Question

A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance of 12 m from the source, the intensity of the sound is 5.0 × 10−3 W/m2. What is the total sound power P emitted by the source?

Answer 1

To solve this problem we will apply the concept related to Intensity, that is, the acoustic power transferred by a sound wave per unit of normal area to the direction of propagation:

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

Where,

P = Power

A = Acoustic Area

Our values are given as,

r= 12 m

$I = 4.3*10^{-3} W/m^2$

The Area then would be

$A = 4\pi r^2$

$A = 4\pi (12)^2$

$A = 1809.55m^2$

Replacing the values we have that

$P = (4.3*10^{-3} W/m 2)(1809.55m^2 )$

$P = 7.781 W$

The total sound power P emitted by the source is 7.781W