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Suppose a vibrating string held at both ends can produce standing waves given by sinusoids $f_1$, $f_2$, $f_3, \ldots$ with increasing frequencies.

According to Wikipedia, "in terms of a superposition of sinusoids (e.g. Fourier series), the fundamental frequency is the lowest frequency sinusoidal in the sum."

So, for the waveform $f_2+f_3$, is the fundamental frequency equal to the frequency of $f_2$, or is it fixed by the length of the string, i.e. always equal to the frequency of $f_1$?

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  • $\begingroup$ For a string fixed at two ends, the system will have a fundamental frequency dependent on the length of the string (1st harmonic). Think of the fundamental frequency as half of a wavelength along the length of the string, in that there are no nodes. Then the higher harmonics contain higher energies, containing nodes. Check out this high school level analogy with guitar strings. physicsclassroom.com/class/sound/Lesson-5/Guitar-Strings $\endgroup$ – bleuofblue Oct 31 '16 at 20:20
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The length (and tension, mass per unit length) of the string dictates the lowest possible frequency of oscillation of a string and that frequency is called the fundamental or first harmonic.

This is still true even if the first harmonic is absent.
The interesting thing is that most listeners will not actually realise that there is a missing fundamental the brain interpreting the note as though the fundamental was present.

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  • $\begingroup$ Wikipedia states that "in terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum." Is this definition incorrect then? $\endgroup$ – anon Nov 2 '16 at 4:39
  • $\begingroup$ No, the fundamental frequency is the first harmonic. The fact that for some notes "allowed" frequencies are not produced by musical instruments does not change the definition of the fundamental. $\endgroup$ – Farcher Nov 2 '16 at 9:20

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