# Amplitude, Period and Frequency

## Key Questions

• If $f \left(x\right) = a \sin \left(b x\right)$ or $g \left(x\right) = a \cos \left(b x\right)$, then their amplitudes are $| a |$, and the periods are $\frac{2 \pi}{|} b |$.

I hope that this was helpful.

• Frequency and period are related inversely. A period $P$ is related to the frequency $f$
$P = \frac{1}{f}$

Something that repeats once per second has a period of 1 s. It also have a frequency of $\frac{1}{s}$. One cycle per second is given a special name Hertz (Hz). You may also say that it has a frequency of 1 Hz.

A sin function repeats regularly. Its frequency (and period) can be determined when written in this form:

$y \left(t\right) = \sin \left(2 \pi f t\right)$

• "(Amplitude)"=1/2["(Highest Value)"-"(Lowest Value)"]

graph{4sinx [-11.25, 11.25, -5.62, 5.625]}

In this sine wave the highest value is $4$ and the lowest is $- 4$

So the maximum deflection from the middle is $4$k.

This is called the amplitude

If the middle value is different from $0$ then the story still holds
graph{2+4sinx [-16.02, 16.01, -8, 8.01]}

You see the highest value is 6 and the lowest is -2,
The amplitude is still $\frac{1}{2} \left(6 - - 2\right) = \frac{1}{2} \cdot 8 = 4$

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