Question

Find the intensity of a sound wave from 1km away, with a power of 20kw

Answer 1

Answer:

$1.59\cdot 10^{-3} W/m^2$

Explanation:

The intensity of a wave propagating in all directions from a source is given by the inverse square law:

$I=\frac{P}{4\pi r^2}$

where

I is the intensity of the wave at a distance r from the source

P is the power of the source

r is the distance from the source

The formula arises from the fact that the wave propagates over the surface of a sphere of radius r, so over a surface of $4\pi r^2$ (surface of a sphere).

In this problem, we have:

$P=20 kW = 20,000 W$ is the power of the source of the sound wave

$r=1 km = 1000 m$ is the distance at which we want to calculate the intensity

Therefore, the intensity of the sound wave is:

$I=\frac{20,000}{4\pi (1000)^2}=1.59\cdot 10^{-3} W/m^2$