Question

Given that the sound intensity 4.0 m from the sound source is 5.0 x 10−6w𝑚−2.

What is the intensity at 2.0 m?

Answer 1

Explanations & Calculations

• For this, you need to use the formula for intensity at a given point from the source.
• You can use it separately for the given 2 situations and find the intensity in the second situation.

$\qquad\qquad \begin{aligned} \small I&=\small \frac{P}{A}\\ \small I&=\small \frac{P}{4\pi r^2}\\ \small I& \approx\frac{1}{r^2}\\ \\ \small 5\times10^{-6}& \approx \small\frac{1}{4^2}\cdots(1)\\ \\ \small I_1 & \approx \small \frac{1}{2^2}\cdots(2)\\ \\ \small \frac{I_1}{5\times10^{-6}}&=\small \frac{4^2}{2^2} \end{aligned}$

• Once you subject $\small I_1$ , you get the answer.