Frequency

The frequency of the waveform is given in cycles per second or Hertz (Hz).
Frequency is equivalent to the inverse of the period of the waveform,

$\displaystyle f = 1/T$ Hz $\displaystyle .$
The radian frequency $\omega$ , given in radians per second, is equivalent to the frequency in Hertz scaled by $2\pi$ ,

$\displaystyle \omega = 2\pi f$ (rad/sec) $\displaystyle .$
The radian frequency is equal to the time derivative of the instantaneous phase of the sinusoid:

$\displaystyle \omega = \frac{d}{dt}(\omega t + \phi)$
Note: if the phase is time varying, the instantaneous frequency is given by

$\displaystyle \frac{d}{dt}[\omega t + \phi(t)] = \omega + \frac{d}{dt}\phi(t).$

``Music 270a: Sinusoids'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).