How does helmholtz resonator work

Some whistles are Helmholtz resonators. The air cavities in some string instruments including the guitar are Helmholtz resonators. The Romans and others used vases with a small amount of cloth fiber to damp out undesirable frequencies.

Modern airplanes use acoustic panels with Helmholtz resonators to damp out engine noise. The theory of Helmholtz resonators is widely used in exhaust systems for internal combustion engines and loudspeaker systems especially ported speakers and subwoofers.

Understanding Sound by abbottds is licensed under a Creative Commons Attribution 4. Skip to content Musical instruments. Wolfe, J. For the bottles in the animation at the top of this page, the wavelengths are and 74 cm respectively, so this approximation is pretty good, but it is worth checking whenever you start to describe something as a Helmholtz oscillator.

The consequence of this approximation is that we can neglect pressure variations inside the volume of the container: the pressure oscillation will have the same phase everywhere inside the container. Let the air in the neck have an effective length L and cross sectional area S. Some complications about the effective length are discussed at the end of this page.

Now you might think that the pressure increase would just be proportional to the volume decrease. That would be the case if the compression happened so slowly that the temperature did not change. In vibrations that give rise to sound, however, the changes are fast and so the temperature rises on compression, giving a larger change in pressure.

This is explained in an appendix. See notes. So the wavelength is 2. This justifies, post hoc , the assumption made at the beginning of the derivation. Resonance, impedance, phase and frequency dependence This section can be read on its own, but if you want more detailed background, see Oscillations , Forced Oscillations and Acoustic compliance, inertance and impedance.

Let's return to the mechanical representation and look at the Helmholtz resonator from the outside, as shown in the first schematic: we are pushing with an oscillatory force F , with frequency f ,the mass m the air in the neck of the resonator , which is supported on the spring the enclosed air with spring constant k , whose other end is fixed the air in the resonator can't escape. Unrealistically, we'll neglect gravity and friction for now. The force required to accelerate the mass is proportional to the acceleration and so proportional to f 2.

At sufficiently low frequency , the force required to accelerate the mass is negligible, so F only has to compress and extend the spring. The spring force is — kx. The mechanical impedance of the system at this low frequency is compliant or spring-like. Acoustically, it looks like an acoustic compliance : we push the mass of air in the neck and compress the air in the resonator.

Remember that f 2 dependence of the acceleration. So, at sufficiently high frequency , the spring force is negligible in comparison with that accelerating the mass. It is a mechanical or acoustic inertance. At the resonant frequency still talking about the sketch above , the amplitude can be large for very small force.

So at resonance, the impedance is very low, when viewed from force applied to the mass from outside the diagram above. At resonance, there is maximum flow into and out of the resonator. Now consider what happens if we look at the pressure inside the resonator away from the neck. Here we are looking at the force on the spring, so our mechanical analogue looks like this schematic.

This time, low frequency means that the force can be small for a given amplitude: the spring and mass move together as a mass, and the system this time looks inertive at low frequency. At high frequency, the mass hardly moves, and the system is spring-like or compliant. Complications involving the effective length The first diagram on this page draws the 'plug' of air as though it were a cylinder that terminates neatly at either end of the neck of the bottle.

This is oversimplified. In practice, an extra volume both inside and outside moves with the air in the neck — as suggested in the animation above. The extra length that should be added to the geometrical length of the neck is typically and very approximately of 0. However, again the restoring force of the air in the body compresses the air. And again, the mass of air in the neck is pushed upwards, and this cycle repeats again and again.

This process can be viewed as a simple harmonic motion, producing a resonance.