Frequency and Period

Frequency and period are two very important properties of any wave.

The frequency is the number of oscillations that the wave makes in a single second. The frequency is commonly denoted $f$, and the dimension is the reciprocal of the time dimension. Thus, the SI unit is the reciprocal of a second, more commonly called Hertz.

The period is the amount of time for the wave to make a single oscillation. The period is commonly denoted $T$ in equations, and the dimension is the same as that of time. Thus, the SI unit is seconds.

Notice that frequency and period are not independent! In fact, the frequency and period of a wave are connected by this very simple equation: $$Tf=1$$ This is quite easy to prove; if a wave takes $x$ seconds to make an oscillation, then clearly it makes $\frac{1}{x}$ oscillations in one second. Similarly, if a wave makes $x$ oscillations in a second, then it takes $\frac{1}{x}$ seconds for a single oscillation. Thus, the frequency and period of a wave are reciprocals.