Frequency

Symbol $f$, unit the hertz (Hz), where 1 Hz is one cycle per second. AP Physics 2 EK 14.2.A.1.ii puts it as the rate at which the wave repeats, and $T = 1/f$ is printed on the AP Physics 1, AP Physics 2 and AP Physics C equation sheets.

Frequency belongs to the source, not the medium. EK 14.3.A.1.iv is explicit: the frequency of a wave does not change when it travels from one medium to another. Speed and wavelength both change at a boundary, $f$ does not. That one fact settles a large share of refraction and thin-film questions.

What it controls. The pitch of a sound (EK 14.2.A.1.v), and per EK 14.2.A.1.iv the energy of the wave, which increases with frequency. It is independent of amplitude.

Hertz against radians. $f$ counts cycles per second. Angular frequency $\omega$ counts radians per second, and $\omega = 2\pi f$. Substituting one for the other is a factor of $2\pi$ error, and it is the usual reason an SHM answer is out by about 6.3.

Finding $f$ from a graph, from a speed or from a wavelength is the job of the wave speed, frequency and wavelength guide, which owns that procedure.