# Chapter 20 - Traveling Waves - Exercises and Problems - Page 586: 18

(a) The x-coordinate of the source is -2.0 meters (b) The y-coordinate of the third listener is 4.6 meters.

#### Work Step by Step

(a) If the same wave front reaches two listeners, the two listeners must be the same distance from the source. We can find the x-coordinate $r$ of the source. $r = \frac{r_1+r_2}{2}$ $r = \frac{-7.0~m+3.0~m}{2}$ $r = -2.0~m$ The x-coordinate of the source is -2.0 meters. (b) If the same wave front reaches a third listener at the same time, the third listener must be the same distance from the source. Since the first two listeners are a distance of 5.0 meters from the source, the listener on the positive y-axis must be a distance of 5.0 meters from the source. We can find the y-coordinate of this listener. $\sqrt{r^2+y^2} = 5.0~m$ $r^2+y^2 = 25.0~m^2$ $y = \sqrt{25.0~m^2- 4.0~m^2}$ $y = 4.6~m$ The y-coordinate of the third listener is 4.6 meters.

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