You are exciting a helmholtz resonance any time you blow across the top of a bottle and it makes a low humming sound. I don't think this is a strong effect in a traditional scattering configuration, but it is used a lot in guided systems. Think of stubs, radial stubs, and maybe even ring resonators could be considered a helmholtz resonance. These are used for matching, filtering, and more.
You could consider an Helmhotz resonator as a "selective" and "singular point" of sound absorption. In a large room (up to 200-300 m3 , as a theatre) several and well distribuited Helmohtz resonators on walls and ceiling can probaly induce some localized scattering effect.
A Helmholtz resonator is made of a cavity with a short neck. As Dr Kumpf suggested, conventionally it is often used in a waveguide geometry, since radiation from the neck is often used to modulate the transmission or reflection. However, if you calculate the scattering cross-section of such a cavity with a neck, you will find some unique solutions. The fundamental mode of such a resonator can be thought of the following: a plug of fluid moves in and out of the neck region, causing compression and rarefaction of the fluid in the cavity. This mode can have a scattering cross-section some 10 times larger than its geometric cross-section. A good reference can be found in
L.E. Kinsler, Fundamentals of Acoustics, 3rd Ed, Wiley 1982.
I would describe a Helmholtz Resonator as an acoustic device which can be modeled as a Single Degree of Freedom (SDOF) system, and as such has a well determined resonance frequency, which is usually related to its neck geometry (the inertial part) and cavity volume (which acts as a spring because of its compressibility), as said by previous comments.
The scattering effect could be explained from the fact that when positioned, for instance, in a wall of a duct, incident waves would find a discontinuity of boundary conditions when reaching the HR, which would cause them to scatter into other duct modes.
Hamed Sharghi Augusto Amador Medeiros Nicholas Fang Alessandro Schiavi
A membrane-type acoustic metamaterial shows a negative effective mass density below the cut-off frequency.
Will a Helmholtz resonator show a negative effective bulk modulus below its cut-off frequency, or resonance frequency?
Nitish Katiyar The negative effective bulk modulus observed below its cut-off frequency might be a mathematical illusion, as it pertains to the frequency domain where the term 'negative' signifies the phase relationship. Furthermore, it's worth noting that the so-called negative bulk modulus, when assessed against an appropriate comparison standard, does not fundamentally enhance acoustic performance.
Please refer to the attached preprint for more detailed information.
Chao Shen Sir I have gone through your research work; you have done a good job. Right now, I am trying to understand this topic theoretically, and there are lots of reported papers on negative bulk modulus, negative mass density, or double negativity.
I have a clear idea of negative effective mass density.
A Helmholz resonator was originally a thin metal container with two openings in them. One for the ear and one in contact with the sorroundings. They were tuned to given pitches which made it possible to do an «analogue frequency analysis» of sounds. I think Helmholz explained the theory behind them and were able to design them on that semiempiric basis.
The flexible wall Helmholz is utilized in musical instruments with a hole in the soundbox and has been so for thousands of years. The principle is also used in bass reflex loudspeakers and subwoofer to improve the low frequency sound output, as the principle does to the musical instruments. The more popular Helmholz resonator is a glass bottle with a neck driven by blowing it strategically across the opening.
The principle is also active in a car at speed. If the window is opened to a given area, a strong low frequency periodic vibration may appear. That is likely to be a driven Helmholz.
Regarding scattering one may expect it to scatter almost omnidirectionally while the object is smaller than the wavelenght in air. One fun application of wave scattering is Colin Goughs measurement of wave scattering by his violin. As the Helmholz is omnidirectional some energy of the incident wave is lost by the scattering of the Helmholz and a little from the other two main «breathing» modes of the violin. Open tube ends do also scatter omnidirectionally.
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