# The displacement y of a particle in a medium can be expressed as: where t is in second and x in meter. The speed of the wave is Option 1) Option 2) Option 3) Option 4)

As we learnt in

Travelling Wave Equation -

$y=A \sin \left ( Kx-\omega t \right )$

- wherein

$K=2\pi /\lambda$

$\omega = \frac{2\pi }{T}$

$\lambda =$  wave length

$T =$ Time period of oscillation

Given wave equation

$y= 10^{-6}\sin \left ( 100t+20x+\frac{\pi }{4} \right )m$

Standard equation :$y= a sin\left ( \omega t+kx+\phi \right )$

$Compare\: the\: two$

$\therefore \omega = 100\: and\: k= 20$

$\therefore \frac{\omega }{k}= \frac{100}{20}\Rightarrow \frac{2\pi n}{2\pi /\lambda }= n\lambda = \nu = 5$

$\therefore \nu = 5m/s$

Correct option is 2.

Option 1)

This is an incorrect option.

Option 2)

This is the correct option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.

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