What Is the Maximum Transverse Velocity at x=0 for a Moving Wave Pulse?

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Homework Statement

I'll try to translate the problem as faithfully as I can:

A wave pulse moves along the positive OX axis. Its form when t=0 is
f(x) = y0/[1 + (x/a)^2]
Find the expression for the transverse velocity as a function of x and t.
At the point x=0, what will be its max transverse velocity, if v = 210m/s (I assume this is phase velocity), y0 = 1.3cm, and a = 5cm?

The Attempt at a Solution

For the first part, should I substitute x for (x -vt) and take the partial with respect to t of the whole function? That should give me the expression for "vertical" velocity. Then I'd simply substitute x=0, v, y0 and a to get the velocity?

I thought "transverse" meant along the x-axis. The question looks really ambiguous and misleading but I think that's what's being asked, any thoughts?

 

[ehild]

Transverse means that the displacement of the "disturbance" is perpendicular to the direction of propagation. This wave travels along the x axis, in positive direction, the displacement is in the y direction. Imagine that the wave travels along a string, and the particles of the string move up and down. You can find the vertical velocity as you outlined. Do the differentiation with respect to time, substitute x=0 and the given values of v and y0, and find the maximum.

ehild