Helmholtz resonance

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Helmholtz described in his 1862 book, "On the Sensations of Tone", an apparatus able to pick out specific frequencies from a complex sound. The Helmholtz resonator, as it is now called, consists of a rigid container of a known volume, nearly spherical in shape, with a small neck and hole in one end and a larger hole in the other end to admit the sound.

When the resonator's 'nipple' is placed inside one's ear, a specific frequency of the complex sound can be picked out and heard clearly. In Helmholtz’ book we read: When we "apply a resonator to the ear, most of the tones produced in the surrounding air will be considerably damped; but if the proper tone of the resonator is sounded, it brays into the ear most powerfully…. The proper tone of the resonator may even be sometimes heard cropping up in the whistling of the wind, the rattling of carriage wheels, the splashing of water."

A set of varied size resonators was sold to be used as discrete acoustic filters for the spectral analysis of complex sounds.

There is also an adjustable type, called a universal resonator, which consists of two cylinders, one inside the other, which can slide in or out to change the volume of the cavity over a continuous range. This type of resonator is in use in the Fourier analyzer, and is equivalent to tone variator in its function.[2] When air is forced into a cavity, the pressure inside increases. When the external force pushing the air into the cavity is removed, the higher-pressure air inside will flow out. Due to the inertia of the moving air the cavity will be left at a pressure slightly lower than the outside, causing air to be drawn back in. This process repeats, with the magnitude of the pressure oscillations increasing and decreasing asymptotically after the sound starts and stops.

The port (the neck of the chamber) is placed in the external meatus of the ear, allowing the experimenter to hear the sound and to determine its loudness. The resonant mass of air in the chamber is set in motion through the second hole, which is larger and doesn't have a neck.

A gastropod seashell can form a low Q Helmholtz resonator, amplifying many frequencies, resulting in the "sounds of the sea".

The term Helmholtz resonator is now more generally applied to include bottles from which sound is generated by blowing air across the mouth of the bottle. In this case the length and diameter of the bottle neck also contribute to the resonance frequency and its Q factor.

By one definition a Helmholtz resonator augments the amplitude of the vibratory motion of the enclosed air in a chamber by taking energy from sound waves passing in the surrounding air. In the other definition the sound waves are generated by a uniform stream of air flowing across the open top of an enclosed volume of air.

Quantitative explanation[edit]

See also Resonance of a sphere of air

It can be shown[3] that the resonant angular frequency is given by:



  • is the cross-sectional area of the neck;
  • is the mass in the neck;
  • is the static pressure in the cavity;
  • is the static volume of the cavity.

For cylindrical or rectangular necks, we have



  • is the equivalent length of the neck with end correction, which can be calculated as :, where is the actual length of the neck and is the hydraulic diameter of the neck;[4]
  • is the volume of air in the neck,



From the definition of mass density (): , thus:





The speed of sound in a gas is given by:


thus, the frequency of the resonance is:





Helmholtz resonance finds application in internal combustion engines (see airbox), subwoofers and acoustics. Intake systems described as 'Helmholtz Systems' have been used in the Chrysler V10 engine built for both the Dodge Viper and the Ram pickup truck, and several of the Buell tube-frame series of motorcycles. In stringed instruments as old as the veena or sitar, or as recent as the guitar and violin, the resonance curve of the instrument has the Helmholtz resonance as one of its peaks, along with other peaks coming from resonances of the vibration of the wood. An ocarina is essentially a Helmholtz resonator where the combined area of the opened finger holes determines the note played by the instrument.[6] The West African djembe is the original Helmholtz resonator with a small neck area, giving it a deep bass tone. It has been in use for thousands of years.







This effect might also be used to reduce skin friction drag on aircraft wings by 40%.[7]

Helmholtz resonance sometimes occurs when a slightly open single car window makes a very loud sound, also called side window buffeting or wind throb.[8]


Further reading[edit]