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. 100
B. 92
C. 8
D. 4

Answer

A

Explanation

At x = 0
`y = y_(1) + y_(2) = A cos (100 pi t) + A cos (92 pi t)`
`= 2A cos ((100 + 92)/(2)) pi t cos ((100 - 92)/(2)) pit`
`= 2A cos (96pi t) cos (4pi t)`
Between t = 0 to t = 1s, `cos (96pi t)` will become zero 96 times and `cos (4pi t)` will become zero 4 times.
`:.` The resultant displacement `(y = y_(1) + y_(2))` will become zero 100 times in one second.