Helmholtz Resonator Calculator

A Helmholtz resonator is an acoustic device consisting of a rigid cavity with a small opening (neck or port). Named after Hermann von Helmholtz, it resonates at a specific frequency determined by the cavity volume and neck geometry. Common examples include guitar bodies, bass reflex speaker ports, and automobile exhaust systems.

Air in the neck acts like a mass on a spring, where the compressible air inside the cavity acts as the spring. When sound at the resonant frequency enters the neck, the air plug oscillates in and out, amplifying that frequency. At resonance, energy transfer between the incoming wave and the cavity air is at its maximum.

The resonant frequency is calculated using the formula: f = (c / 2π) × √(A₀ / (V × L₀)), where c is the speed of sound (~344 m/s in air), A₀ is the neck cross-sectional area, V is the cavity volume, and L₀ is the effective neck length. This calculator handles the math for you given your shape parameters.

The end correction accounts for the extra mass of air that vibrates just outside the neck opening. For a circular opening of radius r, a flanged end adds approximately 0.85r to the effective neck length. Using end corrections gives a more accurate resonant frequency, especially when the neck is short relative to its diameter.

In automotive exhaust systems, Helmholtz resonators are tuned chambers attached to the exhaust pipe designed to cancel out specific undesirable noise frequencies. By tuning the resonator's cavity volume and neck dimensions to the offending frequency, destructive interference reduces the sound level at that frequency reaching the cabin or exterior.

Helmholtz resonance is found in many familiar objects: blowing across the top of a bottle, the bass boost from a guitar's soundhole, ported subwoofer enclosures, room acoustic panels, noise-reducing earmuffs, and even ancient Greek theatre amphitheatres which used resonating vessels to amplify certain frequencies.

Yes — temperature changes the speed of sound in air (approximately 331 + 0.6×T m/s at temperature T in °C). Since resonant frequency is directly proportional to the speed of sound, a warmer environment raises the resonant frequency slightly. This calculator lets you adjust the speed of sound to match your environmental conditions.

Yes. This calculator supports arbitrary volumes (enter directly), parallelepipeds (boxes), spheres, and cylinders for the cavity, and arbitrary, circular, or rectangular shapes for the neck opening. For sphere or cylinder shapes, volume is calculated automatically from the dimensions you enter.