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

`0.38 W/m^2`

Step-by-step 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 (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 (r_1^2)/(r_2^2)=(1.0\cdot 10^2) (6^2)/(97^2)=0.38 W/m^2`