876 seconds / 365.5 days
where a proper time of 365.25 days has been used.
4

(b) Theory of Special Relativity requires no acceleration ✔

(The spacecraft/frame of reference is) accelerating ✔

Alternative answer:

Theory of Special Relativity requires inertial reference

frame ✔

(The spacecraft/frame of reference is) not an inertial

reference frame ✔
Accept change in direction / speed / velocity as
alternatives for accelerating.
2
[6]

Q23.
(a) f = 1 / (2π √LC)
C = 1/ f24π2L
C = 1/ (910 × 103)2 × 4 × π2 × 1.1 × 10–3
C = 27.8 pF (accept 28pF)
Formula with correct substitution / evidence of correct
working
Answer
1
1
(b)
General shape around f0 and to max of 1.0 on relative
voltage gain axis
1
10 kHz bandwidth
at 0.71 gain
1
Frequencies (905 – 910 – 915) kHz (identified / used)
1

(c) Smaller Q factor leads to:

(Any two from)

(i) Broader bandwidth
(ii) More noise / (hiss) detected
(iii) Less selectivity
(iv) More susceptible to crosstalk from neighbouring
stations on the frequency spectrum.
(v) Less gain due to energy loss / loss of signal detail
2
[7]

Q24.
(a) Photoconductive (accept reverse bias)
1

(b)
Tick (✔) if
correct
Non-inverting amplifier
Comparator ✔
Summing amplifier
Difference amplifier
1

(c) Light level ~ 1000 lux +/- 10%

(d) Vx = IR; Vx = 100 μA × 20 kΩ = 2 V

(e) Rule that if V– > V+ then Vout is 0 V (low)

1
Voltage drop across LED so LED is ON
Do not allow LED is ON if supported by incorrect
reason
1
[6]

Q25.
(a) qq̄✔
1

(b) Total energy = 2keV + 2 × 511 keV = 1024 keV✔

= 1024 × 1.6 × 10−19 = 1.64 × 10−13J✔

Energy of each photon = 1.64 × 10−13/2 = 8.19 × 10−14 (J) ✔

First mark for calculating the total energy in keV.
Second mark is for converting correctly into joules.
Third mark is for dividing by two so ecf for incorrect
conversion into joules. Student must show at least 3sf.
3

= 2.43 × 10−12 (m) ✔

First mark for the correctly rearranged equation or
correct values substituted into equation.
Correct answer only scores 2 marks, ecf from 1 (b)
2

(d) Ek= 2 keV = 2000 × 1.6 × 10−19 J = 3.2 × 10−16J✔

= 2.65 × 107(m s−1) ✔

First mark for converting KE into joules.
Second mark for rearranging equation correctly or
substituting correct values into equation.
Third mark for correct answer, must be to at least 3sf.
3

(e) ✔

= 2.75 × 10−11(m) ✔
First mark for rearranging equation correctly or
substituting correct values into equation.
Second mark for correct answer.
2

(f) Recognition that separation is 1.5 × 10−10 m and compared to 0.28 × 10−10
(ecf)✔

wavelength is about 5 times less than gap width✔

yes (diffraction would be observable)✔

Or words to that effect
4
[15]

Q26.
(a) π / 180° out of phase ✔
Do not allow “out of phase”.
1

(b) wavelength = 0.44 m ✔

c (= f λ) = 145 (m s−1) ✔
2

(c) First harmonic frequency = 110 Hz✔

T = 4 × 1102 × 0.662 × ✔

71.8 N✔
3

(d) Extension of string = 3 × 2π × 3.0 × 10−3 (= 5.65 cm)✔

energy stored = 0.5 × 71.8 × 0.0565 = 2.03 (J)✔

Compares calculated energy quantitatively to another energy and draws

correct inference, e.g. wire would be moving at about 80 mph so a risk / 2 J is
the equivalent of 1 kg mass dropped through 0.2 m so a risk✔
3
[9]
Q27.
(a) Refers to relative direction of oscillations to that of the direction of propagation
/ transfer of energy ✔

For transverse waves oscillations are at right angles to direction of propagation

while in longitudinal waves they are in the same direction ✔
allow direction the wave is travelling in
2

(b) Correct value for µ = (1 ×) ρ = 7.5 × 10−4 (kg m−1)✔

Tension = 126 N (allow 9.7 × 105 × their value for µ) ✔

(c) Max tension permissible before breaking = 3.0 × 109 ×

= 288 (289)(290) N ✔

This is greater than required tension so wire is suitable. ✔

stress in operation = = 1.3 × 109 (N m−2)✔

which is less than breaking stress ∴ safe to use✔

Allow ecf for incorrect area in 2.2
2

(d) Shows second harmonic λ = ✔

Identify f and T are constant so λ is proportional to ✔

λ increases from A to B ✔

mass per unit length decreases from A to B so A has a greater diameter✔

4
[10]

Q28.
(a) 1eV = 1.6 × 10−19 J

kinetic energy = 1.6 × 10−19 × 4.9 × 106 = 7.8(4) × 10−13 J ✔

ke lost = pe gained = 7.8(4) × 10−13 J ✔
2

(b) using V = Q / 4πεor and Ep = qV

r = qQ/4πεoEp✔

= (2 × 1.6 × 10−19) (79 × 1.6 × 10−19)/4π × 8.85 × 10−12 × 7.84 × 10−13✔

r = 4.67(4.64) × 10−14 m ✔
3

= (7.16 × 10−15 / 1.23 × 10−15 m)3 ✔

= 197 placed on the dotted line ✔

(d) r gets smaller ✔

less force so needs to travel further to lose same initial ke ✔

Fewer protons means that r will be smaller when alpha
particle has the same electrostatic potential energy (as
initial kinetic energy)
2
[10]

Q29.
(a) Initially the path difference is zero/the two waves are in phase when they
meet/the (resultant) displacement is a maximum ✓
Alternative:
Constructive interference occurs when the path
difference is a whole number of wavelengths and the
waves are in phase
1

As the movable tube is pulled out, the path difference increases and the
two waves are no longer in phase, so the displacement and loudness
decrease ✓
Destructive interference occurs when the path
difference is an odd number of half wavelengths and
the waves are in antiphase
1

When the path difference is one half wavelength, the two are in
antiphase and sound is at its quietest. ✓
Initially the path difference is zero and the sound is
loud
1

As the path difference continues to increase, the two waves become

more in phase and the sound gets louder again. ✓
As the pipe is pulled out the path difference gradually
increases, changing the phase relationship and hence
the loudness of the sound
1

(b) Use of wavelength = speed / frequency

The first mark is for calculating the wavelength
1

To give: 340 / 800 = 0.425 m ✓

Path difference = one half wavelength = 0.21 m ✓

The second mark is for relating the wavelength to the
path difference

Path difference = 2 (d2 – d1) = 2 (distance moved by movable tube)

Distance moved by movable tube = 0.10 m. ✓

The final mark is for relating this to the distance moved
by the tube and working out the final answer.
1

(c) Start with d1 = d2

(Alternative mark scheme involving changing frequency
and measuring to first min for each one can gain equal
credit)

Measure distance moved by movable tube for each successive minima

and maxima✓
Start with d1 = d2
Measure distance moved by movable tube for first
minimum.
1
Each change in distance is equal to one quarter wavelength. ✓
Distance is equal to one quarter wavelength
1

Continue until tube is at greatest distance or repeat readings for

decreasing distance back to starting point. ✓
Repeat for different measured frequencies.
1

Use speed = frequency x wavelength ✓

Use speed = frequency x wavelength)
1
[11]

Q30.
(a) A combination of resistors in series connected across a voltage source
(to produce a required pd) ✓
Reference to splitting (not dividing) pd
1

(b) When R increases, pd across R increases ✓

Pd across R + pd across T = supply pd ✓

So pd across T / voltmeter reading decreases ✓

Alternative:

Use of V= ✓

Vtot and R2 remain constant ✓

So V increases when R1 increases ✓
3

(c) At higher temp, resistance of T is lower ✓

So circuit resistance is lower, so current / ammeter reading increases ✓

(d) Resistance of T = 2500 Ω

Current through T = V / R = 3 / 2500 = 1.2 × 10−3 A ✓

(Allow alternative using V1/R1 = V2/R2)

pd across R = 12 − 3 = 9 V
The first mark is working out the current
1

Resistance of R = V / I = 9 / 1.2 × 10−3 = 7500 Ω✓

The second mark is for the final answer
1

(e) Connect the alarm across R instead of across T ✓

allow: use a thermistor with a ptc instead of ntc.
1
[9]

Q31.
(a) 2.9% ✓
Allow 3%
1

(b) seen ✓
1

0.29 mm or 2.9 x 10-4 m✓ must see 2 sf only

(d) Clear indication that at least 10 spaces have been measured to give a
spacing = 5.24 mm✓
spacing from at least 10 spaces
Allow answer within range ±0.05
1

(e) Substitution in d sinθ = nλ✓

The 25 spaces could appear here as n with sin θ as
0.135 / 2.5
1

d = 0.300 x 10-3 m so

number of lines = 3.34 x103✓
Condone error in powers of 10 in substitution
Allow ecf from 1-4 value of spacing
1

(f) Calculates % difference (4.6%) ✓

and makes judgement concerning agreement ✓

Allow ecf from 1-5 value
1

(g) care not to look directly into the laser beam✓

OR
care to avoid possibility of reflected laser beam ✓
OR
warning signs that laser is in use outside the laboratory✓
ANY ONE
1
[10]

Q32.
(a) 6.5 × 1010 Pa ✓
1

(b) kg m-1 s-2 ✓

(c) Direction of movement of particles in transverse wave perpendicular to

energy propagation direction✓
1

Parallel for longitudinal✓

(d) ρ1c1=ρ2c2✓

E=ρc2 or ρc = seen
1

(e) [ and cx = 2cy ]

0.5✓
1

(f) speed of the wave in seawater is less than speed of the wave in glass✓
1

argument to show that watern glass <1✓

so tir could be observed when wave moves from water to glass ✓

1
[10]

Q33.
(a) Core is transmission medium for em waves to progress (by total internal
reflection) ✓
Allow credit for points scored on a clear labelled
diagram.
1

Cladding provides lower refractive index so that total internal reflection

takes place ✓
1

And offers protection of boundary from scratching which could lead to

light leaving the core. ✓
1

(b) Blue travels slower than red due to the greater refractive index

Red reaches end before blue, leading to material pulse broadening ✓

The first mark is for discussion of refractive index or for
calculation of time difference.
1

Alternative calculations for first mark

Time for blue = d / v = d / (c / n) = 1200 / (3 × 108 / 1.467) = 5.87 × 10-6

Time for red = d / v = d / (c / n) = 1200 / (3 × 108 / 1.459) = 5.84 × 10-6

Time difference = 5.87 × 10-6 – 5.84 × 10-6 = 3(.2) × 10-8 s ✓

The second mark is for the link to material pulse
broadening
1

(c) Discussions to include:

Use of monochromatic source so speed of pulse constant

Use of shorter repeaters so that the pulse is reformed before significant

pulse broadening has taken place.

Use of monomode fibre to reduce multipath dispersion ✓ ✓

Answer must make clear that candidate understands
the distinction between modal and material broadening.
2
[7]

Q34.
(a) Suitable experiment eg diffraction through a door / out of a pipe ✓
1

(b) Using c = d / t

t = 2 500 / 480 = 5.2 s ✓

Calculation assumes that light takes no time to reach observer, ie speed

is infinite ✓
Do not allow “could not know speed of light”
1

(d) Sound from gun is a mixture of frequencies. ✓

Alternative for 1st mark ‘(so speed is independent of
frequency) the sound of the gun is similar when close
and far away’
1

All the sound reaches observer at the same time, ✓

(e) More accurate, as it is closer to the accepted value. ✓

(f) When θ = 0 °C c = 331.29 m s–1

Therefore

331.29 = k √273.15 ✓

k = 20.045 ✓
1

(g) The method and value are published ✓

other scientists repeat the experiment using the same method ✓

1
[10]

Q35.
(a) speed of light in free space independent of motion of source and / or the
observer✓
and of motion of observer
1

(b) laws of physics have the same form in all inertial frames
laws of physics unchanged from one inertial frame to another ✓
1

(c) time taken(= )=1.2 × 10–7 s✓

(d) t=✓
Allow substitution for this mark
1

time taken for π meson to pass from one detector to the other = 58 ns
✓
1

2 half-lives (approximately) in the detectors' frame of reference. ✓

two half-lives corresponds to a reduction to 25 % so 75% of the π

mesons passing the first detector do not reach the second detector. ✓
OR
Appreciation that in the lab frame of reference the time is about 6
half-lives had passed✓
1

In 6 half-lives 1 / 64 left so about 90% should have decayed✓

Clear conclusion made

Either Using special relativity gives agreement with experiment
or Failure to use relativity gives too many decaying (WTTE)
1
[8]

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Waves

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Q1.

Describe the interference pattern now seen on the white screen.

Use a calculation to support your answer.

The student suggests the following changes:

• decrease slit separation s

The student decides to make each change independently.

Calculate the refractive index nB of glass B.

Give your answer to an appropriate number of significant figures.

speed of light in a vacuum = 2.998 × 108 m s–1

(b) Figure 2 shows a cross-sectional view of an optical fibre strain gauge.

A maximum intensity of the reflected light is produced due to superposition of

This maximum intensity occurs at a particular wavelength λR.

Discuss how the value of λR changes.

The refractive index of this glass is 1.5

What is the path of the ray of light?

The time for the ray to travel along optical fibre P is

where c is the speed of light in a vacuum.

What is the lowest frequency heard?

What is the number of lines per mm of the diffraction grating?

v / 107 m s–1 λ / 10–11 m

Planck constant = ____________________ J s

(b) The vibrating length of one of the strings of a violin is 0.33 m

speed of waves = ____________________ m s–1

The string with its initial tension of 25 N is vibrating at a frequency of 370 Hz

Assume that there is no change in the diameter of the string.

The wave travels to R by two routes, P → Q → R and P → R. The speed of the

What will increase the fringe spacing?

A increasing the separation of the single slit and the

B increasing the width of the single slit

C decreasing the distance between the double slits and

Use these data to estimate an age, in seconds, of the Universe.

Your answer should include:

• an explanation of why a shift of the fringe pattern was predicted

State this postulate.

(c) State the other postulate of Einstein’s theory of special relativity.

(d) One consequence of the special theory of relativity is length contraction.

Figure 2 shows how the percentage of the number of muons remaining in a

In a particular experiment, muons moving with a velocity 0.990c travel a

Determine the percentage of muons that reach the detector.

(b) ​ Determine the frequency of the microwaves that are transmitted.

Explain why the minimum intensity between C and D is not zero.

State and explain the effect on the signal strength as it is rotated.

Young modulus of copper = 1.2 × 1011 Pa

Calculate the tension in each supporting cable so that there is no resultant

(d) ​ Calculate the mass of a 1.0 m length of the aerial wire.

Density of copper = 8900 kg m–3

To do this, monochromatic light is reflected normally off the mirror, creating

(a) ​ Show that the wavelength of the light is 600 nm.

phase difference = ____________________________ rad

Using an appropriate equation of motion, calculate the acceleration due to

wavelength of the light = 600 nm

acceleration due to gravity = ____________________________ m s–2

Determine the gradient of the line when the time is 0.12 s.

(e) ​ State what this gradient represents.

The table shows the results of the experiment.

where T is the tension in the nylon string.

Determine the length l of the string used.

Refractive index of the glass used = 1.6

angle of incidence = ____________________ degrees

Calculate the refractive index of the liquid.

A microwave transmitter T and a receiver R are arranged on a line marked on the

Figure 1 shows side and plan views of the arrangement.

The distance y between T and R is recorded.

T is switched on and the output from T is adjusted so a reading is produced on the

The reading decreases to a minimum reading which is not zero.

where λ is the wavelength of the microwaves and y is the distance defined in

The student plots the graph shown in Figure 4.

(e) ​ Determine λ using your results for Gmax and Gmin.

(f) ​ Determine the percentage uncertainty in your result for λ.

percentage uncertainty in λ = ____________________ %

Result Reduced Not affected increased

(a) ​ Determine the peak-to-peak voltage V of the waveform shown in Figure 4.

(b) ​ Determine the frequency f of the waveform shown in Figure 4.

The oscilloscope is connected across the capacitor.

When S is closed (on) the oscilloscope displays the waveform shown in

Determine the time constant of the circuit in Figure 5.

(b) Determine the frequency of the microwaves that are transmitted.

(d) Calculate the mass of a 1.0 m length of the aerial wire.

(a) Show that the wavelength of the light is 600 nm.

(e) State what this gradient represents.

(e) Determine λ using your results for Gmax and Gmin.

(f) Determine the percentage uncertainty in your result for λ.

(a) Determine the peak-to-peak voltage V of the waveform shown in Figure 4.

(b) Determine the frequency f of the waveform shown in Figure 4.

(b) In which mode is the operational amplifier being used in Figure 1?

(b) The tube starts in the position shown in Figure 1.

frequency of sound from loud speaker = 800 Hz

(c) Quincke’s tube can be used to determine the speed of sound.

(d) The battery has an emf of 12.0 V. At a temperature of 0 °C the resistance of

(b) Determine the grating spacing.

(c) State the absolute uncertainty in the value of the spacing.

(d) The student sets up the apparatus shown in Figure 1 in an experiment to

(e) Calculate the number of lines per metre on the grating.

(a) Calculate the magnitude of the Young modulus for glass.

(b) State your answer to (a) in terms of SI fundamental units.

(a) Explain what is meant by this postulate.

(b) State the other postulate.

(d) π mesons are unstable and decay with a half-life of 18 ns.