Asource 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 3.5 × 10-3 w/m2. what is the total sound power p emitted by the source?

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:

Where,

P = Power

A = Acoustic Area

Our values are given as,

r= 12 m

The Area then would be

Replacing the values we have that

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

8.325 W

Explanation:

Acoustic Power =

where;

I = the intensity of the sound = 4.6 × 10⁻³ W/m²

r = distance from the source = 12 m

Acoustic Power =

Acoustic Power = (4.6 × 10⁻³ W/m²) *4*3.142*(12)²

Acoustic Power = 8.325 W

Therefore, the total sound power emitted by the source is 8.325 W

1.58 W

Explanation:

Since the sound spreads uniformly in all directions, it must be in a form of a circle with radius of 12 m. So the area of the circle is

From the intensity of the sound we can calculate the power at 12 m