Helmholtz resonance

A Helmholtz resonator (named after Hermann von Helmholtz ) is an acoustic resonator. To the layman it is likely generated as a bottle neck blown in on a sound, be part of everyday life. Helmholtz developed in 1859 this resonator to the upper acute opening a single tone from a sound mixture, which penetrated into the lower opening to prove with his ear. The resonator was initially blown glass and later formed from sheet brass.

Design and function

A Helmholtz resonator consists of an air volume in any form, which has a cylindrical narrow short neck with an opening to the outside. By the elasticity of the volume of air inside, in combination with the inertial mass of the air contained in the opening creates a mechanical mass -spring system with a pronounced resonance frequency, wherein the spherical shape is assumed. Cylinders or cuboids already have several natural frequencies. A cube is the spherical shape nor the next.

The spring constant can be calculated as a function of the cross sectional area of the resonator neck and the enclosed air volume.

Thus, for the resonant angular frequency of the system

And consequently for the resonant frequency

However, the flow velocity at the resonator throat changes smooth and not abrupt ( as assumed in this derivation ). The neck forms a cavity open at both ends for themselves. This has the consequence that the Resonatorhalslänge at the ends by the amount of so-called end correction of the opening or cavity correction increases are to be expected. Helmholtz stated for approximately π / 4 R, when the neck is short and has the radius r. This estuary correction depends on the shape and configuration ( round, square, slot-shaped ) of the estuary. Taking account of the opening correction, the formula for the resonant frequency

  • : Speed ​​of sound ()
  • : Volume of the enclosed gas ()
  • : Cross-sectional area of the opening at the resonator neck ()
  • : Length of the resonator neck ()
  • : Estuary correction ()

Musical Instruments

Helmholtz resonators are built especially for low tones in a bass marimba. You have the advantage of low dimension compared to cylindrical resonators. A developed only in 2000 musical instrument called slope also makes use of, among other things such as the ghatam or Udu the properties of a Helmholtz resonator.

Helmholtz resonators as an absorber in room acoustics

Resonance absorber includes the sound absorbers, and essentially consist of an oscillating mass and a spring. The incident sound energy is converted into kinetic energy of the mass. The maximum absorption occurs in the region of the natural frequency where the mass oscillates most. The mass of both plates, such as plywood, gypsum board, particle board, vinyl or foil can ( plate transducers ) are used, as well as perforated plates vibrating in the hole air ( perforated plate vibrator and Helmholtz resonators). As spring acts the trapped air volume behind the plate.

The role of sound absorbers is to convert sound energy into other forms of energy. They come in the field of noise and room acoustics for use. Sound absorbers according to their functioning divided into the following groups:

  • Porous absorber,
  • Resonance absorber and
  • Combinations of the two.

In the porous absorber, the sound energy is converted through friction of the air molecules in the absorber to heat. This process is referred to as the dissipation. The absorbance, described by the dimensionless sound absorption coefficient α is frequency dependent and is determined by the porosity of the structure factor and the longitudinal flow resistance. The advantages of the porous absorber are in a high absorption in the middle and upper frequency range. The disadvantage is generally in a low absorption at low frequencies. The advantage of the resonance absorber is a high sound absorption in low frequencies. Disadvantage is the low sound insulation at the middle and high frequencies.

The absorption capacity of resonance absorbers is described by the equivalent sound absorption area and is dependent upon the arrangement of the resonator space. Knowledge of the resonant frequency, however, is not sufficient to describe the absorption capacity of a resonator. The "goodness", which tells about the bandwidth, a resonator the sound field extracts energy is also an important characteristic of resonators. Also, the maximum absorbance (at the resonant frequency ) is crucial. This is described by the equivalent sound absorption area of the resonator. Into the space edges, the effectiveness is greater than in the middle of the room space. However, the efficacy is greatest in the arrangement in the corners. When using multiple resonators these can be arranged at the closed surfaces next to each other.

The applications of resonators are very diverse. In room acoustics Helmholtz resonators can be used specifically for the absorption of narrow-band, low-frequency spatial modes. You can for example be used in concert halls, theaters, studios, offices and conference rooms or schools. They can be either visible part of the interior decoration, as can also be arranged concealed behind an open suspended ceiling.

Speakers

Helmholtz resonators found in loudspeaker for a long time in the form of bass reflex enclosures use. 2003, the developer Bernd Timmermanns presented the possibilities of an internal Helmholtz absorber for the suppression of individual standing waves inside of loudspeaker cabinets of all types.

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