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Communication using waves

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# Frequency, wavelength, amplitude and wave speed

You need to know about these quantities used in waves - what they mean, the symbols used for them and the units used to measure them.

The amplitude, a, of a wave is the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough. Be careful with this quantity - the centre line is not always given in a diagram. Amplitude is measured in metres (m). The greater the amplitude of a wave then the more energy it is carrying.

The wavelength, λ, of a wave is the distance from any point on one wave to the same point on the next wave along. (The symbol is a Greek letter, 'lambda'.) To avoid confusion, it is best to measure wavelength from the top of a crest to the top of the next crest, or from the bottom of a trough to the bottom of the next trough. Wavelength is also measured in metres (m) - it is a length after all.

The frequency, f, of a wave is the number of waves passing a point in a certain time. We normally use a time of one second, so this gives frequency the unit hertz (Hz), since one hertz is equal to one wave per second.

Don't get confused with this quantity frequency. It is not a distance travelled by waves, nor is it a speed, although it is linked to both of these quantities. For water waves and sound waves the unit hertz is usually good enough but radio and TV waves have such a high frequency that the kilohertz (kHz) or even the megahertz (MHz) are better units.

• 1 kHz = 1,000 Hz
• 1 MHz = 1,000,000 Hz

The speed (or sometimes you might see it called velocity) of a wave, v, is how far the wave travels in a certain time.

Wave speed is measured in metres per second (m/s).

All the electromagnetic waves travel at 300,000,000 metres per second (3 x 108 m/s). Sound travels at about 340 metres per second.

Copy out the following table and complete it to give you a summary of these four important quantities used in waves.

QuantitySymbolUnit
amplitude
wavelength
frequency
wave speed

Video: Sound Waves

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## Example question

In the following diagram the waves move from left to right and then stop. The motion of the waves lasts for 2 seconds.

Answer these questions about the waves shown. If you need to, re-run the motion of the waves. Remember to include units where necessary.

Question

What is the amplitude of the waves?

The amplitude of the waves is 0.4 metre (40 cm) - from the centre line to the top of a crest.

Question

What is the wavelength of the waves?

The wavelength of the waves is two metres - from one crest to the next crest along.

Question
• a How many waves are shown on the diagram?
• b So how many waves are generated in the two seconds?
• c So what is the frequency of the waves?
• a Two waves are shown on the diagram.
• b So two waves are generated in the two seconds.
• c So the frequency of the waves is 1 hertz - 1 wave per second.
Question

What is the wave speed?

The wave speed is two metres per second - the waves travel four metres in two seconds. If you are not sure of any of these answers, go back and try again, or re-run these notes.

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