Two sources of sound `S_1 and S_2` vibrate at same frequency and are in phase. The intensity of sound detected at a point P as shown in the figure is `I_0` . (a) If theta equals `45^@`, what will be the intensity of sound detected at this point if one of the sources is switched off ? (b) What will be the answer of the previous part if `theta= 60^@` ?

Options

A. `I_0/4 , I_0/2`
B. `I_0/2 , 3I_0/4`
C. `I_0/4 , I_0/4`
D. `I_0/2 , I_0/4`

Answer

C

Explanation

The two sources of sound `S_1 and S_2` vibrate at same phase and frequency.
Resultant intensity 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 `I_0/4`.
b. When `theta=60^@`
path difference is also 0.
similarly it can be proved that the intensity at P is `I_0/4` when source is switched off.