Question

Two coherent sources of sound, $S_1$ and $S_2$, produce sound waves of the same wavelength $\lambda =1\text{m}$, in phase. $S_1$ and $S_2$ are placed $1.5\text{m}$ apart (see fig.). A listener, located at $L$, directly in front of $S_2$ finds that the intensity is a minimum where he is $2\text{m}$ away $S_2$. 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. $\text{12 m}$
• B. $\text{5 m}$
• C. $\text{2 m}$
• D. $\text{3 m}$

Answer 1

The correct option is D $\text{3 m}$

Initially,
$S_{2}L=2\text{m}$
$S_{1}L=\sqrt{2^2+{\frac{3}{2}}^2}=\frac{5}{2}=2.5\text{m}$
Path difference, $\Delta x=S_{1}L-S_{2}L=0.5=\frac{\lambda }{2}$
$\lambda =1\text{m}$

When the listener move from $L$, first maxima will appear if path difference is integral multiple of wavelength.
For example

$\Delta x=n\lambda =1\lambda$ ($n=1$ for first maxima)
$\therefore \Delta x=\lambda =S_1{L}^{\prime }-S_{2}L$
$\Rightarrow 1=d-2\Rightarrow d=3\text{m}$