Helmholtz Resonator

The Helmholtz resonator is an acoustic filter element. It is effectively a mass on a spring (single degree of freedom system). The large volume is the spring and the volume of air in the neck is the mass.

The acoustic length of the neck is longer than the physical length. An additional amount must be added at each end. This amount is related to whether the end of the duct is flanged or unflanged and the radius, a of the duct. In the drawing the end that terminates within the volume is termed flanged (extra length 0.85a) and the end that opens into the atmosphere would be termed unflanged (extra length 0.6a).

For the case shown the effective length, L′ is:

The resonant frequency, f0 is:

Historical Notes

  1. The Romans used helmholtz resonators formed from clay urns to tune the acoustic characteristics of ampitheatres.
  2. Before the arrival of sophisticated electronic equipment for the analysis of a sound field helmholtz resonators were used to establish the frequency content of a sound field. The helmholtz resonator was placed in the sound field and when the external sound field was switched off the helmholtz resonator would continue to resonate ('sing') for a short while, indicating the presence of the excitation frequency.

Reference

L. E. Kinsler, A. R. Frey, A. B. Coppens, J. V. Sanders, (1982), "Fundamentals of Acoustics" Wiley, New York

J. W. S. Rayleigh, (1945) "The Theory of Sound, Volume II", Dover, New York, Art. 293.

A. Selamet, P. M. Radavich, N. S. Dickey, J. M. Novak, "Circular concentric Helmholtz resonators", Journal of the Acoustical Society of America

See also: Acoustic Duct End Correction, Acoustic Filter Elements, Expansion Chamber, Helmholtz Hermann, Quarter Wave Tube, Resonator, Side Branch Orifice.

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Subjects: Noise & Vibration