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

Answer:

The intensity would be 0.01432 W/$m^{2}$

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/$m^{2}$