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