Standing Waves: Understanding the Basics

[deltafee]

Hi,
I am working on my notes dealing with standing waves and I was wondering would a graph of the equaion y(x,t)= 2Acos(ωt)sin(kx) just a regular wave? Also I was wondering why are standing waves called standing waves. I am sorry if this is the wrong forum.

 

[DiracPool]

Also I was wondering why are standing waves called standing waves.

They're called standing because they stay put, kind of. The counterpart of the standing wave is the traveling wave, because it isn't standing, it's walking, or traveling in some direction, either left or right in the typical 2-d plane they're represented in.

I said "kind of" above, because standing waves only appear to be standing because of the wave dynmaics. That is, what you have is one wave traveling to the right while another wave is simultaneously traveling to the left. The end result is a superposition or interference pattern that sets up apparent stationary oscillations which represent certain harmonics of a fundamental frequency depending on the boundary conditions of the system. Those being the length of, say, a rope that two people are shaking at either end.

As far as your equation above, that looks like a traveling wave equation to me, a standing wave equation specifies one wave traveling in each direction. However, I haven't double checked that.

 

[elgen]

If you define "wave" as a function that satisfies the wave equation, then your expression of the standing wave is considered "a wave".

If you define "wave" as a function that carries the real power, then your expression is not a wave. No power is transported from one place to another.

It is worth noticing that standing wave also forms if the power carried by the forward traveling wave is not equal to the power carried by the backward traveling wave.

Personally, I think "wave" is used loosely here.