Two sources of sound are located on the x axis, and each emits power uniformly in all directions. there are no reflections. one source is positioned at the origin and the other at x = +78.0 m. the source at the origin emits four times as much power as the other source. where on the x axis are the two sounds equal in intensity? note that there are two answers.

The intensity is same at and at  

Explanation:

Let the 2 sources have the same intensity at a  distance 'x' from the origin

Since the energy of the wave front emitted will be distributed over a sphere we have

For source 1, located at origin  intensity at a distance of 'x' from origin is given by

For source 2, located at x = +78.0 m  intensity at a distance of 'x' from origin  is given by

Now it is also given that

Thus equating the intensities we get

Solving the equation for x we get

Solving using both the values we get

Similarly the other value is obtained as

the one with the highest speed