Beats & Echo - Notes | Study Physics Class 11 - NEET

10. Beats 

When two sources of sound that have almost the same frequency are sounded together, an interesting phenomenon occurs. A sound with a frequency average of the two is heard and the loudness of sound repeatedly grows and then decays, rather than being constant. Such a repeated variation in amplitude of sound are called 'beats".

If the frequency of one of the source is changed, there is a corresponding change in the rate at which the amplitude varies. This rate is called beat frequency. As the frequencies come close together, the beat frequency becomes slower. A musician can tune a guitar to another source by listening for the beats while increasing or decreasing the tension in each string, eventually the beat frequency becomes very low so that effectively no beats are heard, and the two sources are then in tune.

We can also explain the phenomenon of beat mathematically. Let us consider the two superposing waves have frequencies n₁ and n₂ then their respective equations of oscillation are

On superposition at a point, the displacement of the medium particle is given as

There equation (4) gives the displacement of medium particle where superposition takes place, it shows that the particle executes SHM with frequency , average of the two superposing frequencies and with amplitude R which varies with time, given as

 ...(5)

Here R becomes maximum when

or  [N Î I]

or

or at time

At all the above time instants the sound of maximum loudness is heard, similarly we can find the time instance when the loudness of sound is minimum, it occurs when

or  [N Î I]

or

or at time instants

Here we can see that these time instants are exactly lying in the middle of the instance when loudest sound is heard. Thus on superposition of the above two frequencies at a medium particle, the sound will be increasing, decreasing, again increasing and decreasing and so on. This effect is called beats. Here the time between two successive maximum or minimum sounds is called beat period, which is given as

Beat Period T_B = time between two successive maxima = time between two successive minima

Thus beat frequency or number of beats heard per second can be given as

The superposition of two waves of slightly different frequencies is graphically shown in figure. The resulting envelope of the wave formed after superposition is also shown in figure (b). Such a wave when propagates, produces "beat" effect at the medium particles.

10.1 Echo 

The repetition of sound produced due to reflection by a distant extended surface like a different, hill well, building etc. is called an echo. The effect of sound on human ear remains for approximately one tenth of a second. If the sound is reflected back in a time less then 1/10 of a second, no echo is heard. Hence human ears are not able to distinguish a beat frequency of 10 Hz or more than 10 Hz.