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Waves

Beats

The diagrams below represent graphs of displacement against time for waves of slightly different frequencies, f1 and f2.
...

At t = 0, the two oscillations are in phase with each other. At t = tA, they are in anti-phase and at t = tP they are again in phase.

The next diagram represents the sum of the two waves.

If the graphs represent sound waves, then we would hear a loud sound at t = 0 and t = tP but a quiet sound near t = tA.

These variations in loudness are called beats.

T1 is the time period of wave 1, T2 is the time period of wave 2 and T is the time period of the beats.

If there are N time periods of wave 1 between t = 0 and t = tP, then there will be (N+1) time periods of wave 2.

Therefore, .....................NT1 = T .......and ............(N+1)T2 = T

Eliminating N from these two equations and remembering that frequency = 1/Time period, we find that the beat frequency, f, is given by

f = |.f1 f2.|

 

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