Pipe Resonance Frequency Calculator
When sound waves travel inside a tube or pipe and reflect from the ends, standing waves form at specific frequencies called resonant frequencies or harmonics. Open pipes (open at both ends, like flutes) support all integer harmonics; closed pipes (closed at one end, like clarinets and some organ pipes) support only odd harmonics. These resonances are the acoustic basis of all wind instruments. Enter the pipe length and the harmonic number to find the resonant frequency for both open and closed configurations.
Pipe resonance formulas
Open pipe: fn = n × c / (2L)
Closed pipe (odd n only): fn = n × c / (4L)
Where n is the harmonic number, c is the speed of sound in m/s, and L is pipe length in metres. For closed pipes, even harmonics do not exist; enter odd values of n.
Example: 1 m pipe at 343 m/s
- Open, n=1 (fundamental): 343 / (2 x 1) = 171.50 Hz
- Open, n=2: 343 x 2 / (2 x 1) = 343.00 Hz
- Closed, n=1 (fundamental): 343 / (4 x 1) = 85.75 Hz
- Closed, n=3: 343 x 3 / (4 x 1) = 257.25 Hz
Frequently asked questions
What is pipe resonance?
Pipe resonance occurs when a standing wave forms inside a tube. The natural frequencies at which this happens are the resonant frequencies or harmonics of the pipe. They depend on pipe length and whether the ends are open or closed.
What is the formula for an open pipe?
For a pipe open at both ends, all harmonics are present: f_n = n x c / (2L), where n = 1, 2, 3... c is the speed of sound, and L is the pipe length. The fundamental (n=1) is the lowest resonant frequency.
What is the formula for a closed pipe?
A pipe closed at one end and open at the other supports only odd harmonics: f_n = n x c / (4L), where n = 1, 3, 5... The fundamental is half the frequency of an equivalent open pipe of the same length.
How does pipe length affect pitch?
Shorter pipes produce higher frequencies. Doubling the pipe length halves the resonant frequency (lowers pitch by one octave). This is why bass organ pipes are physically large.
Does temperature affect the result?
Yes. The speed of sound in air increases with temperature: c approximately 331 + 0.6T m/s where T is in degrees Celsius. This calculator uses 343 m/s (20 degrees C). Organ tuners and woodwind players must account for temperature changes.
Official sources
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
- AES: Audio Engineering Society.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.