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 waxing and waning

Answer

D

Explanation

Given : `y_(1)=4(sin600pit),y_(2)=5(sin608pit)`
`therefore omega_(1)=600pior2piupsilon_(1)=600piorupsilon_(1)=300Hz`
`A_(1)=4`
and `omega_(2)=608pior2piupsilon_(2)=608pi or upsilon_(2)=304Hz`
`A_(2)=5`
Number of beats heard per second
`=upsilon_(2)-upsilon_(1)=304-300=4Hz`
`(I_(max))/(I_(min))=((A_(1)+A_(2))^(2))/((A_(1)-A_(2))^(2))=((4+5)^(2))/((4-5)^(2))=(81)/(1)`