 # Relation Between Amplitude And Frequency

The amplitude is the highest deviation of the wave from zero. The frequency is the number of complete waves passing through a point in a second. The relation between Amplitude and Frequency for a sine wave is mathematically written as-

### Wave equation

 $$A=\frac{y(t)}{sin(2\pi ft+\phi )}$$

Where,

• A is the amplitude of the wave.
• y(t) is the sine wave as a function of time.
• t is time.
• f is the frequency of the wave.
• ?? is the phase of the wave. (Position of the wave at t=0)

## Relationship Between Amplitude And Frequency

Although there is no direct dependency of the frequency with amplitude or other way around. They can be expressed individually by rearranging the terms of the wave equation.

### Amplitude to Frequency formula

We can rearrange the wave equation to express amplitude in terms of frequency and other parameters-

$$A=\frac{y(t)}{sin(2\pi ft+\phi )}$$

### Frequency to Amplitude formula

We can rearrange the wave equation to express frequency in terms of amplitude and other parameters-

$$f=\frac{Sin^{-1}\left ( \frac{y(t)}{A} \right )-\phi }{2\pi t}$$

Hope you understood the relation and conversion between Frequency of a wave and the Amplitude of a wave.

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