Frequency

Frequency refers to the number of times an event occurs in a given period of time. In the context of functions, it refers to the number of times the graph of a function repeats itself in a given amount of time. For example, the average resting heart rate of a human adult ranges from 60 to 100 beats per minute (bpm), so the average adult's heart beats at a frequency of 60-100 bpm.

Frequency and period

Frequency and period are inversely related. In other words:

This means that if we know either the frequency or the period of a function, we can determine the other value. The period of a function is the time it takes the function to complete one full cycle. Given the graph of a function, the period of the function can be determined by measuring from peak to peak. It doesn't necessarily need to be peak to peak, but the peaks of a function are one of the more easily recognizable characteristics of a function; any two consecutive matching points can be used to measure the period. Below is an example using the graph of sin(4x).

The figure shows 4 periods of the sine function in the interval [0, 2π]. Beginning at 0, the graph of sin(4x) repeats every (the period), as labeled in the figure, so the frequency is .

Given an equation in general form,

y = A · sin(B(x - C)) + D

we can determine the frequency as (and the period as ). A is the amplitude, C is the phase shift, and the vertical shift is D.