When two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed.

Formation of beats

When two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed. This phenomenon is known as beats. The number of amplitude maxima per second is called beat frequency. If we have two sources, then their difference in frequency gives the beat frequency.

Number of beats per second

n = | *f*1 - *f*2| per second

Consider two sound waves with wavelengths 5 *m* and 6 *m*. If these two waves propagate in a gas with velocity 330 *ms*-1. Calculate the number of beats per second.

Given *λ*1 = 5*m* and *λ*2 = 6*m*

Velocity of sound waves in a gas is *v *= 330* ms*-1

The relation between wavelength and velocity is *v* = *λf* => *f** *= v/λ

The number of beats per second is

| *f*1 − *f*2| = |66 − 55| = 11 beats per sec

Two vibrating tuning forks produce waves whose equation is given by *y*1 = 5 sin(240*π t*) and *y*2 = 4 sin(244*πt*). Compute the number of beats per second.

Given *y*1 = 5 sin(240*π t*) and *y*2 = 4 sin(244*πt*)

Comparing with *y* = *A* sin(2*π f*1*t*), we get

2*πf*1 = 240*π* ⇒ *f*1 = 120*Hz*

2*πf*2 = 244*π* ⇒ *f*2 = 122*Hz*

The number of beats produced is | *f*1 − *f*2| = |120 − 122| = |− 2|=2 beats per sec

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11th Physics : Waves : Formation of beats - Waves |

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