Doppler Effect-Am not understanding why my answer is wrong.

Question

You're standing on the dock at Portsmouth down by the tugboats. You notice that one of the three usual tugboats is missing, but you can hear it's ship whistle. The ship's whistle is designed to emit at 780 Hz but the frequency that you hear is 810 Hz. The speed of sound is 343 m/s in this problem.

How fast is the tugboat moving [in m/s]?

I got 13.2 m/s as my answer after using the observed frequency equation and rearranging it to solve for the velocity of the source. This is the wrong answer, and I am confused. Please help me get to the right one.

Answer 1

Since you are stationary, and you are hearing a higher frequency, the tug is moving toward you. In this case the appropriate formula is

Fo / Fs = Vsound - 0 / Vsound - Vs where Vs is the speed of the tug.

1.04 = 343 / 343 - Vs solve for Vs

Vs = 12.5 m/s

Check math.