Helmholtz resonator/Bernoulli's Principle

[trueacoustics]

First, I find the term "resonance" and its relatives to be used quite loosely. What is the actual definition according to physics/acoustics.

An example of its used:
The port of a Helmholtz Resonator resonates at the system's resonant frequency.

The port itself is not that thing resonating correct? It is rather the air within the port.

Second, how does the Helmholtz resonator actually work. It has been defined as follows by multiple sources:
"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. 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. 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." (University of South Wales: http://www.phys.unsw.edu.au/jw/Helmholtz.html)

However, this "lump" contained by the neck is just as compressible as the air inside. Similarly, it is just as springy. Therefore, how is it possible to separate this lump of air in the neck from the air inside?

This is supported by observing a reed pipe Helmholtz resonant system. The "neck" of the port is the same diameter as the body of the chamber. The lengths are adjusted, thus adjusting volume, while everything else remains constant. Intuitively, the pipes with larger internal volumes play lower tones.

It has then been established that by adjusting the cross sectional area of the neck and its length, you can adjust the resonant frequency of the system in a formulaic manner. This formula being greatly based upon the relationship between the mass of the air contained by the neck and mass of air contained inside the chamber. However, according to my assumption above, the total volume is simply being adjusted. This is where I run into a problem. If my assumption were true, the following would not be possible:
Given a fixed volume of air, we can create different resonant frequencies by adjusting the size and length of a port. Let's say that the port has a large diameter, but shallow depth. This would result in a relatively high resonant frequency. Now, let's make the port considerably smaller but keep the same length. The resonant frequency is now much lower. This is counter intuitive to previous assumption because the total volume has been lowered, but the resonant frequency has also been lowered.
My assumption is therefore wrong, and I am back to square one.
I then look towards Bernoulli's Principle. This principle intuitively relates the area of an opening with pressure. I just cannot see how it works with this system. This is greatly due to the inquires above. I am yet again back to my initial question. I am desperately trying to understand how this system works in an intuitive way. I am the type of person who needs to "see" what is happening to really "get it." I would appreciate any help. I have some more questions from which these questions have stemmed in regards to speaker enclosures. However, maybe if I can understand this, those questions will also be answered.

Thanks for your time,

Tony

 

[Studiot]

I'm not quite sure what the question is here, although you have provided a deal of information.

Helmholtz resonators are characterised by the "bottle properties" that is there is a volume of air trapped in an enclosure with a small opening to the outside. This opening may or may not have a neck or port. The enclosure may be empty except for the air or it may contain a porous low density material.

The air within the enclosure or chamber has a natural frequency of vibration given by its shape and size. It is able to accept and retain sound energy at this frequency rather readily by the phenomenon known as resonance.

The air outside it in a much larger chamber or even open air and has no special resonance frequency like that inside. So it has little or no capacity to accept the sound energy back again.

So once inside the chamber the sound energy of a specific frequency does not reasily return to the outside. It is dissipated in the walls and or filling material of the chamber.

The small size of the opening connecting the air inside the enclosure with the outside serves as a constriction separating the two sound systems.

The helmholtz resonator is used as an acoustic silencer in buildings and motor exhaust systems to control specific frequencies.

 

[trueacoustics]

The air within the enclosure or chamber has a natural frequency of vibration given by its shape and size. It is able to accept and retain sound energy at this frequency rather readily by the phenomenon known as resonance.

One of the questions was to define the term resonance.

The air outside it in a much larger chamber or even open air and has no special resonance frequency like that inside. So it has little or no capacity to accept the sound energy back again. So once inside the chamber the sound energy of a specific frequency does not reasily return to the outside. It is dissipated in the walls and or filling material of the chamber.

I do not understand what this means. Are you saying that frequencies which are not resonant are dissipated within the enclosure?

The small size of the opening connecting the air inside the enclosure with the outside serves as a constriction separating the two sound systems.

Can you elaborate on this further?

The helmholtz resonator is used as an acoustic silencer in buildings and motor exhaust systems to control specific frequencies.

This is exactly opposite of its used when designing speaker enclosures...well, for the most part. Maybe I should have stated speaker design as the origin of these questions. Let me explain what I mean. The rearward waves of a speaker interact with the forward waves when the wave length of the frequency being created is larger then the diameter of the driver. When this occurs, the out of phase waves cancel each other, and output is nullified. Therefore, an enclosure is needed to enclose the rearward waves, preventing them from interacting with the forward. This enclosure can be sealed or port. When ported, a Helmholtz Resonator is used. This is done to boost certain frequency levels. Frequencies played above the system resonance are "silenced," while those at or near the resonant are now in phase with the speaker. This then boosts the output. Those significantly lower are then out of phase, and cancellation occurs.

I did not want to look at a system with an extra variable, such as a speaker, when trying to understand the Helmholtz resonator. I was looking for an understanding of how a typical HR produces a large sound at a particular frequency, and how changing the neck/port's cross sectional area/length and/or interior volume of enclosure can change the resonant frequency.

Tony

 

[Studiot]

One of the questions was to define the term resonance.

One of the facilities offered by Physics Forums is the ability to search. You can also do this using the Google search box at the top.

Here are a couple of threads about resonance in general.

https://www.physicsforums.com/showthread.php?t=513131&highlight=handkerchief

https://www.physicsforums.com/showthread.php?t=513131&highlight=handkerchief

I do not understand what this means. Are you saying that frequencies which are not resonant are dissipated within the enclosure?

Sorry if this was not clear.
It was a description of the mechanism of sound reduction by Helmholtz cavities. Selected sound only enters from the ouside world via the ports, is trapped inside and finally dissipates within the cavity. The selection is due to the resonance of the cavity, not the characteristics of the port.
This is how exhaust systems remove (reduce) unwanted engine noise.

Alternatively, since you are interested in loudspeakers, if the cavity is driven (excited) by another agent eg a speaker cone the port will couple the sound from within the cavity to the outside world. Have you heard of acoustic impedance?

 

[trueacoustics]

Have you heard of acoustic impedance?

Haha yes, and that is another thing I have had trouble understanding. I have only seen it used electrically, now it is being brought up with acoustics. Apparently it is tied hand and hand with resonators. I need further explanation of how it works as well.