standing wave on string (BR Phys Ch. 5 passage II # 9-12)

[dougkaye]

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This is bothering me, because I swear I've done questions where the authors ask for the speed of standing wave on string (string fixed at both ends) and they say it's b/c it's not propogating thru space.

Now, BR is saying that such a string (it's between a wall and oscillator) DOES have velocity (I'm assuming they mean propogation velocity). So what's the deal?! Question 9 for instance asks "How does the speed of the wave on String I compare to the speed of the wave on String II?" Again, these are both standing waves between an oscillator and a wall. They differ in terms of wavelength but have same frequency.

Any ideas are welcome. Intuitively, it seems like a wave on a fixed string is not propagating through space, whereas an EM or sound wave is. But this passage doesn't support that logic. Help!

 

[Rabolisk]

They differ in terms of wavelength but have same frequency.

I don't know anything about this passage, but if a wave has the same frequency but different wavelength, then it must have different velocity.

 

[epsilonprodigy]

Don't think of it as velocity as in the whole thing propagating through space like it's doing the worm. Think of individual particles that make up the string. Even in a standing wave there is motion (of the particles that make up the string) and thus, there is a nonzero velocity.

v= (tension)/(mass of string)/(length of string)

This is sometimes denoted as Tension/mu, where "mu" is analagous to the "density" or mass/length of the string. The string is its "own" medium.

In a standing wave, the particles of the string exhibit sinusoidally oscillating velocity. In other words, they periodically "squish and spread." Like in other examples of simple periodic motion, the wave representing acceleration exactly opposes this (i.e. when v is at its max, a is at its min, etc.)


Hope that helps or at least makes sense. Check out BR's explanation if you can. I believe Khan Academy has a few good illustrations as well.