Standing Wave Calculator (fₙ = nv / 2L)
Standing Wave Calculator (fₙ = nv / 2L)
A string fixed at both ends (like a guitar or violin string) can only vibrate at specific frequencies - its harmonics - each fitting a whole number of half-wavelengths between the two fixed ends. Enter the harmonic number (1st, 2nd, 3rd...), the string length, and the wave speed on the string, and this calculator finds that harmonic's frequency and wavelength, along with a diagram showing the standing wave pattern.
- fₙ = n × v / (2L), so the 2nd harmonic (n=2) of a 1 m string with a wave speed of 340 m/s is f₂ = 2 × 340 / (2×1) = 340 Hz.
- The wavelength of the nth harmonic is λₙ = 2L/n - the 1st harmonic (fundamental) fits half a wavelength on the string, the 2nd harmonic fits a full wavelength, the 3rd fits 1.5 wavelengths, and so on.
- Every harmonic has fixed nodes (zero displacement) at both ends and n-1 additional nodes in between, spaced evenly - this is exactly why musical instruments with strings or air columns produce specific, related pitches rather than arbitrary frequencies.
How do I calculate the frequency of a string's harmonic?
Use fₙ = n × v / (2L), where n is the harmonic number, v is the wave speed on the string, and L is the string length. The 2nd harmonic of a 1 m string at 340 m/s is 2 × 340 / 2 = 340 Hz.
What is the fundamental frequency?
The fundamental (or 1st harmonic, n=1) is the lowest possible frequency a string can vibrate at, given by f₁ = v / (2L) - all higher harmonics are whole-number multiples of it.
Standing Wave Calculator (fₙ = nv / 2L)
A string fixed at both ends (like a guitar or violin string) can only vibrate at specific frequencies - its harmonics - each fitting a whole number of half-wavelengths between the two fixed ends. Enter the harmonic number (1st, 2nd, 3rd...), the string length, and the wave speed on the string, and this calculator finds that harmonic's frequency and wavelength, along with a diagram showing the standing wave pattern.
- fₙ = n × v / (2L), so the 2nd harmonic (n=2) of a 1 m string with a wave speed of 340 m/s is f₂ = 2 × 340 / (2×1) = 340 Hz.
- The wavelength of the nth harmonic is λₙ = 2L/n - the 1st harmonic (fundamental) fits half a wavelength on the string, the 2nd harmonic fits a full wavelength, the 3rd fits 1.5 wavelengths, and so on.
- Every harmonic has fixed nodes (zero displacement) at both ends and n-1 additional nodes in between, spaced evenly - this is exactly why musical instruments with strings or air columns produce specific, related pitches rather than arbitrary frequencies.
How do I calculate the frequency of a string's harmonic?
Use fₙ = n × v / (2L), where n is the harmonic number, v is the wave speed on the string, and L is the string length. The 2nd harmonic of a 1 m string at 340 m/s is 2 × 340 / 2 = 340 Hz.
What is the fundamental frequency?
The fundamental (or 1st harmonic, n=1) is the lowest possible frequency a string can vibrate at, given by f₁ = v / (2L) - all higher harmonics are whole-number multiples of it.