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My question is simple:

How is it that a standing wave has velocity? I mean, it's not travelling...

A lot of equations depend on this concept, for example: $f_n = \frac{nv}{2L}$

Here we're finding the frequency of the nth harmonic given the velocity of the wave on a string.

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The velocity term here means the speed of a wave traveling through the medium. Take, for instance, a pipe resonating, like in an organ (the equations are basically the same). The v term means the speed of sound in air, even though the wave is standing. The same thing applies here - v means "speed of any wave" not just "speed of this particular wave".

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    $\begingroup$ Ok, but there is a difference between what 'v' means in a travelling pulse and the standing wave, right? Like, the 'v' term for a standing wave is representing something a lot more obscure right? edit: even though both would give exactly the same cypher. $\endgroup$ – DLV Jun 24 '14 at 20:25
  • $\begingroup$ @David A wave's velocity is given by its frequency multiplied by its wavelength. A standing wave has both, giving it a velocity, even though it doesn't appear to "move" in the sense that other waves do. $\endgroup$ – Dave Coffman Jun 24 '14 at 20:37
  • $\begingroup$ I thought people would stop answering if they saw your answer was accepted. But I'll accept you now. Sorry for being so selfish :). Im new here so I don't know if you can accept more than one answer. $\endgroup$ – DLV Jun 24 '14 at 22:59
  • $\begingroup$ If you are so kind, could you maybe explain to me how exactly does a standing wave have a velocity? I mean, I can understand that the velocity could be useful as an analogy, but I just dont see it travelling :(. edit: Like you if consider the nodes, these are always at a fixed point... how is it possible that the wave travelled across this point? $\endgroup$ – DLV Jun 24 '14 at 23:01
  • $\begingroup$ @David In coming up with an answer to your last comment, I realized that what I said in my first comment was wrong. A standing wave has no velocity, hence the name. A standing wave, though, is not a traditional wave - it is the sum of two out-of-phase waves with the same frequencies moving in opposite directions, which causes the unique behavior of the standing wave. Both of these waves move at the velocity "v" which appears in the equation, but because they move in opposite directions, the velocities cancel, leaving the standing wave stationary. $\endgroup$ – Dave Coffman Jun 25 '14 at 0:37
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The velocity of the standing wave is the velocity of the incoming and reflecting wave that formed this standing wave. See http://www.physicsclassroom.com/class/waves/Lesson-4/Formation-of-Standing-Waves

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In that formula, v is the speed of wave propagation in the medium, not the speed of that particular standing wave. Frequency of a standing wave is so conspicuously supposed to depend on the wave speed in the medium. Faster the component waves travel, higher will be the frequency with which the 'points' of standing wave change phase.

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