Why Strings Only Play Certain Notes

Lesson notes

Key points

• Both fixed ends must be nodes, so only whole numbers of half wavelengths fit along the string's length L.
• Using v = fλ, the allowed frequencies are fₙ = nv/2L, called harmonics or normal modes.
• Wave speed depends on tension T and mass per unit length μ, so tightening a string raises its pitch.
• The lowest mode, n = 1, is the fundamental; higher harmonics are integer multiples of it and shape the instrument's tone.

Takeaway: Fixed ends force fₙ = nv/2L, with v = √(T/μ).

Boundary conditionsHarmonicsTension and pitchFundamental