Question involving a dropped tuning fork.?

Question

Using a highly sensitive parabolic sound collector, Tom records the frequency of a tuning fork as it drops into the Grand Canyon. He drops the vibrating tuning fork from rest at t=0. He records a frequency of 1653.0 Hz at t=4.870 s. What is the natural frequency of the tuning fork? Use Vsound=343.0 m/s.

anyone have any equations that relate these values?
thank you

Answer 1

The velocity of the fork is v = g*t

The frequency shift at that velocity is given by the doppler effect:

The observed frequency is f', the natural frequency is f, the velocity of sound = c

f" = f * v / (v + c)

Using v calculated above, find f from

f = f' * (v + c)/v