Two source of sound `S_(1)` and `S_(2)` vibrate at the same frequency and are in phase . The intensity of sound detecter at a point `P` (as shows in figure) is `I_(0)`.

(a) If `theta = 45^(@)` what will be the intensity of sound detected at this point if one of the source is switched off?
(b) What will be intensity of sound detected at `P` if `theta = 60^(@)` and both the source are now switched on?

Answer

A, B, D

Explanation

The two sources of sound `S_1 and S_2` vibrate at same phase and frequency.
Resultant intensitgy at `P=I_0`
a. Let the amplitude of the waves at `S-1 and S_2` be r
When `theta=45^@`
path difference =S_1P-S_2P=0`
`[S_1P=S_2P]`
So, when source is switched off, intensity of sound at P is `10/4`.
`b. When`theta60^@` path differenc is also 0.
similarly it can be proved that the intensity at P is `I_0/4` when source is switched.