Question

At a maximum level of loudness, the power output of a 75-piece orchestra radiated as sound is 72.0 W. What is the intensity of these sound waves to a listener who is sitting 20.0 m from the orchestra? Answer in units of W/m2 .

Answer 1

The intensity would be 0.01432 W/
`m^(2)`

Step-by-step explanation:

The sound intensity is the power that is transmitted by a sound wave per unit area.

Given that

Power output P of the 75-piece orchestra = 72.0 W

The listener's distance r = 20.0 m

The intensity of sound waves (I) can be obtained with the expression below;

I = P/A .............. 1

where P is the power

A is the area, in this case, at the distance r the sound is radiated through a sphere.

A = area of a sphere = 4π
`r^(2)`

putting it into equation 1, the intensity would be;

I = P/ 4π
`r^(2)`

Substituting our values we have;

I = 72.0 W / 4 π
`20^(2)`
`m^(2)`

I = 0.01432 W/
`m^(2)`

Therefore the intensity would be 0.01432 W/
`m^(2)`