Three sound waves of equal amplitudes have frequencies `(v - 1), v, (v + 1)`. They superpose to give beats. The number of beats produced per second will be :

Options

A. 4
B. 3
C. 2
D. 1

Answer

D

Explanation

Take three sound waves as
`y_(1)=Acos2pi(upsilon-1)t`
`y_(2)=Acos2piupsilont and y_(3)=Acos2pi(upsilon+1)t`
Resultant wave is
`y=y_(1)+y_(2)+y_(3)`
`=Acos2pi(upsilon-1)t+Acos2piupsilont+Acos2pi(upsilon+1)t`
`=2Acos2pitcos2piupsilont+Acos2piupsilont=A(1+2cos2pit)cos2piupsilont`
The amplitude `A(1+2cos2pit)` becomes maximum 1 time in 1 sec
`therefore` number of beats per second = 1.