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

Answer

A

Explanation

`omega_(1) = 600 pi," "omega_(2) = 608 pi`
`v_(1) = 300" "v_(2) = 304`
Beat frequency `= |v_(2) - v_(1)|`
`= |304 - 300| = 4` Hz = 5 beats/sec.
Intensity is maximum and minimum during waxing and waning respectively.
`(I_(1))/(I_(2)) = ((A_(1) + A_(2))^(2))/((A_(1) - A_(2))^(2))`
`= ((5 + 4)/(5-4))^(2)`
`(I_(1))/(I_(2)) = (81)/(1)`