(1) A string of length 1 m and mass per unit length 20 g m−1 is fixed at both ends and is under a tension of
32 N. Find the fundamental frequency of transvers oscillations of the string.
Ans: 𝟐𝟎 𝐇𝐳
1 𝑇 1 32 N
𝑓= √ = ×√ = 20 Hz
2𝐿 𝜇 2 × 1 m 20 × 10−3 kg m−1
(2) A string of mass per unit length 20 g m−1 is fixed at both ends and is under a tension of 800 N. Find the
length of the string if its fundamental frequency is 50 Hz.
Ans: 𝟐 𝐦
1 𝑇 1 800 N
𝐿= √ = ×√ = 2m
2𝑓 𝜇 2 × 50 Hz 20 × 10−3 kg m−1
(3) A string of length 1 m and mass per unit length 20 g m−1 is fixed at both ends. Find the tension needed
for a fundamental frequency of 100 Hz.
Ans: 𝟖𝟎𝟎 𝐍
𝑇 = 4𝑓 2 𝐿2 𝜇 = 4(100 Hz × 1 m)2 × 20 × 10−3 kg m−1 = 800 N
A coin at the bottom of a beaker containing a transparent organic liquid appears to be 5 cm below the
surface of the liquid when the depth of liquid is 7 cm. What is the refractive index of the liquid?
Ans: 𝟏. 𝟒
𝑛 = 𝑑real /𝑑apparent = (7 cm)/((5 cm) = 1.4
Glycerin has a refractive index of 1.47. What is the apparent depth of an object immersed in glycerin to
a real depth of 9.8 cm.
Ans: 𝟔. 𝟕 𝐜𝐦
𝑑apparent = 𝑑real /𝑛 = 9.8 cm/1.47 = 6.7 cm
Kerosene has a refractive index of 1.45. At what depth in kerosene will a coin appear to be 20 cm
below the surface?
Ans: 𝟐𝟗 𝐜𝐦
𝑑real = 𝑛𝑑apparent = 1.45 × 20 cm = 29 cm
Contest 26a
(1) The mass of a 2 m string fixed at both ends is 16 g. Determine the fundamental frequency of transverse
vibrations of the string when it is under a tension of 20 N.
Ans: 𝟒. 𝟎 𝐇𝐳
1 1
𝑓= √𝑇𝐿⁄𝑚 = × √(20 N × 2 m)/(16 × 10−3 kg) = 4.0 Hz
2𝜋𝐿 2𝜋 × 2 m
(2) The mass of a 1 m long string fixed at both ends is 9 g. Determine the fundamental frequency of
transverse vibrations of the string when it is under a tension of 40 N.
Ans: 𝟏𝟏 𝐇𝐳
1 1
𝑓= √𝑇𝐿⁄𝑚 = × √(40 N × 1 m)/(9 × 10−3 kg) = 11 Hz
2𝜋𝐿 2𝜋 × 1 m
(3) The mass of a string that is 1 m long and fixed at both ends is 32 g. Determine the fundamental
frequency of transverse vibrations of the string when it is under a tension of 20 N.
Ans: 𝟒. 𝟎 𝐇𝐳
1 1
𝑓= √𝑇𝐿⁄𝑚 = × √(20 N × 1 m)/(32 × 10−3 kg) = 4.0 Hz
2𝜋𝐿 2𝜋 × 1 m
A sonometer with a uniform 0.20 kg m−1 wire stretched by a 1.52 kg mass in a 0.10 kg pan
has two bridges that are 0.50 m apart. What is the fundamental frequency of the sound
produced when the wire between the bridges is plucked?
Ans: 𝟐. 𝟗 𝐇𝐳
1 𝑇 1 (1.52 kg+0.10 kg)×10 ms−2
𝑓 = 2𝜋𝐿 √𝜇 = 2𝜋×0.50 m √ = 2.9 Hz
0.20 kg m−1
A sonometer with a uniform 0.8 kg m−1 wire stretched by a 1.9 kg mass in a 0.1 kg pan has
two bridges that are 0.5 m apart. What is the fundamental frequency of the sound produced
when the wire between the bridges is plucked?
Ans: 𝟏. 𝟔 𝐇𝐳
1 𝑇 1 (1.9 kg + 0.1 kg) × 10 ms −2
𝑓= √ = √ = 1.6 Hz
2𝜋𝐿 𝜇 2𝜋 × 0.50 m 0.8 kg m−1
A sonometer with a uniform 0.4 kg m−1 wire stretched by a 0.9 kg mass in a 0.1 kg pan has
two bridges that are 20 cm apart. What is the fundamental frequency of the sound produced
when the wire between the bridges is plucked?
Ans: 𝟒 𝐇𝐳
1 𝑇 1 (0.9 kg + 0.1 kg) × 10 ms −2
𝑓= √ = √ = 4 Hz
2𝜋𝐿 𝜇 2𝜋 × 0.2 m 0.4 kg m−1
1. What is the speed of a wave with period and wavelength ?
ANSWER:
1. What is the distinction between oscillations in sound waves and those in light waves?
ANSWER: Sound wave oscillations are longitudinal whereas light wave oscillations are
transverse
1. What property distinguishes red light from blue light?
ANSWER: The frequency of blue light is greater than that of red light
Accept: The wavelength of red light is greater than that of a blue light
2. Name a property of transverse waves that longitudinal waves do not have.
ANSWER: Polarization: Longitudinal waves cannot be polarized
1. Find the wavelength of the fundamental mode of a stretched 2 m wire fixed at both ends.
ANSWER: 𝟒 𝐦
𝜆 = 2𝐿 = 4 m
2. Find the frequency of the fundamental mode of a 2 m wire fixed at both ends if the speed of
transverse waves on the wire is 100 m/s.
ANSWER: 𝟐𝟓 𝐇𝐳
𝑓 = 𝑐/𝜆 = 100 m/s ÷ 4 m = 25 Hz
3. Find the speed of transverse waves on a stretched 2 m wire fixed at both ends if the frequency
of the fundamental mode is 200 Hz.
ANSWER: 𝟖𝟎𝟎 𝐦/𝐬
𝑐 = 𝑓𝜆 = 200 Hz × 4 m = 800 m/
1
. Calculate the angular frequency of a vibration that has a frequency of Hz
2
SOLUTION:
w 2f
1
2 ( )
2
w 1rad / s
4. Calculate the frequency of a traveling wave whose velocity has a magnitude of
2 where is the wavelength.
SOLUTION:
v = f
v
f=
2
f=
f =2Hz
1. Find the magnification produced by a 20 cm focal length lens of an object 100 cm from the lens.
ANSWER: 𝟎. 𝟐𝟓 𝑀 = 𝑓/(𝑢 − 𝑓) = 0.25
PREAMBLE: A cell phone emits 900 MHz radio waves at a power of 0.3 W.
Approximate values of physical constants are as follows: ℎ = 6.6 × 10−34 J s; the Wien law
constant 𝑏 = 2.9 × 10−3 K m; the Stefan-Boltzmann constant 𝜎 = 5.7 × 10−8 W m2 K −4 ;
𝑐 = 3.0 × 108 m/s.
1. How many photons does the cell phone emit in 1 s?
ANSWER: 5 × 1023 photons/s
𝑛 = 𝑃/(ℎ𝑓) = 0.3 W ÷ (6.6 × 10−34 J s × 900 × 106 Hz) = 5 × 1023 photons/s
2. Determine the temperature of a blackbody whose peak emission wavelength equals the
wavelength of the radiation emitted by the cell phone.
ANSWER: 9 mK
𝑇 = 𝑏/𝜆 = 𝑏𝑓/𝑐 = 2.9 × 10−3 K m × 900 × 106 Hz ÷ 3 × 108 m/s = 8.7 × 10−3 K
1. What is the frequency of the beats produced when a 257 Hz note and a 253 Hz note are sounded
together?
ANSWER: 4 Hz
The beat frequency is the difference in frequency of the notes:
.
2. What is the frequency of the beats produced when a 256 Hz note and a 253 Hz note are sounded
together?
ANSWER: 3 Hz
3. What is the frequency of the beats produced when a 444 Hz note and a 451 Hz note are sounded
together?
ANSWER: 7 Hz
When two notes are sounded together, a 2 Hz beat is heard.
1. What are the frequencies of the notes if the note frequencies are lower than 256 Hz and the lower
frequency note produces a 6 Hz beat with a 256 Hz note?
ANSWER: and
and so and .
2. What are the frequencies of the notes if the note frequencies are higher than 256 Hz and the
lower frequency note produces a 6 Hz beat with a 256 Hz note?
ANSWER: and
and so and .
3. What are the frequencies of the notes if the note frequencies are lower than 256 Hz and the
higher frequency note produces a 6 Hz beat with a 256 Hz note?
ANSWER: and
and so and .
Frequency is non-negative.
1. An x-ray target is bombarded by electrons accelerated through a potential difference
of 8 x 104 eV. Calculate the highest frequency of the emitted photons.
Plank’s constant h = 4 x 10-15 eVs
SOLUTION:
hf = eV
4 x 10-15f = 8 x 104
8 104
f=
4 1015
f = 2 x 1019 Hz
2. An x-ray target is bombarded by electrons accelerated through a potential difference
of 6 x 104 eV. Calculate the highest frequency of the emitted photons. (Planck’s
constant h = 4 x 10-15 eVs
SOLUTION: hf = eV
4 x 10-15f= 8 x 104
6 104
f=
4 1015
f =1.5 x 1019 Hz
(3) The wavelength of the most intense thermal radiation emitted by a blackbody is observed to decrease
from 2.4 μm to 1.2 μm. What is the ratio of the initial temperature to final temperature of the
blackbody?
Ans: 𝟐. 𝟎
𝑇𝑓 /𝑇𝑖 = 𝜆𝑖 /𝜆𝑓 = (2.4 μm)/(1.2 μm) = 2.0
(1) Light falls at normal incidence on a diffraction grating ruled with 800 lines mm−1 . Find the wavelength
diffracted at 30° in first order.
Ans: 𝟔𝟐𝟓 𝐧𝐦
0.5
𝜆 = 𝑑 sin 𝜃 = 1/(800 mm−1 ) × sin 30° = mm = 625 nm
800
(1) Light falls at normal incidence on a diffraction grating ruled with 800 lines mm−1 . Find the wavelength
diffracted at 30° in first order.
Ans: 𝟔𝟐𝟓 𝐧𝐦
0.5
𝜆 = 𝑑 sin 𝜃 = 1/(800 mm−1 ) × sin 30° = mm = 625 nm
800
(1) Light falls at normal incidence on a diffraction grating ruled with 800 lines mm−1 . Find the wavelength
diffracted at 30° in first order.
Ans: 𝟔𝟐𝟓 𝐧𝐦
0.5
𝜆 = 𝑑 sin 𝜃 = 1/(800 mm−1 ) × sin 30° = mm = 625 nm
800
(1) What is the difference in linear momentum between a 200 nm photon and a 400 nm photon?
Ans: 𝟏. 𝟔 × 𝟏𝟎−𝟐𝟕 𝐍 𝐬
1 1
Δ𝑝 = ℎ(1/𝜆1 − 1/𝜆2 ) = 6.63 × 10−34 J s × ( − ) = 1.6 × 10−27 N s
200 × 10 m 400 × 10−9 m
−9
(1) What is the speed of 743 nm electromagnetic waves in silicon nitride? The refractive index of silicon
nitride is 2.0 at a wavelength of 743 nm.
Ans: 𝟏. 𝟓 × 𝟏𝟎𝟖 𝐦 𝐬 −𝟏
𝑣 = 𝑐/𝑛 = 3.0 × 108 m s−1 /2.0 = 1.5 × 108 m s−1
(2) Light of wavelength 743 nm is incident from silicon nitride into air. The refractive index of silicon
nitride is 2 at 743 nm. Find the minimum angle of incidence at which total internal reflection occurs.
Ans: 𝟑𝟎°
𝜃𝑐 = sin−1 1/𝑛 = sin−1 1/2 = 30°
1. Given that the speed of light is c = 3 x 108 m/s, calculate the wavelength of a radio
transmission at a frequency of 100MHz.
SOLUTION:
C=f
3 x 108 = 100 x 106
3 108
=
100106
= 3m
2. Given that the speed of light is c = 3 x 108 m/s, calculate the frequency of a radio
transmission at a wavelength of 2cm.
SOLUTION:
C = f
f = C/
3 108
f=
2 102
f = 1.5 x 1010 Hz
f = 15 GHz
1. What is the wavelength of the lowest frequency standing waveon a 1 m long vibrating string
fixed at both ends?
ANSWER: 2 m
2. What is the wavelength of a standing wave with 5 antinodes on a 1 m long vibrating string fixed
at both ends?
ANSWER: 0.4 m [ so ]
3. How many antinodes are there in a stationary wave with wavelength 0.2 m on a 1 m long
vibrating string fixed at both ends?
ANSWER: 10
(3) When a tuning fork of frequency 440 Hz is sounded together with a guitar string, 8 beats are heard in
2 s. When the guitar string is tightened, the beat frequency decreases. What is the frequency of the
string before tightening?
Ans: 𝟒𝟑𝟔 𝐇𝐳
𝑓 = 440 Hz − 𝑓𝑏𝑒𝑎𝑡 = 440 Hz − (8/2) Hz = 436 Hz
(3) An x-ray tube is operated with a potential difference of 45 kV between anode and cathode. Find the
wavelength of the most energetic x-ray photons the target emits.
Ans: 𝟐𝟖 𝐩𝐦
𝜆 = ℎ𝑐/𝑈 = 6.6 × 10−34 J s × 3.0 × 108 m s−1 /(45 × 103 V × 1.6 × 10−19 C) = 2.8 × 10−11 m
PREAMBLE: The Wien constant is approximately 2.9 × 10−3 K m. Find the wavelength of
peak emission intensity at the given blackbody temperature.
1. 200 K
ANSWER: 1.45 × 10−5 m = 14.5 𝜇m
𝜆 = 2.9 × 10−3 K m ÷ 200 K = 1.45 × 10−5 m
2. 1000 K
ANSWER: 2.9 𝜇m
3. 5000 K
ANSWER: 0.58 𝜇m
The speed of sound in air is at .
1. A stationary observer hears a note from an approaching siren moving at on a
day when the temperature is . What is the frequency emitted by the siren?
ANSWER: [ ]
2. What is the frequency heard by a stationary observer from a receding siren moving at
and emitting a note at an air temperature of .
ANSWER: [ ]
3. What is the frequency heard by an observer moving at towards a stationary siren
emitting a note at an air temperature of .
ANSWER: [
1. Two loud speakers facing each other emit the same note. What phenomenon accounts for the
observation that the intensity of sound varies with position between them?
ANSWER: Interference of waves
2. What phenomenon accounts for the observation that sound emitted by a moving source has a
different frequency from the same sound emitted from a stationary source?
ANSWER: Doppler Effect
3. When an obstacle is placed directly in front of a sound source, it is observed that the highest
intensity occurs directly behind the obstacle in the region of the geometrical shadow. What
phenomenon accounts for this?
ANSWER: Diffraction
1. Name the hydrogen atom spectral line series that lies in the ultraviolet.
ANSWER: Lyman
2. Determine the wavelength of the fundamental note emitted by a 10 cm pipe closed at one end.
ANSWER: 𝟒𝟎 𝐜𝐦 = 𝟎. 𝟒 𝐦
1. What is the phenomenon by which the intensity of a wave decreases as it passes through a
substance?
ANSWER: Absorption (Accept attenuation.)
2. What is the phenomenon by which the frequency of a wave changes as the speed of an
observer changes?
ANSWER: Doppler Effect
3. What is the phenomenon by which two waves combine to produce zero intensity?
ANSWER: Destructive interference𝜆 = 4𝑙 = 40 cm
1. A mono-energetic beam of particles each of mass 4.0 × 10−26 kg and energy 5.0 × 10−21 J is
incident on a grating. Find the wavelength of photons that will produce the same diffraction
pattern as the beam.
ANSWER: 𝟑. 𝟑 × 𝟏𝟎−𝟏𝟏 𝐦 = 𝟑𝟑 𝐩𝐦
𝜆 = ℎ/𝑝 = ℎ/√2𝑚𝐸 = 6.6 × 10−34 J s ÷ √2 × 4 × 10−26 kg × 5 × 10−21 J
= 3.3 × 10−11 m
2. Give the relationship between focal length and radius of curvature for a concave spherical mirror.
ANSWER: Radius of curvature equals twice focal length
3. What is the kinetic energy of a 0.4 kg ball dropped from a height of 2 m when it strikes the
ground?
ANSWER: 𝟖 𝐉
𝑇 = 𝑚𝑔ℎ = 0.4 kg × 10 m s−2 × 2 m = 8 J
PREAMBLE: The displacement at time 𝑡 of a particle at position 𝑥 in a transverse wave is
given by𝑦(𝑥, 𝑡) = 𝐴 cos(𝑘𝑥 − 𝜔𝑡).
1. What is the velocity of the particle at position 𝑥?
ANSWER: 𝒗(𝒙, 𝒕) = 𝑨𝝎 𝐬𝐢𝐧(𝒌𝒙 − 𝝎𝒕) 𝑣 = 𝜕𝑦/𝜕𝑡
2. What is the maximum speed of the particle at position 𝑥?
ANSWER: 𝑨𝝎
3. What is the acceleration of the particle at position 𝑥?
ANSWER: 𝒂(𝒙, 𝒕) = −𝑨𝝎𝟐 𝐜𝐨𝐬(𝒌𝒙 − 𝝎𝒕)
1. A converging lens has a focal length of 20 cm. How far from the pole of the lens must a paraxial
object be placed to form an image with a magnification of 5?
ANSWER: 𝟐𝟒 𝐜𝐦
𝑢 = 𝑓 + 𝑓/𝑀 = 20 cm × (1 + 1/5) = 24 cm
2. What is the focal length of a converging lens which produces an image with a magnification of 5
of a paraxial object placed 30 cm from its pole?
ANSWER: 𝟐𝟓 𝐜𝐦 𝑓 = 𝑢𝑀/(1 + 𝑀) = 30 cm × 5/6 = 25 cm
3. Find the magnification of the image produced by a 50 cm focal length converging lens of a
paraxial object 75 cm from the pole of the lens.
ANSWER: 𝟐 𝑀 = 𝑓/(𝑢 − 𝑓) = 50 cm ÷ (70 cm − 50 cm) = 2
1. Find the wavelength of the fundamental note of a pipe open at both ends whose length is 0.5 m.
Ignore end effects.
ANSWER: 1 m
𝜆0 = 2𝑙 = 1 m
2. Find the frequency of the fundamental note of a pipe open at both ends whose length is 1 m if
the speed of sound is 340 m/s. Ignore end effects.
ANSWER: 170 Hz
𝑓0 = 𝑐/2𝑙 = 340 m/s ÷ (2 × 1 m) = 170 Hz
3. Find the wavelength of the first overtone of a pipe open at both ends whose length is 0.5 m.
Ignore end effects.
ANSWER: 0.5 m
𝜆1 = 𝑙 = 0.5 m
PREAMBLE: The intensity of radio signals emitted by a transmitter is 100 W/m2 1 m
from the antenna of the transmitter. Assume the antenna emits spherical waves and neglect
the effects of any walls or other materials that may be present. Find the intensity of the radio
signal from the transmitter at the given distance 𝑅 from it.
1. 𝑅 = 5 m
ANSWER: 4 W/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (5 m)2 = 4 W/m2
2. 𝑅 = 10 m
ANSWER: 1 W/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (10 m)2 = 1 W/m2
3. 𝑅 = 100 m
ANSWER: 0.01 W/m2 = 10 mW/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (100 m)2 = 0.01 W/m2
PREAMBLE: The intensity of radio signals emitted by a transmitter is 100 W/m2 1 m
from the antenna of the transmitter. Assume the antenna emits spherical waves and neglect
the effects of any walls or other materials that may be present. Find the intensity of the radio
signal from the transmitter at the given distance 𝑅 from it.
4. 𝑅 = 5 m
ANSWER: 4 W/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (5 m)2 = 4 W/m2
5. 𝑅 = 10 m
ANSWER: 1 W/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (10 m)2 = 1 W/m2
6. 𝑅 = 100 m
ANSWER: 0.01 W/m2 = 10 mW/m2
𝐼 = 𝐼1 𝑅12 /𝑅 2 = 100 W/m2 × 1 m2 ÷ (100 m)2 = 0.01 W/m2
1. The peak voltage of a sinusoidal signal is 10 V. Find its rms voltage.
ANSWER: 7V
𝑉rms = 𝑉peak /√2 = 7 V
2. The rms voltage of a sinusoidal signal is 28 V. Find its peak voltage.
ANSWER: 40 V
𝑉peak = √2𝑉rms = 39.6 V
3. The peak voltage of a pure sinewave signal is 10 V. Find its average voltage.
ANSWER: 0V
The speed of light in vacuum is approximately 3.0 × 108 m/s.Give your answer in standard form.
1. What is the frequency of a green photon whose wavelength is 540 nm?
ANSWER: 5.6 × 1014 Hz
𝑓 = 𝑐/𝜆 = 5. 5̇ × 1014 Hz
2. What is the frequency of the light emitted by a red laser operating at 630 nm?
ANSWER: 4.8 × 1014 Hz
𝑓 = 𝑐/𝜆 = 4.8 × 1014 Hz
3. What is the wavelength of a sodium street lamp whose frequency is 5.1 × 1014 Hz?
ANSWER: 590 nm = 5.9 × 10−9 m
1. PREAMB Determine the speed of a wave with frequency 100 Hz and wavelength 0.5 m.
ANSWER: 50 m/s
2. Find the wavelength of a wave with frequency 500 Hz if the speed of the wave is 200 m/s.
ANSWER: 0.4 m
3. Find the frequency of a wave with wavelength 0.2 m if the speed of the wave is 200 m/s.
ANSWER: 1 kHz
PREAMBLE: A particle has mass 2 × 10−30 kg.The Planck constant is approximately 7 × 10−34 J s.
1. What is the de Broglie wavelength associated withthe particle when it is moving at 700 m/s?
ANSWER: 5 × 10−7 m = 0.5 𝜇m
𝜆 ≅ ℎ/(𝑚𝑣)
2. Find the speed at which the de Broglie wavelength of the particleis 5 𝜇m.
ANSWER: 70 m/s
𝑣 ≅ ℎ/(𝑚𝜆)
3. Find the change in de Broglie wavelength when the speed of the particle changes from 100 m/sto
200 m/s.
ANSWER: −2 𝜇m
ℎ 1 1
Δ𝜆 ≅ ( − ) = −1.75 𝜇m
𝑚 𝑣𝑓 𝑣𝑖
PREAMBLE: The mass per unit length of a string is 0.2 kg/m.
1. Find the speed of waves on the string when a tension of 80 N is applied to it.
ANSWER: 20 m/s
𝑣 = √𝑇/𝜇 = √80 N ÷ 0.2 kg/m = 20 m/s
2. Find the tension required for a wave speed of 50 m/s.
ANSWER: 500 N
𝑇 = 𝑣 2 𝜇 = (50 m/s)2 × 0.2 kg/m = 500 N
3. Find the tension required for a wave speed of 5 m/s.
ANSWER: 5N
𝑇 = 𝑣 2 𝜇 = (5 m/s)2 × 0.2 kg/m = 5 N
1. Rank the following in increasing order of mass: proton, electron, neutron.
ANSWER: Electron, proton, neutron.
2. Rank the following photons in increasing order of energy: infrared, ultraviolet, visible.
ANSWER: Infrared, visible, ultraviolet
3. Rank the following in increasing order of distance from the sun: Mercury, Moon, Venus.
ANSWER: Mercury, Venus, Moon
1. What property of the sound produced by an instrument distinguishes it from the sound
produced by other instruments?
ANSWER: Timbre
Accept quality
2. What property of a sound note is determined by frequency?
ANSWER: Pitch
3. Two notes are one octave apart. What is the relationship between their frequencies?
ANSWER: One is twice the other
A string has mass per unit length 5 g/m.
1. Find the speed of transverse waves on the string when it is under a tension of 200 N.
ANSWER: 200 m/s
𝑣 = √𝑇/𝜇 = √200 N ÷ (5 × 10−3 kg/m) = 200 m/s
2. Find the tension in the string at which the speed of transverse waves on the string is 300 m/s.
ANSWER: 450 N
𝑇 = 𝑣 2 𝜇 = 90000m2 /𝑠 2 × 5 × 10−3 kg/m = 450 N
3. Find the speed of transverse waves on the string when it is under a tension of 8 N.
ANSWER: 40 m/s
𝑣 = √𝑇/𝜇 = √8 N ÷ (5 × 10−3 kg/m) = 40 m/s
4. Find the resultant amplitude when two equal frequency sound waves each of amplitude 5 units interfere
with a phase difference of 4𝜋.
ANSWER: 10 units
Constructive interference
5. Find the resultant amplitude when two equal frequency sound waves each of amplitude 5 units interfere
with a phase difference of 7𝜋.
ANSWER: 0
Destructive interference
6. Find the resultant intensity when two equal frequency sound waves each of intensity 4 units interfere
with a phase difference of 4𝜋.
ANSWER: 16 units
Constructive interference; resultant amplitude is 4 units so resultant intensity is 16 units
