Equations · equation
Standing Waves
Waves & Optics · 1701
- Equation
- f_n = n v / (2L), n = 1, 2, 3… (stopped pipe: f_n = n v / (4L), odd n only)
- Field
- Waves & Optics
- Symbols
- f_n the nth resonant frequency · v wave speed on the string or in the pipe · L its length · n the harmonic number
- Year
- 1701
Significance
Confine a wave and only those wavelengths that fit — a whole number of half-waves — survive; the rest cancel. That is why a string, a pipe and a laser cavity have a fundamental and overtones, why a bridge has modes, and why an electron in an atom has discrete energies. A pipe stopped at one end fits quarter-waves instead and keeps only the odd harmonics, which is why a clarinet overblows a twelfth where a flute overblows an octave, and why it sounds an octave lower than its length suggests. Sauveur named the harmonics in 1701.
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.