Question

Two sources of sound $S_1$ and $S_2$ vibrate at same frequency and are in phase (figure 16-E8). The intensity of sound detected at a point P as shown in the figure is $I_0$. (a) If $\theta$ equals ${45}^{\circ }$, 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 $\theta ={60}^{\circ }$?

Answer 1

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 $\theta ={45}^{\circ },$

path difference $=S_{1}P-S_{2}P=0$

$[S_{1}P=S_{2}P]$

So, when source is switched off, intensity of sound at P is $\frac{10}{4}.$

(b)When $\theta ={60}^{\circ }$, path difference is also 0. SImilarly it can be proved that, the intensity at P is $\frac{I_0}{4}$ when source is swithced off.