Acoustic Resonance Frequency Calculator

A tube of length L filled with a fluid of sound speed v supports a discrete set of standing-wave resonances. The boundary conditions at each end — open (free air, pressure node) or closed (rigid wall, pressure antinode) — determine which harmonics are present and at what frequencies. This calculator covers the three classic cases of pipe resonance and cavity resonance, plus the Levine–Schwinger end correction that all serious tube acoustics work needs. For the complementary problem of room-sized cavities, see the room mode calculator.

Open – Open tube (e.g. flute, organ flue pipe, PVC resonator)

Both ends are pressure nodes (open to atmosphere). Standing waves fit an integer number of half-wavelengths in the tube: L = n·λ/2, giving f_n = n·v/(2L). All integer harmonics are present: 1×, 2×, 3×, … the fundamental. The fundamental wavelength is twice the tube length. DIY instrument builders often use PVC pipe to prototype open–open resonators before cutting metal or bamboo.

Open – Closed tube (e.g. clarinet body, bottle, organ stopped pipe, bass reflex port)

One open end (pressure node) and one closed end (pressure antinode). Standing waves fit an odd number of quarter-wavelengths: L = (2n−1)·λ/4, giving f_n = (2n−1)·v/(4L). Only odd harmonics exist: 1×, 3×, 5×, … the fundamental. The fundamental wavelength is four times the tube length — so a closed pipe sounds an octave lower than an open pipe of the same length. This is why the clarinet (effectively closed at the reed) overblows at 3× (a twelfth) rather than 2× (an octave) like the flute. Ported subwoofer enclosures use a related quarter-wave port principle to boost bass output at the tuning frequency.

Closed – Closed tube (e.g. enclosed cavity, muffler resonator chamber)

Both ends are pressure antinodes (rigid walls). Same formula as open–open (f_n = n·v/(2L)) but with pressure nodes/antinodes swapped. No end correction applies — there's no open end to "see" beyond. This mode describes sealed exhaust resonator chambers and some muffler designs.

End correction (Levine–Schwinger, ~0.6·r)

An open end behaves as if the tube were slightly longer than its physical length. The air column "bulges" out beyond the rim a small distance — the end correction δ. For an unflanged circular open end, δ ≈ 0.6133·r (Levine & Schwinger 1948). For a flanged open end (e.g. a tube ending in a baffle), δ ≈ 0.85·r. This calculator uses the unflanged value. Without end correction, predicted frequencies are systematically too high — typically by a few percent for a typical instrument tube radius.

Temperature and the speed of sound

Sound speed in air varies with temperature: v ≈ 331.3 + 0.606·T °C (m/s). At 20 °C v = 343 m/s; at 0 °C it drops to 331 m/s — a 3.5% difference that shifts every resonant frequency by the same proportion (about half a semitone). The effect is especially audible when calculating organ pipe frequency: a pipe voiced at 20 °C will play sharp in a cold church at 5 °C by nearly a semitone. For precision work such as organ pipe voicing or ultrasonic transducer design, always use the actual room temperature when calculating expected resonant frequencies. Use the medium selector to pick a pre-set v, or match it to your measured temperature. You can verify the sound speed assumption with the speed of sound calculator.