Two sources of sound S₁ and S₂ vibrate at the same frequency and are in phase as shown in the figure. The intensity of sound detected at point P is I₀ when both sources are active. If one source is switched off, what will be the intensity at P ? Consider (a) = 45^ and (b) = 60^ .

Step-by-step solution

From the given figure, point P lies on the perpendicular bisector of S₁S₂ , so the path difference is zero ( x = 0 ). Let the intensity of each individual source at P be I' . Since the sources are in phase and the path difference is zero, they interfere constructively. The resultant intensity is: I₀ = I' + I' + 2 I' I' 0^ = 4I' If one source is switched off, the intensity at P is solely due to the single remaining source, which is I' . New intensity = I' = I₀ 4 This result depends only on the path difference being