Speed of sound source-frequency

Question

A source of sound moves toward you at speed Vs and away from Jane, who is standing on the other side of it. You hear the sound at twice the frequency as Jane.

What is the speed of the source? Assume that the speed of sound is 340 m/s.

Answer 1

f' = f (vm / (vm + v)) where vm = velocity of sound in the medium, f = actual frequency, & f' = observed frequency, and v = radial components of the velocity of the object emitting the sound.

In this case fy = the frequency you hear, fj = frequency Jane hears.  Additionally, since the sound is moving directly toward you and away from Jane, the v for both is the same magnitude but in opposite directions, so toward you is +v and away from Jane is -v.

fj = f (vm / (vm - v))

fy = f (vm / (vm + v)) = 2 f (vm / (vm - v))  "twice the frequency as Jane hears"

Solve for v.