Work out standing wave harmonics instantly with clear inputs, formula shown and shareable results.
A string fixed at both ends supports standing waves whose wavelengths fit a whole number of half-waves into its length, so f(n) = n.v/(2L). A 0.65 m string carrying waves at 200 m/s has a 153.8 Hz fundamental, and its third harmonic sits at 461.5 Hz with four nodes. The harmonic series is exactly integer, which is why plucked strings sound musical.
Harmonic frequencies
f(n) = n v / (2L)
Mode wavelength
lambda(n) = 2L / n
Because both ends must be nodes, so only whole numbers of half-wavelengths fit. Drums and bells have two-dimensional modes and are not so simple.
Shorten it, tighten it or use a lighter string. Frequency goes inversely with length and with the square root of tension.