A Doppler calculator

You will build a small Doppler calculator for sound.

The idea. With speeds along the line, measured in the air, $f' = f\,\dfrac{v + v_o}{v - v_s}$. Here $v_o$ is positive when the listener moves towards the source, and $v_s$ is positive when the source moves towards the listener. An echo from a reflector coming towards you at $u$ is $f\,\dfrac{v + u}{v - u}$. The beats between the echo and the sent sound are $f\,\dfrac{2u}{v - u}$.

Your tasks.

1. In heard, return the frequency heard, in Hz.
2. In echo, return the frequency of the echo, in Hz.
3. In speed_from_beats, return the speed $u$ of the reflector, in m/s, from the beats. Solve $f_b = f\,\dfrac{2u}{v - u}$ for $u$.