By considering the superposition of two waves propagating through a string, one representing the original or incident wave and the other representing the wave reflected at the fixed end, if both ends of the string is fixed then the waves can reflected and travel back and forth. Standing wave can be formed if the length of the string is an integer numbers of half wavelength.

I just wonder what will we get if the length of the string is NOT an integer numbers of half wavelength and both ends are fixed?

  • $\begingroup$ To me, it always resembled white noise on an oscilloscope. $\endgroup$ – Jim Jul 3 '15 at 15:09
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    $\begingroup$ There will be no standing waves and the nodes and anti-nodes will be moving. $\endgroup$ – CuriousOne Jul 3 '15 at 15:09

According to "Fundamentals of Physics 9ed" by Halliday Resnick (p. 496), "there will not be a steady wave pattern with nodes and antinodes, and the total wave will not be a standing wave." The result will be somewhat like waves reflecting off the irregular shores of a tiny pond - unrecognizable patterns, or like confused seas on the ocean, where the waves generated by several different weather patterns meet. This kind of confusion is notoriously difficult for a sailboat to navigate, because the patterns change frequently and unexpectedly.

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    $\begingroup$ And it'll sound terrible . Signed, a musician who's created such waves by accident now and then. $\endgroup$ – Carl Witthoft Jul 3 '15 at 17:02

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