   Wave Speed
Introduction

During a storm you will always see lightning before you hear the thunder. This is because light waves travel a million times faster than sound waves.

It is important to know the speed of a wave, because this is the speed at which the energy it carries is transferred from one place to another.
Measuring the speed
The
speed
Speed is a measure of how fast something is moving. It is calculated by dividing the distance travelled by the time taken.
speed
of a wave measures how far one particular crest (or trough) moves in a given amount of time. The letter v is used to represent the speed of a wave.

Look at the experiment in Fig.1 below. These are waves moving in a ripple tank.

 Figure 1. Waves in a ripple tank. Use the control bar to vary the frequency. Increase the
frequency
In general, the frequency of an event describes how often it occurs. When talking about waves, the frequency is a measure of how many waves go past a fixed point in a given time.
frequency
of the waves by dragging up on the control bar.

What happens to the
wavelength
The wavelength of a wave is the distance from one peak to the next, or from one trough to the next.
wavelength
when you increase the frequency?
• Now reduce the frequency of the waves.

What happens to the wavelength when you decrease the frequency?
• What happens to the speed of the waves as you change the frequency?
• Calculating the speed
The equation below relates the speed of a wave (v) to its frequency (f) and its wavelength (λ).

If frequency is measured in hertz (Hz), wavelength in metres (m) then the speed is in metres per second (m/s)

Follow the steps below to work through an example. 8 waves go past every second and each wave is 4 metres long. What is the speed of the waves? The frequency, f = 8 Hz. The wavelength, λ = 4 m. The speed of the waves is given by f × λ.
 The speed is 8 × 4 = 32m/s .

You throw a stone into a pond. You notice that 2 waves reach the shore every second. You also notice that each wave is the length of a duck, around 30 cm. What is the speed of the waves in this pond?
• The wavelength of a certain radio station is 200 m. The speed of the radio waves is 300,000,000 m/s. What is the frequency of this radio station?
•  Hz
• As you have seen, the speed of a wave does not usually depend on its frequency. It only depends on the material the wave is moving through. Waves move faster down a tight spring than a slack one. Light travels faster through air than through glass. Sound moves faster through glass than through air.

Summary

Wave speed, wavelength, and frequency are related by the equation:

The speed of a wave depends upon the material it is travelling through.

Exercises
1. You are making waves on a rope by shaking it from side to side. Decide what happens to each of the wave properties listed below when you slow down how often you shake the rope.
•  Frequency Decreases Does not change Increases Wavelength Decreases Does not change Increases Speed Decreases Does not change Increases
• 2. The frequency of a sports radio station is 909 kHz. The speed of the radio waves is 300,000,000 m/s. Calculate (to the nearest whole number) the wavelength of these radio waves.
•  m
• 3. The speed of sound is 330 m/s. The musical note E has a frequency of 330 Hz. What is the wavelength of the note E?
•  m
• 4. The musical note middle C has a wavelength of 1.3 m. What is the frequency of middle C?
• 5. The period of a wave on the sea is 5 seconds. The wavelength is 80 metres. What is the frequency and speed of this wave?

•  Frequency: Hz Speed: m/s

• Figure 2. 6. Fig.2 shows the side view of a water wave in a ripple tank. As you watch the wave, you count 5 wave crests go past in 10 seconds. Calculate the
amplitude
In general, the amplitude of a quantity is a measure of its size. When talking about waves, the amplitude of a wave is the maximum height of a wave measured from its rest position.
amplitude
, wavelength, frequency, period and speed of the wave.

•  Amplitude: cm Wavelength: cm Frequency: Hz Period: s Speed: cm/s

• Well done!
Try again!