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

C

Explanation

At `x = 0`,
`y = y_(1) + y_(2) = 2A cos 96 pit cos 4 pit`
For `y = 0, cos 96 pi t = 0` or `cos 4 pit = 0`
`rArr` for `0 lt 1 lt 1 cos 4 pi t` becomes `0` at `t = (1)/(8), (3)/(8), (5)/(8), (7)/(8) sec`
But `cos 96pi t` is not `0` at these values but `cos 96 pi t` become `0, 96` times in `1` sec. Therefore net amplitude becomes zero `100` times.