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:

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


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

8.325 W


Acoustic Power = I*4\pi *r^2


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

r = distance from the source = 12 m

Acoustic Power = I*4\pi *r^2

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


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

A = \pi r^2 = \pi 12^2 = 452.389 m^2

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

P = AI = 452.389 * 3.5\times10^{-3} = 1.58 W

Do you know the answer?

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