Measuring wave velocity Revision Notes for AQA GCSE Physics Combined Science

Measuring wave velocity

Being able to find out how fast waves travel is important in physics. You'll need to know how to work out the speed of sound through air and how fast ripples move across water surfaces.

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Understanding wave velocity is essential for many areas of physics, from acoustics to seismology, and forms the foundation for more advanced wave phenomena.

Understanding wave speed

Wave speed tells us how quickly a wave moves from one place to another. There are two main ways to calculate this:

Using distance and time: $v = \frac{d}{t}$ (measured in m/s)
Using wave properties: $v = f \times \lambda$ (measured in m/s)

The first method works when you can measure how far a wave travels and how long it takes. The second method uses the wave's frequency (how many waves per second) and wavelength (the length of one complete wave).

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The symbol $v$ represents velocity/speed, $d$ represents distance, $t$ represents time, $f$ represents frequency, and $\lambda$ (lambda) represents wavelength.

Finding the speed of sound in air

Method 1: The echo technique

This method uses the fact that sound bounces back from surfaces.

Steps to follow:

Stand a measured distance away from a large wall or building
Make a sharp sound (like clapping your hands)
Use a stopwatch to time how long it takes to hear the echo come back
Calculate the speed using: $v = \frac{d}{t}$

chatImportant

Remember the sound travels to the wall AND back again, so the total distance is twice the distance to the wall.

Getting better results: Repeat this several times at different distances. This gives you more accurate results and helps reduce errors.

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Taking multiple measurements allows you to calculate an average, which reduces the impact of random errors and gives a more reliable result.

Method 2: Using microphones and an oscilloscope

This method compares sound waves at different positions.

Equipment needed:

Two microphones
An oscilloscope (shows sound waves on a screen)
A loudspeaker

Steps to follow:

Place both microphones in a straight line from the loudspeaker, with one closer than the other
Set the loudspeaker to make a sound with a known frequency
Look at the wave patterns on the oscilloscope screen
Move the microphones until the wave patterns are exactly one wavelength apart
Measure the distance between the microphones - this equals one wavelength
Calculate speed using: $v = f \times \lambda$

Finding the speed of ripples on water

You can measure how fast water waves travel using a ripple tank.

Equipment setup:

A shallow tank filled with water
A paddle that vibrates at a known frequency
A strobe light that can "freeze" the wave pattern
A screen underneath to see the wave shadows clearly

How it works:

Set the paddle vibrating at a steady frequency to create regular ripples
Use the strobe light to make the wave pattern appear to stand still
Measure the distance between wave crests - this gives you the wavelength
Calculate the wave speed using: $v = f \times \lambda$

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The strobe light is crucial because it lets you see the moving waves clearly enough to measure them accurately. This technique is called stroboscopic analysis.

Worked examples

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Worked Example 1: Echo method

A student claps 480m from a wall and hears the echo 3 seconds later.

Step 1: Calculate total distance Total distance travelled = $480m \times 2 = 960m$ (there and back)

Step 2: Apply the formula

Time taken = 3s
Speed = $\frac{960m}{3s} = 320m/s$

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Worked Example 2: Microphone method

Two microphones are 35cm apart when their signals are one wavelength apart. The sound frequency is 1000Hz.

Step 1: Identify known values

Wavelength = 0.35m
Frequency = 1000Hz

Step 2: Apply the wave equation Wave speed = $f \times \lambda = 1000Hz \times 0.35m = 350m/s$

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Worked Example 3: Ripple tank

A ripple tank paddle vibrates at 4Hz and creates ripples with wavelengths of 8cm.

Step 1: Convert units

Frequency = 4Hz
Wavelength = 8cm = 0.08m

Step 2: Calculate wave speed Wave speed = $f \times \lambda = 4Hz \times 0.08m = 0.32m/s$

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Key Points to Remember:

Two key equations: $v = \frac{d}{t}$ and $v = f \times \lambda$
Echo method: Sound travels to the reflecting surface and back, so double the distance
Microphone method: Move microphones until wave patterns are exactly one wavelength apart
Ripple tank method: Use a strobe light to "freeze" the wave pattern for measurement
Always repeat measurements several times to get more accurate results

Measuring wave velocity (AQA GCSE Physics Combined Science): Revision Notes