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.
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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?
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Now reduce the frequency of the waves.

What happens to the wavelength when you decrease the frequency?
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What happens to the speed of the waves as you change the frequency?
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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?
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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
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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
    Wavelength
    Speed
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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
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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
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4. The musical note middle C has a wavelength of 1.3 m. What is the frequency of middle C?
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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

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Figure 2.  
Display as fullscreen
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

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