Question

Two coherent sources of sound, $S_1$ and $S_2$, produce sound waves of the same wavelength, $\lambda =1m,$ in phase. $S_1$ and $S_2$ are placed $1.5m$ apart (see fig.) A listener, located at $L$, directly in front of $S_2$ finds that the intensity is at a minimum when he is $2m$ away from $S_2$. The listener moves away from $S_1,$ keeping his distance from $S_2$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_1$. Then, $d$ is :

• A. 12m
• B. 3m
• C. 5m
• D. 2m

Answer 1

Answer: (B)

Initially $S_{2}L=2m$
$S_{1}L=\sqrt{2^2+(3/2{)}^2}$
$S_{1}L=\frac{5}{2}=2.5m$
$\Delta x=S_{1}L-S_{2}L=0.5m$
So since $\lambda =1m$
$\therefore \Delta x=\frac{\lambda }{2}$
So while listener moves away from $S_1$
Then, $\Delta x\left(=S_{1}L-S_{2}L\right)$ increases
and hence, at $\Delta x=\lambda$ first maxima will appear.
$\Delta x=\lambda =S_{1}L-S_{2}L$
$1=d-2$
$\Rightarrow d=3m$