 # Amplitude Formula

The amplitude of a wave is the maximum displacement of the particle of the medium from its equilibrium position. It is represented by A. The Amplitude formula can be written as

$$\begin{array}{l}y=Asin(\omega t+\phi )\end{array}$$

where,

y is the displacement of the wave in meters

A is the amplitude of the wave in meters

ω is the angular frequency given by

$$\begin{array}{l}\omega =\frac{2\pi }{t}\end{array}$$

Φ is the phase difference

## Amplitude Solved Examples

Problem 1: If y = 5 sin ω t represents the wave, find the amplitude of the wave.
Solution:

Given: y = 5 sin ω t
The equation is of the form

y = A sin ω t

Henceforth, the amplitude is A = 5.

Problem 2: The equation of a progressive wave is given by

$$\begin{array}{l}y=5\sin (10\pi t-0.1\pi x)\end{array}$$
where x and y are in meters. Find the value of Amplitude

Given:

$$\begin{array}{l}y=5\sin (10\pi t-0.1\pi x)\end{array}$$

The equation is in the form of
$$\begin{array}{l}y=A\sin(\omega t+\phi )\end{array}$$

Henceforth, the amplitude is A = 5.