Question

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

Answer 1

The two sources of sound S1andS2 vibrate at same phase and frequency.

Resultant intensitgy at P=I0

a.} Let the amplitude of the waves at $S_{1}and{S}_{2}ber$

When $\theta ={45}^o$

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

Since the wave reaches in phase $I_o=4I$

$I_{max}a(y_1+y_2{)}^2=(2y_2{)}^2=4{y_2}^2=4I$

b.}When$\theta ={60}^o$ path difference is also $0$.

$\therefore$ $I=\frac{I_o}{4}$ It is independent of $\theta$