Standing Wave Calculator

About this calculator

A standing wave forms on a string fixed at both ends when waves reflecting back and forth interfere to create stationary nodes and antinodes; only wavelengths that fit an integer number of half-wavelengths between the fixed ends survive, giving the harmonic series fₙ = n·v/(2L), where v is the wave speed on the string, L is its length, and n = 1, 2, 3… labels the fundamental and its overtones.

This relationship is the physical basis of every stringed instrument: guitar makers and piano technicians use it to relate string length, tension and mass per unit length (which set v) to pitch, and it's a standard demonstration and lab exercise in introductory physics courses on wave mechanics and acoustics.

Musicians tuning instruments, luthiers designing new ones, acoustic engineers analyzing resonance, and physics students verifying harmonic series experimentally all use this formula to predict or explain the frequencies a vibrating string can sustain.