Two sources of sound placed close to each other are wmitting progressive waves given by `y_1=4sin600pit` and `y_2=5sin608pit`. An observer located near these two sources of sound will hear:

Options

A. `4` beats per second with intensity ratio `25 : 16` between waxing and waning
B. `8` beats per second with intensity ratio `25 : 16` between waxing and waning
C. `8` beats per second with intensity ratio `81 : 1` between waxing and waning
D. `4` beats per second with intensity ratio `81 : 1` between waxing and waning

Answer

D

Explanation

`y_(1) = 4 sin 600 pi t = A_(1) sin 2 pi f_(1) t`
`A_(1) = 4, f_(1) = 300 Hz`
`y_(2) = 5 sin 608 pi t = A_(2) sin 2pi f_(2) t`
`A_(2) = 5, f_(2) = 304 Hz`
Beat frequency `= f_(1)~f_(2) = 4 Hz`
`(I_(max))/(I_(min)) = ((A_(1)+A_(2))/(A_(1)~A_(2)))^(2) = ((4+5)/(4~5))^(2) = (81)/(1)`