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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Cremolinoer · Accepted Answer

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

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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