Two sources of sound are located on the x axis and each emits power uniformly in

Question

Two sources of sound are located on the x axis and each emits power uniformly in all directions. There are no reflections. One source is positioned at the origin and the other at x = +153m. The source at the origin emits four times as much power as the other source. Where on the x axis are the two sounds equal in intensity? Note there are two answers. Two sources of sound are located on the x axis and each emits power uniformly in all directions. There are no reflections. One source is positioned at the origin and the other at x = +153m. The source at the origin emits four times as much power as the other source. Where on the x axis are the two sounds equal in intensity? Note there are two answers.

Explanation / Answer

Here ,

let the point is x m

power of source 1 , P1 = P

power of source 2 , P2 = 4 * P

Intensity = power/(4 * pi * d^2)

for the same intensity

P/(4*pi*x^2) = 4P/(4 *pi*(153 + x)^2)

solving for x

x = 51 m , -153 m

the position where the intensity is equal is x = 51 m , -153 m

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