Question

How far must you be from a 110 W speaker to have an intensity of 0.0439 W/m^2? (Treat the speaker as a point source.)

Answer 1

Answer:

$d=14.12m$

Explanation:

Assume a point sound source that emits a sound power P (in W) evenly in all directions of space. Let us also assume that the medium does not absorb this sound power when it passes through it. At a distance d from the source this power will have been evenly distributed over the surface of a sphere of radius d. Therefore, the acoustic intensity I at distance d will be worth:

$I=\frac{P}{4\pi d^{2}}$

This is the expression of the so-called law of the square of distance: "the intensity is inversely proportional to the square of the distance to the source (considered punctual)".

So

$I=0.0439 \frac{W}{ m^{2}}$

$P=110W$

$d=\sqrt { \frac{P}{4 \pi\\I}$

$d=\sqrt{ \frac{110}{ 4\pi (0,0439)} }$

$d=\sqrt{{199.39}$

$d=14.12m$