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Edexcel GCSE Physics Your notes

4.1 Properties of Waves

Contents
4.1.1 Introduction to Waves
4.1.2 Describing Wave Motion
4.1.3 Transverse & Longitudinal Waves
4.1.4 The Wave Equation
4.1.5 Measuring Wave Speed
4.1.6 Calculating Depth & Distance
4.1.7 Wave Interactions
4.1.8 Refraction
4.1.9 Refraction & Speed
4.1.10 Wave Interactions & Wavelength
4.1.11 Core Practical: Investigating Wave Properties

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4.1.1 Introduction to Waves

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Waves & Energy
Waves transfer energy and information
Waves are described as oscillations or vibrations about a fixed point
For example, ripples cause particles of water to oscillate up and down
Sound waves cause particles of air to vibrate back and forth
In all cases, waves transfer energy without transferring matter

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Examples of Waves
Objects floating on water provide evidence that waves only transfer energy and not matter Your notes

Worked example
The diagram below shows a toy duck bobbing up and down on top of the surface of some water, as
waves pass it underneath.

Explain how the toy duck demonstrates that waves do not transfer matter.

Step 1: Identify the type of wave

The type of wave on the surface of a body of water is a transverse wave
This is because the duck is moving perpendicular to the direction of the wave
Step 2: Describe the motion of the toy duck
The plastic duck moves up and down but does not travel with the wave
Step 3: Explain how this motion demonstrates that waves do not transfer matter
Both transverse and longitudinal waves transfer energy, but not the particles of the medium
This means when a wave travels between two points, no matter actually travels with it, the points on
the wave just vibrate back and forth about fixed positions
Objects floating on the water simply bob up and down when waves pass under them,
demonstrating that there is no movement of matter in the direction of the wave, only energy

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4.1.2 Describing Wave Motion

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Describing Wave Motion
When describing wave motion, there are several terms which are important to know, including:
Amplitude
Wavelength
Frequency
Time Period
Wave velocity
Wavefront
Amplitude
Amplitude is defined as:
The distance from the undisturbed position to the peak or trough of a wave
It is given the symbol A and is measured in metres (m)
Amplitude is the maximum or minimum displacement from the undisturbed position
Wavelength
Wavelength is defined as
The distance from one point on the wave to the same point on the next wave.
In a transverse wave:
The wavelength can be measured from one peak to the next peak
In a longitudinal wave
The wavelength can be measured from the centre of one compression to the centre of the next
The wavelength is given the symbol λ (lambda) and is measured in metres (m)
The distance along a wave is typically put on the x-axis of a wave diagram

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Your notes

Diagram showing the amplitude and wavelength of a wave

Frequency
Frequency is defined as:
The number of waves passing a point in a second
Frequency is given the symbol f and is measured in Hertz (Hz)
Time Period
The time period (or sometimes just 'period') of a wave is defined as:
The time taken for a single wave to pass a point
The time period is given the symbol T and is measured in seconds (s)

Wave Velocity
Wave velocity (or wave speed) is defined as:
The distance travelled by a wave each second
Wavefront

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Wavefronts are a useful way of picturing waves from above: each wavefront is used to represent a
single wave
The image below illustrates how wavefronts are visualised: Your notes
The arrow shows the direction the wave is moving and is sometimes called a ray
The space between each wavefront represents the wavelength
When the wavefronts are close together, this represents a wave with a short wavelength
When the wavefronts are far apart, this represents a wave with a long wavelength

Diagram showing a wave moving to the right, drawn as a series of wavefronts

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4.1.3 Transverse & Longitudinal Waves

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Transverse & Longitudinal Waves
Waves are repeated vibrations that transfer energy
Energy is transferred by parts of the wave knocking nearby parts
This is similar to the effect of people knocking into one another in a crowd, or a "Mexican Wave" at
football matches
Waves can exist as one of two types:
Transverse
Longitudinal
Transverse Waves
Transverse waves are defined as:
Waves where the points along its length vibrate at 90 degrees to the direction of energy
transfer
For a transverse wave:
The energy transfer is perpendicular to wave motion
They transfer energy, but not the particles of the medium
They can move in solids and on the surfaces of liquids but not inside liquids or gases
Some transverse waves (electromagnetic waves) can move in solids, liquids and gases and in a
vacuum
The point on the wave that is:
The highest above the rest position is called the peak, or crest
The lowest below the rest position is called the trough

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Your notes

Transverse waves can be seen in a rope when it is moved quickly up and down
Examples of transverse waves are:
Ripples on the surface of water
Vibrations in a guitar string
S-waves (a type of seismic wave)
Electromagnetic waves (such as radio, light, X-rays etc)
Representing Transverse Waves
Transverse waves are drawn as a single continuous line, usually with a central line showing the
undisturbed position
The curves are drawn so that they are perpendicular to the direction of energy transfer
These represent the peaks and troughs

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Your notes

Transverse waves are represented as a continuous solid line

Longitudinal Waves
Longitudinal waves are defined as:
Waves where the points along its length vibrate parallel to the direction of energy transfer
For a longitudinal wave:
The energy transfer is in the same direction as the wave motion
They transfer energy, but not the particles of the medium
They can move in solids, liquids and gases
They can not move in a vacuum (since there are no particles)
The key features of a longitudinal wave are where the points are:
Close together, called compressions
Spaced apart, called rarefactions

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Your notes

Longitudinal waves can be seen in a slinky spring when it is moved quickly backwards and forwards
Examples of longitudinal waves are:
Sound waves
P-waves (a type of seismic wave)
Pressure waves caused by repeated movements in a liquid or gas
Representing Longitudinal Waves
Longitudinal waves are usually drawn as several lines to show that the wave is moving parallel to the
direction of energy transfer
Drawing the lines closer together represents the compressions
Drawing the lines further apart represents the rarefactions

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Longitudinal waves are represented as sets of lines with rarefactions and compressions
Comparing Transverse & Longitudinal Waves Your notes
Wave vibrations can be shown on ropes (transverse) and springs (longitudinal)

Waves can be shown through vibrations in ropes or springs

The different properties of transverse and longitudinal waves are shown in the table:

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Transverse Waves v Longitudinal Waves Table

Your notes

Worked example
The diagram below shows the direction of a P-wave in a sample of rock during an earthquake.

Draw arrows on the diagram to show how the piece of rock, labelled R, moves as the P-wave passes
through it.

Step 1: Recall if a P-wave is transverse or longitudinal

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P-waves are longitudinal waves

Step 2: Recall the definition of longitudinal waves Your notes
Points along longitudinal waves vibrate parallel to the direction of energy transfer
This means the rock vibrates in a line parallel to the direction of the P-wave drawn
Step 3: Draw arrows at the point labelled R to show it vibrating in parallel to the direction of the
P-wave
This is shown in the image below

Examiner Tip
Exam questions may ask you to describe waves and this is most easily done by drawing a diagram of
the wave and then describing the parts of the wave - a good, clearly labelled diagram can earn you full
marks! Make sure you know the difference between the wavefront diagram and the longitudinal wave
diagram, do not confuse the two!

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4.1.4 The Wave Equation

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The Wave Equation
Wave speed is defined as:
The distance travelled by a wave each second
The wave speed can be calculated in a similar way to calculating the speed of moving objects:

Where:
v = wave speed in metres per second (m/s)
x = distance travelled by the wave in metres (m)
t = time taken in seconds (s)
All waves obey the wave equation, which is another way to calculate the wave speed:

Where:
v = wave speed in metres per second (m/s)
f = frequency in Hertz (Hz)
λ = wavelength in metres (m)

The wave speed equation may need to be rearranged, which can be done using this formula triangle:

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Your notes

Worked example
A wave in a pond has a speed of 0.15 m/s and a time period of 2 seconds.Calculate:
a) The frequency of the wave
b) The wavelength of the wave

Part (a)
Step 1: List the known quantities
Time period, T = 2 s
Step 2: Write out the equation relating time period and frequency

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Your notes

Step 3: Rearrange for frequency, f, and calculate the answer

f=1÷T=1÷2
Frequency, f = 0.5 Hz
Part (b)
Step 1: List the known quantities
Wave speed, v = 0.15 m/s
Frequency, f = 0.5 Hz
Step 2: Write out the wave speed equation
v=f×λ
Step 3: Rearrange the equation to calculate the wavelength
λ=v÷f

Step 4: Use the frequency you calculated in part (a) and put the values into the equation
λ = 0.15 ÷ 0.5

Wavelength, λ = 0.30 m

Examiner Tip
When stating equations make sure you use the right letters:
For example, use λ for wavelength, not L or W
If you can’t remember the correct letters, then just state the word equations
Be careful with units: wavelength is usually measured in metres and speed in m/s, but if the wavelength
is given in cm you might have to give the speed in cm/s
Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

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4.1.5 Measuring Wave Speed

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Measuring Wave Speed
Experiments to Determine the Speed of Sound in Air
There are several experiments that can be carried out to determine the speed of sound
Three methods are described below
The apparatus for each experiment is given in bold
Method 1: Measuring Sound Between Two Points

Measuring the speed of sound directly between two points

1. Two people stand a distance of around 100 m apart
2. The distance between them is measured using a trundle wheel
3. One person has two wooden blocks, which they bang together above their head
4. The second person has a stopwatch which they start when they see the first person banging the blocks
together and stops when they hear the sound
5. This is then repeated several times and an average value is taken for the time
6. The speed of sound can then be calculated using the equation:

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Your notes

Method 2: Using Echoes

Measuring the speed of sound using echoes

1. A person stands about 50 m away from a wall (or cliff) using a trundle wheel to measure this distance
2. The person claps two wooden blocks together and listens for the echo
3. The person then starts to clap the blocks together repeatedly, in rhythm with the echoes
4. A second person has a stopwatch and starts timing when they hear one of the claps and stops timing
20 claps later
5. The process is then repeated and an average time calculated
6. The distance travelled by the sound between each clap and echo will be (2 × 50) m
7. The total distance travelled by sound during the 20 claps will be (20 × 2 × 50) m
8. The speed of sound can be calculated from this distance and the time using the equation:

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Your notes

Method 3: Using an Oscilloscope

Measuring the speed of sound using an oscilloscope

1. Two microphones are connected to an oscilloscope and placed about 5 m apart using a tape measure
to measure the distance
2. The oscilloscope is set up so that it triggers when the first microphone detects a sound, and the time
base is adjusted so that the sound arriving at both microphones can be seen on the screen
3. Two wooden blocks are used to make a large clap next to the first microphone
4. The oscilloscope is then used to determine the time at which the clap reaches each microphone and
the time difference between them
5. This is repeated several times and an average time difference calculated
6. The speed can then be calculated using the equation:

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Measuring the Speed of Ripples on Water Surfaces

Your notes

Creating ripples in water

1. Choose a calm flat water surface such as a lake or a swimming pool
2. Two people stand a few metres apart using a tape measure to measure this distance
3. One person counts down from three and then disturbs the water surface (using their hand, for example)
to create a ripple
4. The second person then starts a stopwatch to time how long it takes for the first ripple to get to them
5. The experiment is then repeated 10 times and an average value for the time is calculated
6. The average time and distance can then be used to calculate the wave speed using the equation:

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Worked example
Your notes
Small water waves are created in a ripple tank by a wooden bar. The wooden bar vibrates up and down
hitting the surface of the water. The diagram below shows a cross-section of the ripple tank and water.

Which letter shows:

a) The amplitude of a water wave?
b) The wavelength of the water wave?

Part (a)
Step 1: Recall the definition of amplitude
Amplitude = The distance from the undisturbed position to the peak or trough of a wave
Step 2: Mark the undisturbed position on the wave
This is the centre of the wave

Step 3: Identify the arrow between the undisturbed position and a peak
The amplitude is arrow D

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Part (b)
Step 1: Recall the definition of wavelength Your notes
Wavelength = The distance from one point on the wave to the same point on the next wave
Step 2: Draw lines on each horizontal arrow
This helps to identify the points on the wave the arrows are referring to

Step 3: Identify the arrow between two of the same points on the wave
The wavelength is arrow C

Examiner Tip
When you are answering questions about methods to measure waves, the question could ask you to
comment on the accuracy of the measurements
In the case of measuring the speed of sound:
Method 3 is the most accurate because the timing is done automatically
Method 1 is the least accurate because the time interval is very short
Whilst this may not be too important when giving a method, you should be able to explain why each
method is accurate or inaccurate and suggest ways of making them better (use bigger distances)
For example, if a manual stopwatch is being used there could be variation in the time measured
which can be up to 0.2 seconds due to a person's reaction time
The time interval could be as little as 0.3 seconds for sound travelling in air
This means that the variation due to the stopwatch readings has a big influence on the results and
they may not be reliable

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4.1.6 Calculating Depth & Distance

Your notes
Calculating Depth & Distance
Higher Tier Only
If the speed of a wave is known, it can be used to calculate the distance to an object, or the depth of an
object - say, underwater
Calculating Distance
The worked example below demonstrates how the speed of sound in air can be used to determine
how far away objects are from an observer

Worked example
A clap of thunder is heard 4 seconds after the corresponding flash of lightning.How far away is the
thunderstorm? (The speed of sound in air is 330 m/s)
Step 1: List the known quantities
Wave speed, v = 330 m/s
Time, t = 4 s
Step 2: Write out the wave speed, distance and time formula

Step 3: Re-arrange the equation to make distance (x) the subject

x=v×t
Step 4: Put known values into the equation
x = 330 × 4 = 1320 m
So the distance to the thunderstorm is 1320 m

Calculating Depth
Echo sounding uses ultrasound to detect objects underwater
The sound wave is reflected off the ocean bottom
The time it takes for the sound wave to return is used to calculate the depth of the water
The distance the wave travels is twice the depth of the ocean

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This is the distance to the ocean floor plus the distance for the wave to return

Your notes

Echo sounding is used to determine water depth

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Worked example
Your notes
The sound wave released from a ship took 0.12 seconds to return. The speed of sound in water is 1500
m/s.What was the depth of the sea?
Step 1: List the known quantities
Wave speed, v = 1500 m/s
Time, t = 0.12 s
Step 2: Write out the wave speed, distance and time formula

Step 3: Rearrange the equation to make distance (x) the subject

x=v×t
Step 4: Put known values into the equation
x = 1500 × 0.12 = 180 m
Step 5: Half the distance to obtain the depth
d = 180 ÷ 2
Depth, d = 90 m

Examiner Tip
Don't forget to take into account if a sound wave has travelled twice the distanceYou can do this one
of two ways:
Halve the time at the beginning, or
Halve the distance at the end

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4.1.7 Wave Interactions

Your notes
Wave Interactions
When a wave reaches an interface (or boundary) between two materials - for example, air and water -
the wave may be:
Reflected
Refracted
Transmitted
Absorbed
Reflection
Reflection occurs when:
A wave hits a boundary between two media and does not pass through, but instead stays
in the original medium
Some of the wave may also be absorbed or transmitted
Echos are examples of sound waves being reflected off a surface
Flat surfaces are the most reflective
The smoother the surface, the stronger the reflected wave is
Rough surfaces are the least reflective
This is because the light scatters in all directions
Opaque surfaces will reflect light which is not absorbed by the material
The electrons will absorb the light energy, then reemit it as a reflected wave
Refraction
Refraction occurs when:
A wave changes speed at the boundary between two materials of different densities
Glass and water are both denser than air, so light waves passing from air into them will slow down (and
speed up if going from them into air)
The change in speed at the boundary can sometimes causes the wave to change direction
Lenses make use of refraction to bend light waves and help focus it in glasses and cameras
Sound, water, electromagnetic and seismic waves can all be refracted
Transmission
Transmission occurs when:
A wave passes through a substance

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For light waves, the more transparent the material, the more light will pass through
Transmission can involve refraction but is not exactly the same
For the process to count as transmission, the wave must pass through the material and emerge from Your notes
the other side
When passing through a material, waves are usually partially absorbed
The transmitted wave may have a lower amplitude because of some absorption
For example, sound waves are quieter after they pass through a wall

When a wave passes through a boundary it may be absorbed and transmitted

Absorption
Absorption occurs when:
Energy is transferred from the wave into the particles of a substance
Waves can be partially or completely absorbed
Sound waves are absorbed by brick or concrete in houses
Light will be absorbed if the frequency of light matches the energy levels of the electrons
The light will be absorbed, and then reemitted over time as heat
If an object appears red, this means:
Only red light has been reflected
All the other frequencies of visible light have been absorbed

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Your notes

The object is seen as red since the red light is reflected whilst the other colours are absorbed

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4.1.8 Refraction
Your notes
Refraction
Refraction can occur when a wave crosses a boundary between two materials with different densities
In some cases, the wave will change direction
The ray diagram below illustrates the change of direction of a light ray at a water-air boundary:

Waves can change direction when moving between materials with different densities
Refraction of light
Refraction also occurs when light passes a boundary between two different transparent media
At the boundary, the rays of light undergo a change in direction
The direction is taken as the angle from the normal
The change in direction depends on the difference in density between the two media:
From less dense to more dense (e.g air to glass), light bends towards the normal
From more dense to less dense (e.g. glass to air), light bends away from the normal
When passing along the normal (perpendicular) the light does not bend at all
Refraction of Light Through a Glass Block

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Your notes

Light enters the glass where the light ray bends towards the normal. Light bends away from the normal
as it exits the glass
The change in direction occurs due to the change in speed when travelling in different substances
When light passes into a denser substance the rays will slow down, hence they bend towards the
normal
As with refraction of water waves, the only properties that change during refraction of light are speed
and wavelength – the frequency of waves does not change
Different frequencies account for different colours of light (red has a low frequency, whilst blue
has a high frequency)
When light refracts, it does not change colour (think of a pencil in a glass of water), therefore, the
frequency does not change

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4.1.9 Refraction & Speed

Your notes
Refraction & Speed
Higher Tier Only
When a wave hits a different medium the different parts of the wave enter the medium at different
times
Hence, this leads to a change in speed
The difference in speed between the parts of the wave in the first medium and the parts in the second
medium causes the wave to bend
Hence, this leads to a change in direction
Refraction can be represented using wavefront diagrams, as shown below:

The different parts of the wave enter the second medium at different times causing the wave to bend

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4.1.10 Wave Interactions & Wavelength

Your notes
Wave Interactions & Wavelength
Higher Tier Only
When waves move from one substance to another the waves might be:
Transmitted
Absorbed
Reflected
Refracted

When waves move from one medium to another they can be transmitted, reflected, refracted or
absorbed
Materials interact differently with waves depending on their wavelength
Whilst some wavelengths might be transmitted, others might be reflected, refracted or absorbed
For example, glass will:
Transmit and/or refract visible light
Absorb UV radiation
Reflect IR radiation

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4.1.11 Core Practical: Investigating Wave Properties

Your notes
Core Practical 2: Investigating Wave Properties
Equipment List

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Your notes

Resolution of measuring equipment:

Metre ruler = 1 mm
Stopwatch = 0.01 s
Signal generator ~ 10 nHz
Experiment 1: Water Waves in a Ripple Tank
Aims of the Experiment
To measure frequency, wavelength and wave speed by observing water waves in a ripple tank
Variables
Independent variable = frequency, f
Dependent variable = wavelength, λ
Control variables:
Same depth of water
Same temperature of water
Method

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Your notes

Set up of ripple tank to investigate wave properties

1. Set up the apparatus as shown and fill the ripple tank with water to a depth of no more than 1 cm
2. Turn on the power supply and the light source to produce a wave pattern on the screen
3. The wavelength of the waves can be determined by using a ruler to measure the length of the screen
and dividing this distance by the number of wavefronts
4. The frequency can be determined by timing how long it takes for a given number of waves to pass a
particular point and dividing the number of wavefronts by the time taken
5. Record the frequency and wavelength in a table and repeat the measurements
An example of the data collection table is shown below:

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Your notes

Analysis of Results
The speed of the waves can be determined using the equation:
Wave Speed = Frequency × Wavelength
v = fλ
Where:
v = wave speed in metres per second (m/s)
f = frequency in Hertz (Hz)
λ = wavelength in metres (m)

Experiment 2: Stationary Waves on a Vibrating String

Aim of the Experiment
To measure frequency, wavelength and wave speed by observing waves on a stretched string or elastic
cord
Variables
Independent variable = frequency, f
Dependent variable = wavelength, λ
Control variables:
Same string
Same masses attached to string
Same length of string
Method

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Your notes

Set up of apparatus to investigate wave properties of a vibrating string

1. Set up the apparatus as shown, then adjust the frequency of the signal generator until a stationary
wave is produced
2. Once the stationary wave is produced, record the frequency shown on the signal generator
3. Use a ruler to measure the wavelength, the length to measure will depend on the number of stationary
waves produced. Or measure the length of multiple wavelengths, and divide by the number of
wavelengths seen
4. Repeat the procedure by adjusting the frequency until another stationary wave is produced

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Your notes

Guide to measuring the wavelength of stationary waves

An example of the data collection table is shown below:

Analysis of Results
The speed of each wave can be determined using the equation:
Wave Speed = Frequency × Wavelength
v = fλ
Evaluating the Experiment
Systematic Errors:
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It can be difficult to identify the wavefronts while they are moving

Use a stroboscope (flashing light) matched to the same frequency of the waves, this will be
indicated by the waves appearing to be stationary Your notes
The frequency can be read from the frequency setting of the stroboscope, and the wavelength will
be easier to determine while the waves appear still
Random Errors:
To improve the accuracy of the wavelength measurement in the ripple tank:
Measure across a number of waves (e.g. 5 of them) and then divide the distance by the number of
waves
To improve the accuracy of the frequency measurement in the ripple tank:
Measure across a longer time period (e.g. a minute) and then divide the number of waves by the
time
When taking repeat measurements of the frequency of the stationary wave, the best procedure is as
follows:
Determine the frequency of the stationary wave when the largest vibration is observed and note
down the frequency at this point
Increase the frequency and then gradually reduce it until the stationary wave is clearly observed
again and note down the frequency of this
If taking three repeat readings, repeat this procedure again
Average the three readings and move onto the next measurement
Safety Considerations
Care should be taken when working with water and electricity in close proximity
Carelessness could lead to electric shock
No food or drink should be consumed near the experiment
If using strobe lighting to see the wavefronts more clearly, ensure no one in the room has
photosensitive epilepsy
Make sure to stand up during the whole experiment, to react quickly to any spills
Use a rubber string instead of a metal wire, in case it snaps under tension
Wear safety goggles to protect the eyes in case the string or cord snaps
Stand well away from the masses in case they fall onto the floor
Place a crash mat or any soft surface under the masses to break their fall

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