# A Helmholtz Resonator: attenuation vs. amplification

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1. Dec 6, 2017

### DrChef

Hello guys,
I read the other threads about HR, resonances and so on, but I couldn't find a clear explanation of what the practical implications of using a HR are.

From one side, HR is described as a "reactive element", used in several contexts to attenuate a specific noise by means of reflection (phase cancellation).
From the other side, HR is used as a "sound amplifier", used in all sort of musical instruments to amplify their sound.

My questions are:

1) A HR is characterized by a very narrow-band resonance, used to address unwanted noise components. However, if that is a proper resonance, that should in theory amplify that frequency instead of dampen it!
Can you help explaining this phenomenon?

2) Each HR has a very narrow-band resonance, therefore it could "amplify" only a single tonal component. However, acoustic guitar/bass bodies effectively and uniformly amplify a wide range of sounds, without any notch or "blind spot" due to the HR noise-cancelling effect.
How does this phenomenon relate to the HR theory?

2. Dec 6, 2017

### litup

When you say 'amplify' I hope you don't mean it puts out more energy than it inputs.

In old timey American music one instrument was the gallon whisky jug which produced a low tone when blown across the open end. That just allows a buildup of sonar energy but in a smaller wavelength band. It would not go 1 watt in and 10 watts out. It would go 1 watt of say, white noise, sound across a very wide frequency band into some fraction of that one watt given out in the tone the bottle produces. Shotgun mics use this effect by having several tubes tuned to different wavelengths of sound which reinforces the voltage given out by the mic in a prefered band, usually the 3 khz region of the human voice.

3. Dec 6, 2017

### tech99

The HR consists of a spring, which is the air in the container, and a mass, which is the slug of air in the neck. These two have a resonant frequency like a
mass hanging on a spring. It is very easy to move such a mass at the resonant frequency - the arrangement resembles a series resonant circuit.
The HR can have a narrow spout at the opposite end to the neck. When the spout is placed in the ear, the HR acts as a sharp bandpass filter and can pick out sounds having the same frequency as the HR resonance. The ear spout seems to not alter the resonance very much, and presumably provides a high pressure, small displacement output suitable for the ear drum.
If used to absorb sound, the HR aperture must look like a hole in the wall of the room at that single frequency. This is because the inertia of the air slug is tuned out by the air spring. Such a hole will have a much larger effect than just its surface area.
The violin body seems to be an HR, and I believe it is tuned near the low frequency end of the instrument to enhance that part of the spectrum. My guess is that the HR absorbs sound via the air slug in the neck, and transforms this to high pressure on the walls of the container. As these walls are flexible to some extent, they will then flex and re-radiate that sound, utilising much more surface area than that of the original string.
I presume that at higher frequencies, the body of a stringed instrument vibrates due to sound "conduction".

4. Dec 6, 2017

### sophiecentaur

I think the term "amplifier" is not always appropriate for an HR. An amplifier is, in the general usage of the term, a device which takes an input signal and an external Power Source to produce an output signal that is of higher Power than the input signal.
A simple resonator does not do this because it has no Power Source. A resonator achieves an improved Matching of the source impedance to the impedance of the propagation medium (Sound in air, Radio Waves in space or along a cable etc). An HR is basically a resonator so, for instance, when its used in a loudspeaker, it just improves matching at low frequencies of a small diameter drive unit to the air, without needing to use a massive horn. The sound is launched better into the air.
When a Jug is used as an instrument, the mechanism is slightly different because the supplied energy is in the form of a current of air ('a DC source') and the air flow is modulated by the varying pressure at the spout (due to the sound resonating in the Jug) and the impedance of the air flow from the lips. It is an Oscillator, rather than an Amplifier or just a Filter because it involves a non-linearity. The same sort of thing happens with a reed instrument, a brass instrument or a bowed string. In each case, energy is transferred from a steady input (breath or moving bow) in pulses as the resonator interacts with a non-linear element. I think the term 'relaxation oscillator' can be applied to this sort of oscillation. It is different for a plucked or struck instrument which has all the energy injected at the start and then it oscillates freely; the matching of the sound board etc. makes it louder.

5. Nov 2, 2018

### YardGang

ugh..I am a mechanical engineer for commercial buildings as well as an amateur music producer, yet much of this is still hard to understand. Sophiecentaur, can I ask you where or what I should be getting into for official education on this? I feel like I have SO MUCH info on all this but it is all piece-wise and lacks curriculum. So I could recite all kinds of acoustic terms while having little understanding the down and dirty, how it all fits together.

6. Nov 2, 2018

### sophiecentaur

That's how I view my knowledge base!!
You have asked a question for which the answer must depend on you. You don't want to be buying books that are too easy or too hard for you, of course but the right book could really help. Acoustics and musical instrument design are not on yer run of the mill Physics courses, afaik but I think you would need some classical physics or engineering in order to understand the basics of waves and oscillations. You could spend a few hours usefully on Google, experimenting with search terms to get something you find useful.
I just read this again. If you use an HR to absorb sound, it will not have a narrow resonance because it's specifically there to absorb energy - that implies a low Q factor. It would need a significant amount of internal absorption and the HR performs matching from the air into the lossy material. I remember coming across flat panel sound absorbers which had absorbance curves down to below 40Hz but response their curve were pretty wide and they worked at frequencies where your heavy furnishings wouldn't absorb. They consisted of a resonant panel of 'hardboard', loaded with that heavy black sound absorbing sheet and were filled with rock wool.

7. Nov 2, 2018

### YardGang

thanks for that quick response! Could you tell me what you mean by "matching"?

I've built four 7' corner bass traps and an 8'x11' ceiling trap using mass loaded vinyl and rock wool and I claim to understand that science (they actually were effective) and now I am shopping for "packless" HVAC duct silencers. This is my first time looking into these. They are virtually the same design as the ones with acoustical material in them except there is no acoustic material and they rely on HR as the attenuation method inside the silencer. Inside the silencer, air blows across the surface of openings with empty chambers. (think of it as air blowing across the top of a guitar with no strings). Like the original commenter, I am struggling with how this makes things quieter at the end of the duct. If I pluck a string without the guitar body, it seems much quieter. Any thoughts on this? Sorry if this is a repeat question.

8. Nov 2, 2018

### sophiecentaur

Matching is what you need in order to get energy to transfer well from one medium with a given impedance to another medium with a different impedance. The best example of this is the way the Ossicles (bones in the ear) match sound energy from the air (a very low impedance = low pressure variations and large movement of a gas) to the high impedance of the liquid medium in the ear (high pressure and small movements). In electronics, a matching transformer can be used to match the power from a transmitter to the impedance of the antenna feed point. There is a lot of air movement in and out of a HR due to the resonance so energy couples in (and out for a loudspeaker).

I imagine that the large volume movement of the air in an HR absorber can dissipate energy in any loading medium in the cavity. If there is a lot of turbulence in an HR, that could account for energy loss. There is also an effect that HRs on a pipe can produce and that is the production of the equivalent of Short circuit at a particular frequency. That can reflect sound back to its source so you don't need a loss mechanism. There are many examples of this basic technique when applied to radio frequency transmission lines and tuned cavities can block unwanted signals from passing along the line - same thing at work. Your duct acts as an acoustic transmission line and the HR is a band-stop filter.

Last edited: Nov 3, 2018