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The displacement y of a particle in a medium can be expressed as:

$y=10^{-6}\sin \left ( 100t +20x+\pi /4 \right )m$ where t is in second and x in meter. The speed of the wave is

Option 1)
$2000 m/s$

Option 2)
$5 m/s$

Option 3)
$20 m/s$

Option 4)
$5\pi m/s$

Answers (1)

best_answer

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)

$2000 m/s$

This is an incorrect option.

Option 2)

$5 m/s$

This is the correct option.

Option 3)

$20 m/s$

This is an incorrect option.

Option 4)

$5\pi m/s$

This is an incorrect option.

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