2 sources each emit sound power uniformly in alldirections. There are no reflect

Question

2 sources each emit sound power uniformly in alldirections. There are no reflections. Both sources are located on the x axis.  One atorigin and another on x=+123m. The source @ the originemits four times more power than the other source. Where on the x axis is the intensity of each source equal?(2answers) Thanks Again 2 sources each emit sound power uniformly in alldirections. There are no reflections. Both sources are located on the x axis.  One atorigin and another on x=+123m. The source @ the originemits four times more power than the other source. Where on the x axis is the intensity of each source equal?(2answers) Thanks Again

Explanation / Answer

The idea is that intensity is proportional to the power andinv prop to the distance squared. If speaker 1 is at the origin,then we know: .     P1 /d12   = P2 /d22       . And we also know:     P1 = 4 P2 . One point we are looking for is between the speakers,so x < 123 m. Then .       d2 = 123- x     and     d1 = x      and wehave .      4 P2 / x2   =   P2 / (123 -x)2 .    4 (123 - x)2   = x2   .     4 x2   -   984 x   +    60516 = x2 .     3 x2   -  984 x   + 60516 = 0        quadratic equation...use quadratic formula and... .            x =   82 m         Noticethat the distance to the stronger speaker, 82 meters, istwice the distance from the weaker speaker, 41 meter. . Now for the point to the right of speaker2...    x > 123   so .     d1 =x      d2 = x -123         and .     4 / x2   =  1 / (x - 123)2 .    using the same process, with quadraticequation... we get    x = 246 meters .    using the same process, with quadraticequation... we get    x = 246 meters

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