Resonance

Helmholtz resonance is the phenomenon of air resonance in a cavity. The name comes from a device created in the 1850s by Hermann Helmholtz to show the height of the various tones. An example of Helmholtz resonance is the sound created when one blows across the top of an empty bottle.

When air is forced into a cavity, the pressure inside increases. Once the external force that forces the air into the cavity disappears, the higher-pressure air inside will flow out. However, this surge of air flowing out will tend to over-compensate, due to the inertia of the air in the neck, and 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 changes decreasing each time.

This effect is similar to that of a bungee jumper bouncing on the end of a bungee rope, or a mass attached to a spring. Air trapped in the chamber acts as a spring. Changes in the dimensions of the chamber adjust the properties of the spring. A larger chamber would make for a weaker spring, and vice versa.

The air in the the neck of the chamber is the mass. Since it is in motion, it possesses some momentum. A longer port would make for a larger mass, and vice versa. The diameter of the port is related to the mass of air and the volume of the chamber. A port that is too small in area for the chamber volume will choke the flow while one that is too large in area for the chamber volume tends to reduce the momentum of the air in the port.

Helmholtz resonance finds application in internal combustion engines, subwoofers and acoustics. In stringed instruments, such 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 area of the neck can be easily varied to produce different tones. The West African djembe has a relatively small neck area, giving it a deep bass tone. The djembe may have been used in West African drumming as long as 3,000 years ago, making it much older than our knowledge of the physics involved.

Helmholtz resonators are used in architectural acoustics to reduce undesirable sounds such as standing waves by building a resonator tuned to the problem frequency, thereby eliminating it. This technique is most usually used for low frequency waves.

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