Instantaneous Particle Velocity from Wave

[rocapp]

Homework Statement

See the attached picture.

Homework Equations

D(x,t) = Asin(kx-ωt+ϕ)

The Attempt at a Solution

The instantaneous velocity of a particle would be the derivative of displacement:
D'(x,t) = -ωAcos(kx-tω+ϕ)

Then plug in the known values:
= -18.84cos((π/15)x-3πt)

The above should be the answer, but since I do not have a specified value for time or distance, I am not sure how to come to a numerical answer. Thanks in advance!

 

[mfb]

since I do not have a specified value for time or distance

You have an indirect one: At point 1, the position is 0. This allows to determine a value for the phase (kx-ωt+ϕ), which you can use in the equation for the velocity.

 

[rocapp]

Thanks!