By Sunil Bhardwaj

6196 Views


Waves are of two types:

1. Progressive Wave

2. Standing Wave

Now progressive wave can be represented as sine wave and cosine wave. So the equations can be …

Sine Wave$$ \Psi = A \sin { \left( \frac { 2\pi }{ \lambda } x \right) } $$

CoSine Wave $$\Psi = A \cos { \left( \frac { 2\pi }{ \lambda } x \right) } $$

Where A is amplitude Here we have added \(\frac { 2\pi }{ \lambda }\) is added to complete the cycle of the wave.

$$ \Psi = A \sin { \left( \frac { 2\pi }{ \lambda } x + \frac { 2\pi }{ \overline { \nu } } t \right) } $$ $$ \Psi = A \sin { 2\pi \left( \frac { x }{ \lambda } + \frac { 1 }{ \overline { \nu } } t \right) } $$ where \(\overline { \nu }\) is wave number. i.e. number of waves.

Also, \(\frac { 1 }{ \overline { \nu } } = \nu\) (frequency of wave) $$ \boxed { \Psi = A \sin { 2\pi \left( \frac { x }{ \lambda } + \nu t \right) } } \qquad ...(1) $$ Similarly if the wave is moving in backward direction we need to substract the time factor. $$ \boxed { \Psi = A \sin { 2\pi \left( \frac { x }{ \lambda } - \nu t \right) } } \qquad ...(2)$$