Question

You measure the intensity of a sound wave to be 9.80 W/m2 . The power output of the signal is 75 W and the signal is emitted in all directions.

Part A

How far away from the source are you?

r = ?

Answer 1

Answer:

r = 0.78 m

Explanation:

If the sound source is emitting the signal evenly in all directions (as from a point source) this means that at any time, the source power is distributed over the surface of a sphere of radius r.

At a distance r of the source, the intensity of the sound is defined as the power per unit area:

I = P/A

As the area is the area of a sphere, we can say the following:

I = P / 4*π*r²

Replacing I and P by the values given, we can solve for r (which is the distance from the listener to the source) as follows:

r² = P / I*4*π ⇒ r = $\sqrt{P/(4*\pi*I)}$ = 0.78 m

Answer 2

The distance between you and the source is 0.78 m.

The given parameters:

• Intensity of the sound, I = 9.8 W/m²
• Output power of the signal, P = 75 W

The area of the source is calculated as follows;

$A = \frac{P}{I} \\\\ A = \frac{75}{9.8} \\\\ A = 7.65 \ m^2$

The distance between you and the source is calculated as follows;

$A = 4\pi r^2\\\\ r^2 = \frac{A}{4\pi} \\\\ r = \sqrt{\frac{A}{4\pi}} \\\\ r = \sqrt{\frac{7.65}{4\pi}} \\\\ r = 0.78 \ m$

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