Two plane harmonic sound waves are expressed by the equations.
`y_(1)(x,t)-A cos (0.5 pi x-100 pit), y_(2)(x,t)=A cos(0.46 pix-92pi t)` (All parameters are in MKS) :
At x=0 how many times the amplitude of `y_(1) + y_(2)` is zero in one second :-

Options

A. 8
B. 6
C. 4
D. 3

Answer

C

Explanation

The two sound waves will interfere and maxima and minima are produced in the resultant sound. This produces beats and beats are heard if the difference in their frequencies is less than 10
The number of maxima produce/second
= No. of beats/sec = beat frequency `(n_(B))`
For `y_(1), n_(1) = (10pi)/(2pi) = 50 Hz`
and for `y_(2), n_(2) = (92pi)/(2pi) = 46Hz`
`:.` Beat frequency `(n_(B)) = n_(1) - n_(2) = 4Hz`
Thus in one second, the sound of maximum intensity is heard 4 times