By Sunil Bhardwaj

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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. $$\boxed { \Psi = A \sin { 2\pi \left( \frac { x }{ \lambda } - \nu t \right) } } \qquad ...(2)$$

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