Question

The intensity of the sound wave from an airplane is 1.0 ×
10^2 W/m^2 at 6 m. What is the intensity at 97 m?

Answer 1

Answer:

$0.38 W/m^2$

Explanation:

A sound wave propagates in all directions radially from its source; therefore, it follows an inverse square law, it means that its intensity decreases inversely proportional to the square of the distance:

$I \propto \frac{1}{r^2}$

where

I is the intensity

r is the distance from the source of the wave

This means that we can rewrite the equation as:

$I_1 r_1^2 = I_2 r_2^2$

where in this problem:

$I_1 = 1.0 \cdot 10^2 W/m^2$ is the intensity of the sound wave when the distance is

$r_1 = 6 m$

$I_2$ is the intensity of the sound wave when the distance is

$r_2 = 97 m$

Solving for I2, we find:

$I_2 = I_1 \frac{r_1^2}{r_2^2}=(1.0\cdot 10^2) \frac{6^2}{97^2}=0.38 W/m^2$