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. 192
B. 48
C. 100
D. 96

Answer

D

Explanation

At `x=0,y=y_(1) +y_(2) =2A cos 96 pi t cos 4 pi t`
Frequency of `cos (96 pit)` function is `48 Hz` and that of `cos (4 pi f)` function is 2 Hz.
In one second cos function becomes zero at 2f times, where f is the frequency. Therefore, first function will becomes zero at 96 times and the sec- and at 4 times. But second will not overlap with first. Hence, net y will become zero 100 times in 1s.