Question

A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = -7.6 m and x = 2.0 m .

1. What is the x-coordinate of the source?

2. A third listener is positioned along the positive y-axis. What is her y-coordinate if the same wave front reaches her at the same instant it does the first two listeners?

Answer 1

Okay since the speed of sound is constant call it s and the sound arrives at -7.6and 2 at the same time, and calling the position of the source x, the following must be true:

(x+7.6)/s=(2-x)/s or x+7.6=2-x which gives us x= -2.8 m (answer to part a).

Now, the distance she is from the source must be the same as the other two receptors so that the wave arrives at the same time. Her distance from the source is (y^2+2.8^2)^(1/2) which must equal 6. So y must be the square root of 28 or about 5.31 m.