- Write the equation of Progressive Wave.
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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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