So, consider a tranverse travelling wave.
Let's say that it is moving in the **x-direction**,
and the displacement of its medium as it travels
is perpendicular to that motion: in the **y-direction**.
We can describe the position of particles in the medium
in the following manner:

As time passes, the position of particles will change. They will oscillate up-and-down as the wave passes. Is there some way to figure out how fast the particles will move?

Q: How fast will the particles move in the tranverse direction?

Yes, there is a way. Since we know the y-position as a function of time, we can simply take the derivative with respect to time to find the y-velocity as a function of time:

Q: Write an equation for v_{y}as a function of space and time.

Fine.

But we don't have to stop there. We can take things one step further.

Q: Is there a way to figure out the tranverse acceleration of particles in the medium?

Yup. Since we know the y-velocity as a function of time, we can simply take the derivative with respect to time to find the y-acceleration as a function of time:

Q: Write an equation for a_{y}as a function of space and time.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.