Figure. shows two snapshots of medium particle supporting a plane progressive wave travelling along positive `x-`axos, corresponding to instants `t=0.002 s` and `t=0.008 s`, respectively shown by curves numbered `1` and `2`.
Assume that the interval between the two snapshots is less than the time period.

Velocity of the wave is

Options

A. `(1700)/(3)m//s`
B. `(1700)/(5)m//s`
C. `(2500)/(7)m//s`
D. `(2500)/(3)m//s`

Answer

d

Explanation

From the graph it is clear
wave velocity `v=((8-3))/(0.006)`
`v=(5xx10^(3))/(6)m//s`
And wave velocity `v=flambda`
`(5xx10^(3))/(6)=f(9-1)implies f=(5xx10^(3))/(6xx8)=104 s^(-1)` Let `y=A sin(omegat-kx+phi)`
for curve (1):
`-(1)/sqrt(2)=1 sin(omega+phi)=-(1)/sqrt(2)`
`implies sin(0.002omega+phi)=(5pi)/(4)` or `(7pi)/(4)`
but as the velocity is downward
so `0.002omega+phi=(5pi)/(4)`
For curve (2):
`1=1 sin (omegaxx0.008+phi)`
`implies0.008omega+phi=2pi+(pi)/(2)` From Eqs. (i) and (ii),
`6omega=1250pi`
`impliesf=(1250pi)/(12pi)=104 Hz`
`v=f lambda=(1250)/(12)xx8=(2500)/(3)m//s`