# Pipe Resonance Calculator - Open & Closed Pipes, End Correction, Wind Instruments > Open, closed and conical pipe resonances with end correction and standing-wave animation; flute vs clarinet, tone holes, resonance tube, bottles, organ pipes. - URL: https://qilingtools.com/en/physics/pipe-acoustics - Category: Physics Tools (https://qilingtools.com/en/physics) - Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education) - Last updated: 2026-10-29 - Price: Free, no sign-up - Privacy: Runs locally in the browser; files are never uploaded Set the pipe type, length, radius and air temperature to get resonance frequencies with end correction, note names and the overblown interval, and watch animated displacement and pressure standing waves. Compare the resonance series of flute, clarinet, oboe, saxophone and trumpet and see why the clarinet overblows a twelfth; work out the pitch with a tone hole open, find resonances in a virtual resonance-tube lab to measure the speed of sound, compute bottle-blowing pitch and how much water to add, and size organ pipes. Every page can play its sounds with Web Audio. ## How to use 1. Choose a pipe type and set length, radius and temperature to see the fundamental, note and resonance series 2. Pick a resonance number, watch the displacement and pressure animation and press play to hear it 3. On the instruments page compare resonance series and overblown intervals, and move or resize a tone hole 4. Use the resonance tube, bottle and organ pages to run the experiment or solve for length and water level ## Features - Open, closed, complete-cone and truncated-cone pipes with flanged or unflanged end correction - Animated displacement and pressure standing waves showing nodes and antinodes at each end - Flute, clarinet, oboe, saxophone and trumpet resonance series with notes and cents - Tone-hole effective length: open hole vs pipe cut at the hole - Virtual resonance tube: drag the water, record lengths, cancel the end correction to get c - Helmholtz resonator (bottle) and organ pipe lengths, all playable with Web Audio ## FAQ ### How do open and closed pipe resonances differ? A pipe open at both ends has pressure nodes at both ends and fits whole numbers of half wavelengths: f_n = n·c/(2L), a complete harmonic series 1, 2, 3… A pipe closed at one end has a pressure antinode at the closed end and fits odd numbers of quarter wavelengths: f_n = (2n−1)·c/(4L), only the odd members 1, 3, 5…, and for the same length its fundamental is an octave lower. ### What is the end correction and why add it? Sound is not reflected exactly at the open end: a little air outside the pipe moves with the column, so the pipe acts slightly longer than it is. For a thin pipe opening into free air the correction is about 0.61r, and for an opening in a large flat baffle (flanged) about 0.82r, where r is the radius. Ignoring it makes the predicted pitch noticeably sharp for wide or short pipes. ### Why does the clarinet overblow a twelfth but the flute an octave? The clarinet is a cylinder closed at the reed end, so it has only odd resonances and the second one is 3× the fundamental: an octave plus a fifth, a twelfth. The flute is open at both ends and the oboe and saxophone are conical, so their resonances form nearly complete harmonic series and the second is 2×, an octave. That is why the clarinet has a register key that jumps a twelfth and needs more fingerings. ### How does the resonance tube lab cancel the end correction? The water surface is the closed end and the rim the open end, so the first two resonances satisfy L₁ + e = λ/4 and L₂ + e = 3λ/4. Subtracting gives L₂ − L₁ = λ/2 with e gone, so c = 2f(L₂ − L₁). You also get e = (L₂ − 3L₁)/2 to compare with the theoretical 0.61r. ### Why does adding water to a bottle raise the pitch? Blowing across a bottle makes a Helmholtz resonator: the air in the neck is a piston and the air in the body a spring, with f = (c/2π)·√(A/(V·L_eff)). Adding water reduces the air volume V, stiffening the spring, so the pitch rises: a quarter of the volume gives an octave higher. The tool can also work backwards to tell you how much water to add for a given note. ## Related tools - [Unit Converter](https://qilingtools.com/en/math/unit): Free online unit converter: length, area, volume, weight, temperature, time, speed, data, pressure, energy and angle — one value converts every unit at once. - [Vector Calculator](https://qilingtools.com/en/math/vector): Free online vector calculator for 2D and 3D: addition, scalar multiples, dot and cross products, magnitude, angle, unit vector and projections, with checks. - [Significant Figures Calculator](https://qilingtools.com/en/math/significant-figures): Free online sig fig calculator: count significant figures digit by digit, round to N sig figs or decimals with six rounding modes, and compute by sig fig rules. - [Tone Generator](https://qilingtools.com/en/audio/tone-generator): Free online tone generator: sine, square, sawtooth and triangle waves from 1 to 20,000 Hz, a note picker, sweeps, white/pink/brown noise and a WAV download. - [Audio Spectrogram](https://qilingtools.com/en/audio/spectrogram): Free online spectrogram generator: see time, frequency and level from a Hann-windowed STFT, with FFT size, log axis, dB range and colour maps. Exports PNG. - [Decibel Meter](https://qilingtools.com/en/audio/decibel): Free online decibel meter: measure noise with your mic in real time, A/C/Z weighting, fast/slow response, min/max/average/Leq, 60-second graph and calibration. - [Physics Formula Calculator](https://qilingtools.com/en/physics/physics): Physics formulas solved with steps: SUVAT, projectiles, Newton’s laws, inclines, energy, Ohm’s law, resistors, RC, buoyancy, waves, lenses, gravity. - [Fourier Series & FFT Visualizer](https://qilingtools.com/en/math/fourier): Fourier series coefficients and animated partial sums for square, sawtooth, triangle or any function (Gibbs), draw-your-own epicycles and FFT spectra.