P22: Wave Properties
Transverse and longitudinal waves, wave measurements including amplitude, wavelength and frequency, the wave speed equation, and the ripple tank practical.
What is a Wave?
A wave is a disturbance that transfers energy from one place to another without transferring matter. The substance through which a wave travels is called the medium.
Waves carry energy from a source to an observer. When waves travel through a medium, the particles of the medium oscillate but do not travel with the wave. Only the energy is transferred.
Transverse Waves
In a transverse wave, the oscillations are perpendicular (at right angles) to the direction of energy transfer.
Examples of transverse waves include:
- Light waves and all electromagnetic waves
- Water waves (ripples on a pond)
- Waves on a string (e.g. a vibrating guitar string)
- S-waves (secondary seismic waves)
You can demonstrate transverse waves by shaking a slinky spring up and down or sideways while a partner holds the other end still. The crests of a transverse wave are called peaks and the troughs are the lowest points.
Longitudinal Waves
In a longitudinal wave, the oscillations are parallel to the direction of energy transfer.
Examples of longitudinal waves include:
- Sound waves in air, liquids and solids
- P-waves (primary seismic waves)
- Ultrasound waves
In a longitudinal wave, there are regions of compression (where particles are close together) and rarefaction (where particles are spread apart). You can demonstrate longitudinal waves by pushing and pulling a slinky spring along its length.
Transverse vs Longitudinal Comparison
| Feature | Transverse Wave | Longitudinal Wave |
|---|---|---|
| Oscillation direction | Perpendicular to energy transfer | Parallel to energy transfer |
| Can travel through vacuum | Yes (EM waves can) | No (need a medium) |
| Key features | Peaks and troughs | Compressions and rarefactions |
| Examples | Light, water waves | Sound, P-waves |
| Demonstrated by | Shaking slinky up and down | Pushing slinky along its length |
Wave Measurements
Amplitude is the maximum displacement of a point on a wave from its undisturbed position (the rest position). It is measured in metres (m).
A larger amplitude means a wave carries more energy. For a sound wave, greater amplitude means a louder sound. For a light wave, greater amplitude means a brighter light.
Wavelength is the distance between the same point on two adjacent waves (e.g. from peak to peak, or trough to trough). It is measured in metres (m) and given the symbol λ (lambda).
Frequency is the number of complete waves passing a fixed point per second. It is measured in hertz (Hz). 1 Hz means 1 wave per second. The symbol is f.
For a sound wave, higher frequency means a higher pitch. For a light wave, higher frequency means a colour towards the violet end of the spectrum.
Period is the time taken for one complete wave to pass a fixed point. It is measured in seconds (s). The symbol is T.
Wave Speed Formula
v = f × λ
v = wave speed (m/s)
f = frequency (Hz)
λ = wavelength (m)
The wave speed equation applies to all types of wave. The speed of a wave depends on the medium it is travelling through, not on its frequency or amplitude.
T = 1 / f
T = period (s)
f = frequency (Hz)
Worked Examples
Example 1: Calculating Wave Speed
A wave has a frequency of 250 Hz and a wavelength of 1.3 m. Calculate the wave speed.
v = f × λ
v = 250 × 1.3
v = 325 m/s
Example 2: Calculating Wavelength
A sound wave travels at 330 m/s through air and has a frequency of 440 Hz. Calculate the wavelength.
v = f × λ, so λ = v / f
λ = 330 / 440
λ = 0.75 m
Example 3: Calculating Period
A wave has a frequency of 500 Hz. Calculate its period.
T = 1 / f
T = 1 / 500
T = 0.002 s (or 2 ms)
Example 4: Calculating Frequency from Period
A wave has a period of 0.005 s. Calculate its frequency.
T = 1 / f, so f = 1 / T
f = 1 / 0.005
f = 200 Hz
Measuring Wave Speed in a Ripple Tank
A ripple tank is a shallow tray of water used to study wave behaviour. Vibrating a bar on the water surface produces straight waves whose wavelength and frequency can be measured.
Method:
- Set up the ripple tank with a shallow layer of water and a vibrating bar connected to a signal generator.
- Adjust the frequency of the signal generator to produce waves with a clear wavelength.
- Use a stroboscope or video camera to freeze the wave pattern so you can measure the wavelength.
- Measure the wavelength by finding the distance across several waves and dividing by the number of waves (reduces uncertainty).
- Record the frequency from the signal generator.
- Calculate wave speed using v = f × λ.
- Repeat for different frequencies and calculate a mean value.
To reduce uncertainty in the wavelength measurement, measure the distance across at least 5 complete waves and divide by 5. This reduces the percentage error in the measurement.
Alternative method: Measure the time for a wave to travel a known distance across the ripple tank. Use v = s / t where s is the distance and t is the time. This avoids having to measure wavelength and frequency separately.
Measuring the Speed of Sound in Air
Method 1 — Two microphones and an oscilloscope:
- Connect two microphones to an oscilloscope at a known distance apart.
- Produce a sound (e.g. using a signal generator and speaker).
- Measure the time delay between the signals reaching each microphone on the oscilloscope.
- Calculate speed: v = distance / time.
Method 2 — Echo method:
- Stand a measured distance from a large, flat wall.
- Make a loud sound (e.g. clapping) and measure the time for the echo to return.
- The sound travels to the wall and back, so total distance = 2 × distance to wall.
- Calculate speed: v = 2d / t.
When using the echo method, remember the sound travels there AND back, so you must double the distance. Also, to reduce uncertainty, measure the time for multiple claps (e.g. 10) and divide.
Waves at Boundaries
When a wave reaches a boundary between two different materials, several things can happen:
- Reflection — the wave bounces off the boundary
- Refraction — the wave changes direction as it enters the new material (due to changing speed)
- Transmission — the wave passes through the material
- Absorption — the wave's energy is absorbed by the material (often as thermal energy)
What happens depends on the properties of the two materials and the wavelength of the wave. Glass, for example, transmits visible light but absorbs some ultraviolet.
Practice Questions
1. A wave in the sea has a wavelength of 40 m and a frequency of 0.5 Hz. Calculate the speed of the wave. [2 marks]
v = f × λ = 0.5 × 40 = 20 m/s
2. Describe the difference between a transverse wave and a longitudinal wave. Give one example of each. [4 marks]
In a transverse wave the oscillations are perpendicular to the direction of energy transfer (e.g. light). In a longitudinal wave the oscillations are parallel to the direction of energy transfer (e.g. sound).
3. A sound wave has a period of 0.0025 s. Calculate its frequency. [2 marks]
f = 1 / T = 1 / 0.0025 = 400 Hz
4. Describe how you would use a ripple tank to measure the speed of water waves. Include how you would reduce uncertainty in your measurements. [6 marks]
Set up a ripple tank with a vibrating bar and signal generator. Use a stroboscope or video to freeze the wave pattern. Measure the distance across at least 5 wavelengths and divide by the number of wavelengths to find one wavelength. Record the frequency from the signal generator. Calculate speed using v = f × λ. Repeat for different frequencies and calculate a mean. Measuring multiple wavelengths reduces the percentage uncertainty in the wavelength measurement.
Required Practical: Measuring Wave Speed in a Ripple Tank
You must be able to describe how to measure the speed of waves in a ripple tank and the speed of sound in air. These are required practicals for this topic.
Ripple Tank Method
- Set up a ripple tank with a shallow layer of water and a vibrating bar connected to a signal generator.
- Adjust the frequency on the signal generator to produce waves with a clear, visible wavelength.
- Use a strobe light or video camera to freeze the wave pattern on a screen below the tank.
- Measure the distance across at least 5 complete wavelengths and divide by the number of waves to find one wavelength. This reduces the percentage uncertainty.
- Record the frequency directly from the signal generator display.
- Calculate wave speed using v = f × λ.
- Repeat for three different frequencies and calculate a mean wave speed.
Measuring the Speed of Sound
- Connect two microphones to an oscilloscope placed a measured distance apart (e.g. 1 m).
- Produce a sharp sound near the first microphone using a signal generator and speaker.
- Measure the time delay between the two traces on the oscilloscope screen.
- Calculate speed: v = distance / time.
- Repeat with different separations and calculate a mean value.
Common sources of uncertainty: human reaction time when using a stopwatch (use an oscilloscope instead), difficulty judging the exact position of a wave peak (measure across multiple waves), and parallax error when reading measurements. Always state how you reduce each uncertainty.
Maths Skills
Core Equations
v = f × λ — wave speed = frequency × wavelength
T = 1 / f — period = 1 / frequency
Rearranging the Wave Speed Equation
If v = f × λ, then:
- f = v / λ (use when you know speed and wavelength)
- λ = v / f (use when you know speed and frequency)
A wave travels at 340 m/s with a wavelength of 0.85 m. Find the frequency: f = 340 / 0.85 = 400 Hz.
Interpreting Oscilloscope Traces
- The horizontal axis represents time. One full wave on screen corresponds to one period T.
- Read the timebase setting (e.g. 2 ms/div) and count the divisions for one complete wave.
- Period T = number of divisions × timebase setting. Then f = 1 / T.
- The vertical axis shows amplitude. Count the divisions for the peak height and multiply by the voltage gain setting (Y-gain).
Oscilloscope Calculation
An oscilloscope has a timebase of 5 ms/div. A complete wave spans 4 divisions. Calculate the frequency.
T = 4 × 5 = 20 ms = 0.020 s
f = 1 / T = 1 / 0.020 = 50 Hz
Standard Form and Unit Conversions
- Frequency of 500 kHz = 500,000 Hz = 5 × 10⁵ Hz
- Wavelength of 750 nm = 750 × 10⁻⁹ m = 7.5 × 10⁻⁷ m
- Always convert to SI base units before calculating
Common Misconceptions
"Higher frequency waves travel faster." — In the same medium, all waves of the same type travel at the same speed regardless of frequency. All electromagnetic waves travel at 3 × 10⁸ m/s in a vacuum, whether they are radio waves or gamma rays. The speed is fixed by the medium, not the frequency. A higher frequency wave simply has a shorter wavelength (v = fλ).
"Amplitude affects wave speed." — Changing the amplitude does not change how fast the wave travels. Amplitude affects the energy carried by the wave (larger amplitude = more energy) but has no effect on wave speed. Wave speed depends only on the medium the wave is travelling through. A louder sound travels at the same speed as a quieter sound.
"Sound travels faster in air than in solids because air has less resistance." Sound actually travels fastest in solids because the particles are closer together, allowing vibrations to pass more quickly from particle to particle. Speed of sound: steel (~5000 m/s) > water (~1500 m/s) > air (~340 m/s).
6-Mark Extended Question
Describe how you would measure the speed of water waves in a ripple tank. Explain how to reduce uncertainty in your measurements. [6 marks]
Set up a ripple tank with a shallow layer of water. Connect a vibrating bar to a signal generator and place it on the water surface. Adjust the frequency to produce clear waves. Use a strobe light or video camera to freeze the wave pattern on a screen below the tank. To find the wavelength, measure the distance across at least 5 complete wavelengths and divide by 5. This reduces the percentage uncertainty compared to measuring just one wavelength because any error in the measurement is spread across a larger total distance. Record the frequency directly from the signal generator. Calculate the wave speed using v = f × λ. Repeat the measurement at three different frequencies and calculate a mean value for the wave speed, which improves reliability. To reduce uncertainty further: use a ruler with the smallest possible scale divisions, view the ruler from directly above to avoid parallax error, and ensure the water depth is constant across the tank. An alternative method is to time how long a wave takes to travel a known distance across the tank and use v = s / t.
AO3: Analyse and Evaluate
A student measures the speed of water waves in a ripple tank. They set the signal generator to 4 Hz and measure 5 complete wavelengths as 62 cm. They then change the frequency to 6 Hz and measure 5 wavelengths as 41 cm.
(a) Calculate the wave speed for each frequency.
(b) The two values should be the same. The student obtains 0.496 m/s and 0.492 m/s. Suggest why they are slightly different.
(c) The actual wave speed in this tank is 0.50 m/s. Calculate the percentage error in the mean result and evaluate the accuracy of the method.
(a) At 4 Hz: wavelength = 62 / 5 = 12.4 cm = 0.124 m. Speed = 4 × 0.124 = 0.496 m/s.
At 6 Hz: wavelength = 41 / 5 = 8.2 cm = 0.082 m. Speed = 6 × 0.082 = 0.492 m/s.
(b) The values differ slightly due to measurement uncertainties. The ruler may only read to the nearest millimetre, the wave positions may be difficult to judge precisely, and parallax error when reading the ruler from an angle could shift the reading. The water depth may also not be perfectly uniform.
(c) Mean speed = (0.496 + 0.492) / 2 = 0.494 m/s. Percentage error = |0.494 – 0.50| / 0.50 × 100 = 1.2%. The method is quite accurate with only 1.2% error. To improve accuracy further, the student could measure across more wavelengths (e.g. 10), use a more precise measuring instrument, or use the alternative timing method with a larger distance to reduce the effect of reaction time.
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