Question

A circular plate of area $0.8{\text{cm}}^2$ is kept at a distance of $2\text{m}$ from a source of sound of power $\pi \text{W}$. Find the amount of energy received by the plate in $4\text{s}$.

• A. $50\mu \text{J}$
• B. $30\mu \text{J}$
• C. $20\mu \text{J}$
• D. $15\mu \text{J}$

Answer 1

The correct option is C $20\mu \text{J}$

Given,
Power of source of sound,
$P=\pi \text{W}$
So, intensity of sound,
$I=\frac{P}{A}=\frac{P}{4\pi R^2}$


$\Rightarrow I=\frac{\pi }{4\pi \times 2^2}=\frac{1}{16}{\text{W/m}}^2$
Now, the energy received by the circular plate will be,
$E^{{}^{\prime }}=It{A}^{{}^{\prime }}$
$[I=\frac{P^{{}^{\prime }}}{A^{{}^{\prime }}}=\frac{E^{{}^{\prime }}}{t{A}^{{}^{\prime }}}]$
$\Rightarrow E^{{}^{\prime }}=\frac{1}{16}\times 4\times 0.8\times {10}^{-4}$
$\Rightarrow E^{{}^{\prime }}=2\times {10}^{-5}\text{J}=20\mu \text{J}$