Question

Figure shows two coherent line sources of sound, $S_1$ and $S_2$ separated by a distance $12\text{m}$. The sources emit same power and their wavelengths are also same. A detector moves along a circular path with centre at $S_2$ and radius $4\text{m}$. The wavelength of the sound is $1\text{m}$. When it is at $‘A^{\prime }$ the intensity of sound is $I_o=25{\text{W/m}}^2$. The intensity of sound (in $W/m^2$) at $B$ due to $S_1$ only is (Take $S_1\text{A=9 m}$)

• A. $9$
• B. $4$
• C. $\frac{9}{\sqrt{10}}$
• D. None of these

Answer 1

The correct option is C $\frac{9}{\sqrt{10}}$

Given $\lambda =1m$
and $I_A=25W/m^2$

Intensity of line source $I\propto \frac{1}{r}$
so $I_{A{S}_1}=\frac{k}{9};I_{A{S}_2}=\frac{k}{4}$
where $k$ is any constant.
Now path difference at $A$ is $5m$ which is integral multiple of $\lambda$$\left(1m\right)$.
So, intensity at A is maxima and is
$(\sqrt{I_1}+\sqrt{I_2}{)}^2$
$2S=(\sqrt{\frac{k}{9}}+\sqrt{\frac{k}{4}}{)}^2$
$⟹k=36$

$I_{S_{1}or{S}_2}\left(r\right)=\frac{36}{r}$

Now $I_{B{S}_1}=\frac{36}{S_{1}B}$
$=\frac{36}{\sqrt{4^2+{12}^2}}=\frac{9}{\sqrt{10}}W/m^2$