Two sources of sound placed closed to each other, are emitting progressive waves given by
`y_(1)=4 sin 600 pi t`
and `y_(2)=5 sin 608 pi t`
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 waning and waxing.

Answer

D

Explanation

Given, `y_(1)=4 sin 600 pit, y_(2)=5 sin 608 pi t`
`:. Omega_(1)=600 pi` or `cos 2 pi f_(1)=600 pi`
or `f_(1)=300`
`A_(1)=4` and `omega_(2)=608 pi` or `f_(2)=304`
`A_(2)=5`
Number of beats heard per second `=f_(2)-f_(1)=304-300=4`
`implies I_("max")/I_("mix")=((A_(1)+A_(2))^(2))/((A_(1)-A_(2))^(2))`
`=((4+5)^(2))/((4-5)^(2))=81/1`