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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.)

User Iluvatar
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1 Answer

4 votes

Answer:


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

User Raaz
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