Question

The pressure amplitude in a medium through which sound is travelling is $1.5\times {10}^{-3}{\text{N/m}}^2$ and intensity is ${10}^{-6}{\text{W/m}}^2$. If the pressure amplitude is increased to $4.5\times {10}^{-3}{\text{N/m}}^2$ by increasing the volume of sound then the intensity will be

• A. $6\times {10}^{-6}{\text{W/m}}^2$
• B. $7\times {10}^{-6}{\text{W/m}}^2$
• C. $8\times {10}^{-6}{\text{W/m}}^2$
• D. $9\times {10}^{-6}{\text{W/m}}^2$

Answer 1

The correct option is D $9\times {10}^{-6}{\text{W/m}}^2$

We know that the intensity of sound is given by,
$I=\frac{P_o^{2}v}{2B}$
where, $P_o$ is the maximum pressure in the medium, $v$ is the speed of sound and $B$ is the bulk modulus of the medium.
Medium of sound is same.
So, $\frac{I_1}{I_2}=\frac{P_{o1}^2}{P_{o2}^2}$
$\Rightarrow I_2=\frac{I_1{P}_{o2}^2}{P_{o1}^2}$
$\Rightarrow I_2=\frac{{10}^{-6}\times (4.5\times {10}^{-3}{)}^2}{(1.5\times {10}^{-3}{)}^2}$
$\Rightarrow I_2=9\times {10}^{-6}{\text{W/m}}^2$