# How to calculate the Rise speed of a travelling wave? [closed]

As you can see in this wikipedia animation

Phase velocity (red) and group velocity (green) are described, and both show different "speed" in the Propagation direction but what about the transverse direction speed?

How do I calculate the rise speed of a cycle in transversal direction ?

(Look at the extremes of the picture the blue pixel going up and down, this is the vertical up-down speed what I want to calculate)

For example in a very simple wave like this

y(x,t) = A* sin(kx - w t), should I calculate derivative of y having x=constant?

What about in general? How to calculate the Rise speed?

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## closed as off-topic by j.c., Stefan Kohl, Ricardo Andrade, Ryan Budney, Chris GodsilOct 30 '14 at 1:17

This question appears to be off-topic. The users who voted to close gave this specific reason:

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Once you know the phase velocity $\omega$, you know that along the $x$ axis the red dot is described by $x(t) = \omega t$. Then you just apply the chain rule. The value of $y(x,t)$ at the red dot is a function of time $y(x(t),t)$. So $$\frac{d}{dt}y(x(t),t) = \frac{\partial}{\partial x}y(x(t),t) \cdot \frac{d}{dt}x(t) + \frac{\partial}{\partial t} y(x(t),t)$$ which we more succinctly write as $$\omega \partial_x y + \partial_t y$$
Then you are just looking at the vertical position change fixing the $x$-coordinate, which means that it is exactly given by just the partial derivative in the time-direction, $\partial_t$. – Willie Wong Jul 26 '10 at 22:07