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) :
How many times does an observer hear maximum intensity in one second :-

Options

A. `4`
B. `6`
C. `8`
D. `10`

Answer

A

Explanation

`y_(1) = A cos (0.5 pi x - 100 pi t)`
`y_(2) = A cos (0.46 pi x - 92 pi t)`
For the first wave angular frequency is `omega_(1) = 100 pi , f_(1) = 50 Hz`.
For the second wave angular frequency is `omega_(2) = 92 pi , f_(2) = 46 Hz`.
Frequency at which the amplitude of resultant wave varies
`f_(A) = (f_(1) - f_(2))/(2) = ( 50 - 46)/(2) = 2`
Time interval between this is maximum.
`Delta t = (1)/( 2 f_(A))`
`Delta t = (1)/(4)`
Therefore , the number of time intensity is maximum in time `1 s is 4`.