Only wavelengths that satisfy certain criteria can create standing waves. In the case of a string fixed at both ends, each of the ends must be a node. Therefore, any energy source that creates a standing wave must complete a half-cycle or an integral multiple of a half-cycle across the length of the string. The potential wavelengths for standing waves are
where n is an integer, l is the length of the string, and l is the wavelength. Given v as the velocity of wave propagation, the possible frequencies are
These frequencies form a harmonic series with the lowest, or fundamental, frequency being the first harmonic. The next frequency is known as the second harmonic or first overtone.
