Beats

Beats are produced when two waves whose frequencies are only slightly different interfere with each other. If we think of the two waves as being initially in phase with each other, then they will interfere constructively and produce a larger wave. However, some time later one of the waves will have drifted out of phase with the other, and the waves will interfere destuctively. Later on the interference becomes constructive again, and so on. When applied to sound this produces the familiar 'wowing' sound which is used to tune interuments. The time taken for the sound to progress from constructive to destructive interference and back again depends only on the difference in frequency of the two original waves, and is described by a beat frequency f_b = | f₁ - f₂ |. When the two frequencies are equal the beats disappear.

In this picture two waves of equal amplitude are interfering. You can control the centre or nominal frequency of the waves and also introduce a small frequency difference between them. When you have set these two controls, click on the centre panel and the computer will draw out the wave.

What to look for:

1. First set the centre frequency to 20, and the frequency difference to 1. Click on the panel to see the pattern. You should see a wave whose amplitude is not a constant. Make a mental note of where the amplitude of the wave becomes zero (or close to zero).
2. Now change the centre frequency while keeping the frequency difference equal to 1. What happens to the picture?
3. Set the centre frequency to 20 again, and the frequency difference to 1. Keep the centre frequency equal to 20, and change the frequency difference. What happens to the picture in this case?