Beats and an unknown fork

You will write three functions for beats.

The idea. Two close frequencies give $f_b = |f_1 - f_2|$ beats each second, and you hear the pitch $\dfrac{f_1 + f_2}{2}$. An unknown fork is $f_{\text{known}} + f_b$ or $f_{\text{known}} - f_b$. Wax lowers the unknown fork. If the beats then get slower, it was above the known fork. If they get faster, it was below.

Your tasks.

1. In beat_frequency, return the number of beats each second, in Hz.
2. In pitch, return the frequency you hear, in Hz.
3. In unknown_after_wax, return the frequency of the unknown fork before the wax, from the beats before and after.