Helmholtz resonance is the phenomenon of air resonance in a cavity. The device was created in the 1860s by Hermann von 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.

Qualitative explanation

---

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, 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 akin 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. Air, being compressible, has a definite spring constant. 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 port acts as the mass. Since it is in motion, it possess some inertia. 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 inertia in the port.

Quantitative explanation

---

We know some useful facts about Helmholtz resonance from simple empirical studies. The resonance is proportional to:

• The inverse square-root of the cavity volume
• The inverse square-root of the length of the cavity outlet
• The square-root of the area of the cavity opening

We can then easily derive the following formula for the resonance frequency:

$f\_\{H\}\; =\; \backslash frac\{v\}\{2\backslash pi\}\backslash sqrt\{\backslash frac\{A\}\{Vl\}\}$

Where v has units of velocity, and is a proportionality constant.

Applications

---

Helmholtz resonance finds application in internal combustion engines (see airbox), subwoofers and acoustics.

External links

---

• HyperPhysics Acoustic Laboratory
• HyperPhysics Cavity Resonance

Acoustics

Helmholtz-Resonator | Risonanza di Helmholtz | Helmholtzresonator