# Definition of fundamental frequency of waves

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 $f_1$?

• 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 – bleuofblue Oct 31 '16 at 20:20