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

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.
Striking the piano key with greater force increases the amplitude of the waves and therefore the volume. From pianissimo (pp) to fortissimo (ff) the hammer velocity changes by almost a factor of a hundred. The hammer contact time with the string shortens from 4 ms at pp to less than 2 ms at ff. If two wires adjusted to the same pitch are struck at the same time, the sound produced by one reinforces the other, and a louder combined sound of shorter duration is produced. If one wire vibrates out of synchronization with the other, they subtract from each other and produce a softer tone of longer duration.