Relation Between Amplitude And Frequency

The amplitude is the highest deviation of the wave from its central or zero position. 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

y(t) = Asin(2πft+Φ)

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.
  • Φ 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 the other way around. They can be expressed individually by rearranging the terms of the wave equation.

Frequency to Amplitude Formula

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

\(\begin{array}{l}A=\frac{y(t)}{sin(2\pi ft+\phi )}\end{array} \)

Amplitude to Frequency Formula

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

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

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

Physics Related Topics:

Amplitude modulation
Propagation constant
Frequency Modulation vs Amplitude Modulation
Gravity waves

Stay tuned with BYJU’S for more such interesting articles. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and an unlimited academic assist.

Frequently Asked Questions – FAQs

Q1

Define the frequency of a wave.

The frequency of a wave is defined as the number of complete waves passing through a given point in a second.
Q2

What is the relation between amplitude and frequency for a sine wave?

y(t) = Asin(2πft+Φ)

Q3

Give the amplitude to frequency formula.

\(\begin{array}{l}A=\frac{y(t)}{sin(2\pi ft+\phi )}\end{array} \)
Q4

Give the frequency to amplitude formula

\(\begin{array}{l}f=\frac{Sin^{-1}\left ( \frac{y(t)}{A} \right )-\phi }{2\pi t}\end{array} \)
Q5

State true or false: The amplitude is the highest deviation of the wave from its central or zero position.

True.
Test Your Knowledge On Relation Between Amplitude And Frequency!

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*