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# Beats

BEATS
If two tuning fork whose frequency is slightly different are sounded together , the sound we hear periodically fluctuates in intensity , i.e intensity increases and decreases suddenly . This periodic variations in intensity of sound are called beats.

So we can define “ Beats are periodic vibration in the intensity of sound when two sound wave of nearly same frequency travel in the same direction. One loud sound followed by a faint sound from one beat and the number of beats formed per second is called beat frequency”.

Graphical method for the formation of beats-

As shown in fig (a) Two waves ( One in dotted and other in dark line). When they superimpose then due to the superposition principle , at T=0 the intensity becomes max and at T= T/2 Intensity becomes minimum which is ‘0’ . This process happening again and again.

And number of beats per second or beats frequency is equal to difference in frequency between these two waves.

Suppose the beat period is T and that during this time one wave of frequency n1 , makes one cycle more than the other wave of frequency n2 . The number of cycle of frequency n1 in time T = n1T. And number of cycle of frequency n2 in time T = n2T.

According to the given condition, n1T-n2T = 1

Or

n1-n2 = 1/T = n0 (resultant frequency).

Analysis of graph shown in figure-

(1)The resultant wave oscillates with the average of the frequencies of the individual waves .

(2) The resultant amplitude oscillates with a beat frequency that is equal to the difference between the two frequencies.

Application of beat phenomenon

(i) Determination of unknown frequency