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# Amplitude of a Wave

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 Sub Topics Have you ever observed the water waves while traveling on the boat? The energy the wave has, makes the boat to move from a point to another. So after reading there lies a question that might wonder you. What is that getting transferred water or energy? Its actually energy that gets transferred from a point to another that actually makes your boat move to your destiny and the water will be in its own place. This energy which a wave carries depends on the amplitude. Tsunami waves carrying higher energy. Its all because of its greater amplitude.

## What is the Amplitude of a Wave?

The amplitude is that which gives the distance from center to either crust or trough of a wave. It is expressed in meters (m). The larger the amplitude is, the more energy it carries.

## Amplitude of a Wave Formula

The Amplitude Formula is given by,
A = $\frac{D}{f}$
where,
D is the distance traveled by the wave and
f is the frequency of the wave.

## Amplitude of a Sound Wave

A sound wave has compressions and rarefaction. The peak tells about the compression and the trough about rarefaction. The greater the distance between peaks and troughs the larger will be the amplitude of the wave.

Amplitude has lot more to say about loudness and volume of sound. Just as bigger waves crash on beach with more force than smaller waves bigger waves stimulate our ear drum and cilia with greater volume than another sound wave.A sound wave carrying greater volume is said to have greater sound pressure level (SPL). It is expressed in decibels.

## Amplitude of a Sine Wave

The amplitude of sine wave equation is given as
y(t) = A sin($\omega$ t + $\phi$ )
where,
A is the amplitude of the sine wave,
$\omega$ is the angular frequency.

The angular frequency is given as
$\omega$ =2 $\pi$ f
where,
f is the frequency,
t is the varying parameter,
$\phi$ is the phase change.

## Amplitude of a Light Wave

The amplitude of light tells about how intense or bright a light wave is relative to other light waves of same wavelength. It gives an idea of how much energy a wave carries. If light from star A is brighter than star B carrying same wavelength. It tells that star A has larger amplitude comparatively.

## How to find the Amplitude of a Wave?

Lets go through same examples on amplitude of a wave:

### Solved Examples

Question 1: Calculate the amplitude of the wave that travels a distance of 50 m carrying a frequency of 100 Hz.
Solution:

Given: Distance D = 50 m, frequency f = 100 Hz

The amplitude of wave is given by
A = $\frac{D}{f}$
= $\frac{50\ m}{100\ Hz}$
= 0.5 decibels.

Question 2: A sine wave is represented by y = 4 sin $\omega$ t. what is its amplitude?
Solution:

The sine wave is expressed in the form y = A sin $\omega$ t
Hence the amplitude is A = 4.