A transverse sinusoidal wave of wavelength 20 cm is moving along a string towards increasing x. the transverse displacement of the string particle at x=0 as a function of time is shown in figure.

Q. The velocity of propagation of the wave is ?

Options

A. `-2cm//s`
B. `+2cm//s`
C. `+1.5cm//s`
D. `-2.5cm//s`

Answer

D

Explanation

Wave equation,
`y=Asin(kx-omegat+phi)=4sin[(2pi)/(20)x-2pixx0.1t+phi]`
At t=0, x=0, y=0
`implies phi=0` or `pi`
But at position x=0 as time progresses, particle starts moving along positive y-direction
`therefore phi=pi` satisfies
`therefore`Equationn of wave will be `y=4sin((pi)/(10)x-0.2pit+pi)`, x in cm and t is sec.
`therefore`Particle-velocity
`v_(p)(x,y)=(deltay)/(deltat)=4cos((pi)/(10)x-0.2pit+pi)xx(0.2pi)`
`therefore v_(p)(0,5)=4cos((pi)/(10)xx0-0.2pixx5+pi)xx(-0.2pi)=-0.8pi=-2.5cm//s`