First slide

Simple harmonic motion

Question

The displacement y of a wave travelling in the x direction is given by $y = 10^{- 4} \sin (600 t - 2 x + π / 3)$ metre. When x is expressed in metres and t in seconds. The speed of the wave motion in $m s^{- 1}$ is

Moderate

A

300
B

600
C

1200
D

200

Solution

The given equation of wave $y = 10^{- 4} \sin (600 t-2x+π / 3)$ ----(1)
Standard equation of wave
$y=asin(wt-kx+φ)$ ----(2), here angular velocity = w, force constant =k
Now comparing equation(1) and (2) we get
${w=600rads}^{-1} {,k=2Nm}^{-1}$
Velocity of wave $= \frac{w}{k} = \frac{600}{2} {=300ms}^{-1}$

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