Raina Gomez

Raina Gomez

Answered

2022-09-26

If the distance to a point source of sound is tripled, by what factor does the intensity of the sound change?

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Answer & Explanation

Cremolinoer

Cremolinoer

Expert

2022-09-27Added 11 answers

Assuming that the sound is not facing any barriers, we can say that it is propagating through a spherical shape, we can then use the intensity of sound I formula:
I = P 4 π r 2
Where P is the power of the sound source and 4 π r 2 is the area of a sphere.
Denoting I 2 the intensity of the sound when the distance was tripled, yields:
I 2 = P 4 π r 2 2
We now replace r 2 with 3 r 1 :
I 2 = P 4 π ( 3 r 1 ) 2 = 1 9 P 4 π r 1 2 = I 1 9
The intensity of the sound was reduced to a ninth of the original intensity.
Result:
I 2 = 1 9 I 1

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