91Ó°ÊÓ

1. Power,$\mathrm{P}=30\text{W}$
2. Area of microphone,$\mathrm{A}=0.75{\text{0 c³¾}}^{\text{2}}$
3. Distance from the source,$\mathrm{r}=\text{200″¾}$

Intensity can be found using power and distance from the relation between power, intensity, and area. Using this intensity, find the power intercepted by the microphone at a given distance.

The relation between intensity and power is given as-

$\mathrm{I}=\frac{\mathrm{p}}{4{\mathrm{Ï€°ù}}^2}$

where, I is intensity, p is power and r is radius.

Now, write intensity in terms of power and area of the sphere as,

$\mathrm{I}=\frac{\mathrm{P}}{4{\mathrm{Ï€°ù}}^2}$

Substituting the values from the given data,

$\begin{array}{c}\mathrm{I}=\frac{\text{30 W}}{\text{4}\left(\text{3.14}\right){\left(\text{200″¾}\right)}^{\text{2}}}\\ =5.97×{\text{10}}^{\text{-5}}{\text{W/m}}^{\text{2}}\end{array}$

Hence, intensity of sound is $5.97×{10}^{−5}{\text{ W/³¾}}^{\text{2}}$.

Power can be written in terms of intensity and area of the microphone as,

$\begin{array}{c}\mathrm{P}=\mathrm{IA}\\ =(0.750×{10}^{−4}{\text{″¾}}^2)(5.97×{\text{10}}^{\text{-5}}\text{ W}/{\text{m}}^{\text{2}})\\ =4.48×{10}^{−9}\text{ W}\end{array}$

Hence, power intercepted by the microphone is $4.48×{10}^{−9}\text{ W}$.