Question

At a maximum level of loudness, the power output of a 75 piece orchestra radiated as sound is 70.0 w. What is the intensity of these sound waves to a listener who is sitting 25.0 m from the orchestra?

Answer 1

Answer:

$0.0089 W/m^2$

Explanation:

The intensity of a sound wave is given by

$I=\frac{P}{A}$

where

P is the power of the wave at the source

A is the area over which the sound wave propagates

In this problem, we have

P = 70.0 W is the power

We want to know the intensity at a distance of r = 25.0 m from the orchestra, so since the sound waves propagates radially, we must consider a spherical surface of radius r, so the area is

$A=4\pi r^2 = 4\pi (25.0 m)^2=7850 m^2$

Therefore, the intensity of the wave is

$I=\frac{70 W}{7850 m^2}=0.0089 W/m^2$