Formation of beats - Waves

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 Î»1 = 5m and Î»2 = 6m

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

The relation between wavelength and velocity is v = Î»f => f = v/λ

The number of beats per second is

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

EXAMPLE 11.19

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

Solution

Given y1 = 5 sin(240Ï€ t) and y2 = 4 sin(244Ï€t)

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

2Ï€f1 = 240Ï€ â‡’ f1 = 120Hz

2Ï€f2 = 244Ï€ â‡’ f2 = 122Hz

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