First slide

Simple harmonic motion

Question

The displacement y of a particle in a medium can be expressed as ${y=10}^{-6} sin (100t+20x+ \frac{π}{4}) m$ where t is in second and x in metre. The speed of the wave is

Moderate

A

$2000 {m s}^{-1}$
B

$5 {m s}^{-1}$
C

$20 {m s}^{-1}$
D

$5 {π m s}^{-1}$

Solution

As given displacement equation of SHM, ${y=10}^{-6} sin (100t+20x+ \frac{π}{4})$ -------(1)
Equation(1) comparing it with $y=Asin(ωt+kx+ φ)$ , we obtain ${ω=100rads}^{-1} {,k=20Nm}^{-1}$
Speed of wave $V= \frac{ω}{K} = \frac{100}{20} {=5ms}^{-1}$ .

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