#### Answer

(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.