The Helmholtz Resonance

A Brief and Not-Too-Technical Introduction to the History and Theory of the Lowest Sound-Producing Mode, and Some Practical Considerations for Instrument Designers

by R.M. Mottola

Originally published in American Lutherie #82, 2005 and Big Red Book of American Lutherie Volume Seven, 2015



Research in physics and acoustics of stringed instruments shows us the mechanism by which sound is produced by those instruments. The plates of the instruments and the air inside vibrate in various patterns, each pattern producing sound in a range around a certain frequency. Each of these patterns can be considered to be a resonator, each with its own characteristics. Some of these resonators exist as modes of vibration of different areas of the plates of an instrument, and some are modes of vibration of the air inside the instrument.

One of the air resonators is composed of the mass of air inside the instrument and the mass of air within and around the soundhole. The natural frequency of this resonator is near the lowest note that an instrument can make. It is generally labeled the A0 resonance, the letter A standing for the word “air” and the numeral 0 indicating that this is the first in a series of air resonances. This resonance is also referred to as the so-called Helmholtz resonance. Understanding how this resonance works in stringed instruments is not difficult, particularly given a historical perspective. Complete understanding involves some math, but a practical understanding can be had without it. Therefore, I am putting off presenting the formulae in the main article and have included them in a sidebar.