Young Blonde Girl Reveals Her Necklace And Hold-ups With Dots On The Chair At The Old Piano

A vibrating wire subdivides itself into many parts vibrating at the same time. Each part produces a pitch of its own, called a partial. A vibrating string has one fundamental and a series of partials. The most pure combination of two pitches is when one is double the frequency of the other.
For a repeating wave, the velocity, v, equals the wavelength, λ, times the frequency, f.
v = λf
On the piano string, waves reflect from both ends. The superposition of reflecting waves results in a standing wave pattern, but only for wavelengths λ = 2L, L, L/2, … = 2L/n, where L is the length of the string. Therefore the only frequencies produced on a single string are f = nv/(2L). Timbre is largely determined by the content of these harmonics. Different instruments have different harmonic content for the same pitch. A real string vibrates at harmonics that are not perfect multiples of the fundamental. This results in a little inharmonicity, which gives richness to the tone but causes significant tuning challenges throughout the compass of the instrument.