Strummel

Meet Strummel, a guitar string who sends waves faster the tighter she is pulled.

When you pluck a string, a wave travels along it. The tension pulls each bit of string back into line, and the mass of the string resists being moved. The wave speed depends on the ratio of tension to the mass per unit length, μ.

A string under 100 N of tension with μ = 0.005 kg/m carries waves at v = √(100 / 0.005) ≈ 141 m/s. Its lowest note on a 0.65 m length is f = v / (2L) ≈ 141 / 1.30 ≈ 109 Hz.

Tightening the string raises the speed and the pitch, which is how you tune a guitar. Thicker, heavier strings have a bigger μ, so they carry slower waves and play lower notes. Pressing on a fret shortens the vibrating length and raises the pitch.

These relations between length, tension, mass and pitch are often called Mersenne's laws, after Marin Mersenne, who described them in the 1630s. Pianos, violins and harps all use them to set their notes.