# Helmholtz Resonators - Basic Analytic Devices

## References

Helmholtz Resonator - Fourier Analysis

Helmholtz Resonator - Fourier Synthesis

Helmholtz Resonator

Helmholtz Resonator (Wolfram Research)

Helmholtz Resonator (3Drums)

Helmholtz Resonator (The University of New South Wales)

Dan Russell's (Kettering University)  Acoustics and Vibration Animations

"A Helmholtz resonator or Helmholtz oscillator is a container of gas (usually air) with an open hole (or neck or port). A volume of air in and near the open hole vibrates because of the 'springiness' of the air inside. A common example is an empty
bottle: the air inside vibrates when you blow across the top, as shown in the diagram at left. (It's a fun experiment, because of the surprisingly low and loud sound that results.)

"Some small whistles are Helmholtz oscillators. The air in the body of a guitar acts almost like a Helmholtz resonator*. An ocarina is a slightly more complicated example. Loudspeaker enclosures often use the Helmholtz resonance of the enclosure to boost the low frequency response."

"…The vibration here is due to the 'springiness' of air: when you compress it, its pressure increases and it tends to expand back to its original volume. Consider a 'lump' of air at the neck of the bottle (shaded in the middle diagrams). The air jet can force this lump of air a little way down the neck, thereby compressing the air inside. That pressure now drives the 'lump' of air out but, when it gets to its original position, its momentum takes it on outside the body a small distance. This rarifies the air inside the body, which then sucks the 'lump' of air back in. It can thus vibrate like a mass on a spring (diagram at right). The jet of air from your lips is capable of deflecting alternately into the bottle and outside, and that provides the power to keep the oscillation going." (source)

 THE HELMHOLTZ RESONATOR (Taken from the 3Drums web site) "The resonators that Helmholtz described performed an incredible feat. When sound would hit the (a) opening, the vibrations would excite the volume of air in the body of the resonator. However, because of its peculiar design, the resonator would only transfer and amplify a single tone to the (b) opening, but only if that tone was present in the sound being made. The volume of the body determined which tone was transferred. "Helmholtz would place the (b) opening in his ear and use it to pick out individual musical tones when many were present. For instance, if a three-noted chord was played, and a resonator was present that was tuned to one of those notes, only that note would be audible to Helmholtz. However, if a resonator were present that was tuned for a note that was not being played, nothing would be heard. Even if the note the resonator was tuned for were extremely quiet in comparison to the rest, the resonator would amplify the correct note, allowing Helmholtz to hear even the faintest of sounds. "Helmholtz had many resonators of different sizes and shapes. In fact, any rigid structure containing a volume of air connected to the outside via a small opening (hole, port, or neck) that amplifies a particular frequency can be considered a Helmholtz resonator. A very common object that classifies is a standard beer bottle. When a person blows across the top of an empty bottle, a low oo (as in tool) can be heard. Regardless of how hard or soft the person blows, the same note is created, just louder or softer." "…When the air in the opening of a Helmholtz resonator is disturbed, it bounces like a mass on a spring in simple harmonic motion, creating sound. The frequency of the sound created is equal to that of the air's vibration. This frequency is determined by a simple formula, where is the frequency, is the speed of sound in air, is the surface area of the hole, is the volume of air in the resonator's body and is the length of the neck or port …."

## Helmholtz Response Curves

 Waveform (top) and sound spectrum (the latter on a log-log scale) of the impact response of a Helmholtz resonator. (source)