Question

Two standing bodies producing progressive waves are given by
` y_(1) = 4 sin 400 pi t and y_(2) = 3 sin 404 pi t`
One of these bodies situated very near to the ears of a person who will hear :
A. ` 2 beats//s` with intensity ratio `4//3` between maxima and minima.
B. ` 2 beats//s` with intensity ratio `49//1` between maxima and minima.
C. ` 4 beats//s` with intensity ratio `7//2` between maxima and minima.
D. ` 4 beats//s` with intensity ratio `4//3` between maxima and minima.

Answer 1

Correct Answer - B
` n_(1) = (omega_(1))/(2 pi) = ( 400 pi)/(2 pi) = 200 Hz`
`n_(2) = (omega_(2))/(2 pi) = ( 404 pi)/( 2 pi) = 202 Hz` ltbr. Therefore , the number of beats ` n = n_(2) - n_(1) = 2 Hz`
Again `A_(1) = 4 and A_(2) = 3`
`(I_(max))/(I_(min)) = ((A_(1) + A_(2))^(2))/((A_(1) - A_(2))^(2)) = (( 4 + 3)/( 4 - 3))^(2) = (49)/(1)`
This is alternative (b) is correct.