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Two sounding bolies are producing progre...

Two sounding bolies are producing progressive waves given by `y_(1) = 2 sin (400 pi t)` and `y_(2) = sin (404 pi t)` where `t` is in second, which superpose near the ears of a persion. The person will hear

A

`2 beats//s` with intensity ratio `9//4` between maximum and minima

B

`2 beats//s` with intensity ratio `9` between maximum and minima

C

`4 beats//s` with intensity ratio `16` between maximum and minima

D

`4 beats//s` with intensity ratio `16//9` between maximum and minima

Text Solution

Verified by Experts

The correct Answer is:
B

`f_(1) = (omega_(1))/(2 pi) = ((400 pi)/(2 pi)) = 200 H_(Z)`
`f_(2) = (omega_(2))/(2 pi) = ((404 pi)/(2 pi)) = 202 H_(Z)`
:. `f_(b) = f_(2) - f_(1) = 2 H_(Z)`
`A_(1) = 2` and `A_(2) = 1`
`(I_(max))/(I_(min)) = ((A_(1) + A_(2))/(A_(1) - A_(2)))^(2) = (9)/(1)`
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