Add two waves and hear the beats

Two waves of $30\ \text{Hz}$ and $33\ \text{Hz}$ (slowed right down so you can see them) are added. You will make the program find the beat frequency, the pitch you would hear, and the time between two loud moments. Then it draws the sum.

The idea. The displacements add. The loudness swells $|f_1 - f_2|$ times each second, at the average pitch $\dfrac{f_1 + f_2}{2}$.

Your tasks.

1. Find beats, the number of beats each second.
2. Find pitch, the frequency you hear, in Hz.
3. Find gap, the time between two loud moments, in seconds.