Question

A straight line source of sound of length $10\text{m}$ emits pulse that travels radially outward from the source. A detector is located at a perpendicular distance of $7\text{m}$ from the source. The total power emitted by the source in the form of sound wave is $2.2\times {10}^4\text{W}$. If the surface area of the acoustic detector is $1.2{\text{cm}}^2$, then the power (in $\text{mW}$) intercepted by the detector is
(Assume waves reaches surface of detector perpendicularly and take $\pi =\frac{22}{7}$)

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is B $6$

The power emitted by the line source will be distributed over the curved surface area of the cylinder of length $10\text{m}$ and radius $7\text{m}$ from the source.


Intensity of sound,
$I=\frac{P}{A}=\frac{P}{2\pi rl}=\frac{2.2\times {10}^4}{2\times \frac{22}{7}\times 7\times 10}$
$\Rightarrow I=50{\text{W/m}}^2$
Now, the power intercepted by the detector is,
$P^{{}^{\prime }}=I{A}^{{}^{\prime }}$
$\Rightarrow P^{{}^{\prime }}=50\times 1.2\times {10}^{-4}=6\times {10}^{-3}\text{W}$
$\therefore P^{{}^{\prime }}=6\text{mW}$