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# Formation of beats - Waves

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 = | f1 - f2| per second ### EXAMPLE 11.18

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.

### Solution

Given λ1 = 5m and λ2 = 6m

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

The relation between wavelength and velocity is v = λf => f = v/λ The number of beats per second is

f1 − f2| = |66 − 55| = 11 beats per sec

### EXAMPLE 11.19

Two vibrating tuning forks produce waves whose equation is given by y1 = 5 sin(240π t) and y2 = 4 sin(244πt). Compute the number of beats per second.

### Solution

Given y1 = 5 sin(240π t) and y2 = 4 sin(244πt)

Comparing with y = A sin(2π f1t), we get

2πf1 = 240π  f1 = 120Hz

2πf2 = 244π  f2 = 122Hz

The number of beats produced is | f1 − f2| = |120 − 122| = |− 2|=2 beats per sec

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