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

`d=14.12m`

Step-by-step 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=(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 (W)/( m^(2))`

`P=110W`

`d=\sqrt { (P)/(4 \pi\\I)`

`d=\sqrt{ (110)/( 4\pi (0,0439)) }`

`d=\sqrt{{199.39}`

`d=14.12m`