Question

Two sources of sound S₁ and S₂ vibrate at same frequency and are in phase. The intensity of sound detected at a point P as shown in the figure is I₀. (a) If θ 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 θ = 60°?
Figure

Answer 1

Given:
Resultant intensity at P = I₀
The two sources of sound S₁ and S₂ vibrate with the same frequency and are in the same phase.
(a) When θ = 45°:
Path difference = S₁P − S₂P = 0

So, when the source is switched off, the intensity of sound at P is $\frac{I_0}{4}$.
(b) When θ = 60°, the path difference is also 0. Similarly, it can be proved that the intensity at P is $\frac{I_0}{4}$ when the source is switched off.