Well, phenomenologically speaking we all know what happens regarding the baffle step. This has been known a long time. I'm not looking for answers about WHAT happens, but WHY it happens.
I am trying to get answers on a more fundamental level about wave support by the baffle plane and how this relates to the baffle step. It's my belief that physics/acoustics will be able to provide the answers I seek, so that is where I am looking.
It's my opinion that the answer to this question will help me to gain a deeper understanding of other phenomena related to baffle step, acoustic shadowing, open baffles, infinite baffles, and so on. I would hardly call a deep understanding in terms of fundamental physics an "academic answer" since this understanding has real world connections to our hobby.
Not yet. I could do a lot of reading/digging myself and try to figure it out. For now I reached out to this guy at PennState (someone linked to his web page earlier in this thread) to see if he can just cut to the chase for me. Have not heard back from him yet, and might not ever, but it is worth a try. I have some other contacts I can reach out to as well.
As a thought experiment, is it inconceivable to consider each molecule, as it responds to the others around it, another source on the wavefront?
Isn't any answer academic until we actually see what's going on?
Isn't any answer academic until we actually see what's going on?
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Yes, each molecule reacts to to the motion of its immediate neighbour, just as the first molecule was initially pushed then pulled by the motion of the loudspeaker diaphragm.
Each molecule oscillates in simple harmonic motion (SHM). Each molecule oscillates about its 'stationary' position to which it is restored when the pushing or pulling force reduces to zero. Each molecule is at a different point in its SHM compared to its immediate neighbour i.e. neighbouring molecules have a different phase. Only at a distance of one wavelength apart are any two molecules exactly in the same phase.
However, this is not the physics that Charlie is looking for!
You just can't come to terms with the non-physical existence of wavelets, can you?
They work well, and until someone comes up with something better I'm running with them 🙂You just can't come to terms with the non-physical existence of wavelets, can you?
I don't think "That's some pretty bad logic" 😉
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Hi, isn't this all just about impedance? Higher impedance of the baffle (compared to air) means "sound hitting" to the baffle will mostly reflect from the impedance boundary than transmit through to the baffle? Even slight impedance difference will cause some reflection.
Lets imagine there is impedance difference x between the space in front of the baffle and just after the baffle has ended, after the edge, where sound wave propagating along the baffle will continue to propagate. The sharper the edge the more sudden impedance change there is between these two impedance conditions and more sound is reflected. How fast the impedance changes must have something to do with the gradual baffle step frequency bandwidth and also edge diffraction.
By fast change I mean how long or short this "impedance change depth" we have in terms of sound propagating through one steady impedance space to another. A rounded baffle edge would yield more gradual change of impedance, which means less reflected sound at any given point in space along the transition "depth". Anyone have thoughts on this? How the different wavelengths are related to the impedance boundary depth, I haven't imagined yet 😀
Lets imagine there is impedance difference x between the space in front of the baffle and just after the baffle has ended, after the edge, where sound wave propagating along the baffle will continue to propagate. The sharper the edge the more sudden impedance change there is between these two impedance conditions and more sound is reflected. How fast the impedance changes must have something to do with the gradual baffle step frequency bandwidth and also edge diffraction.
By fast change I mean how long or short this "impedance change depth" we have in terms of sound propagating through one steady impedance space to another. A rounded baffle edge would yield more gradual change of impedance, which means less reflected sound at any given point in space along the transition "depth". Anyone have thoughts on this? How the different wavelengths are related to the impedance boundary depth, I haven't imagined yet 😀
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I was also considering what happens when the part of the sound wave propagating along the baffle surface continues to propagate into the free air beyond the edge of the baffle.
Most of the energy will be transmitted into the free air, but some energy will be reflected back along the baffle like tmuikku has said.
I wonder if the physics of 'boundary behaviour' would have any application here?
Most of the energy will be transmitted into the free air, but some energy will be reflected back along the baffle like tmuikku has said.
I wonder if the physics of 'boundary behaviour' would have any application here?
Attachments
Well, here is my guess about the origin of the baffle step. This is still a bit of hand waving but for now this is all I've got.
See the attached image, taken from the top of the page here:
Diffraction Information & Graphs
It's a representation of Olson's experiment for the sphere and point source on its surface. I am using this image because the diffraction ripples are absent and only the more general trend vs frequency is shown. NOTE that the actual image from Olson's paper is shown lower down on the page, and is slightly different.
Previously I had been envisioning the baffle step level reaching +6dB compared to low frequencies within some "finite transition zone". But if you look closely at the image, you can see that the low and high frequency behavior is actually asymptotic. This seems to make much more sense to me, rather than a defined region that transitions between the two limits, which was where my mind was stuck previously.
It's easy for me to envision what is going on in the very HF or LF limits, but the "in between" has been puzzling me, and still does to some extent.
In the meantime I found a nice 2006 Master's Thesis on Loudspeaker Cabinet Diffraction that compares some different models like DED, Huygens/Wavelets, etc. and has the related physics. But it seems that the actual physical mechanism is not understood 100%. For example, in "Chapter 4 Edge Diffraction Model", it's attributed to a radiation impedance change at the cabinet edge, which leads to reflection and the "phantom source" I have mentioned before. But it's not clear whether that is just a guess/model of the diffraction process or the established physics of it. So I am still trying to get to the bottom of it...
Anyway, the thesis is a good review and shows the weaknesses of the various diffraction models that are discussed. Get it here:
Tore Skogberg - Loudspeaker Cabinet Diffraction
See the attached image, taken from the top of the page here:
Diffraction Information & Graphs
It's a representation of Olson's experiment for the sphere and point source on its surface. I am using this image because the diffraction ripples are absent and only the more general trend vs frequency is shown. NOTE that the actual image from Olson's paper is shown lower down on the page, and is slightly different.
Previously I had been envisioning the baffle step level reaching +6dB compared to low frequencies within some "finite transition zone". But if you look closely at the image, you can see that the low and high frequency behavior is actually asymptotic. This seems to make much more sense to me, rather than a defined region that transitions between the two limits, which was where my mind was stuck previously.
It's easy for me to envision what is going on in the very HF or LF limits, but the "in between" has been puzzling me, and still does to some extent.
In the meantime I found a nice 2006 Master's Thesis on Loudspeaker Cabinet Diffraction that compares some different models like DED, Huygens/Wavelets, etc. and has the related physics. But it seems that the actual physical mechanism is not understood 100%. For example, in "Chapter 4 Edge Diffraction Model", it's attributed to a radiation impedance change at the cabinet edge, which leads to reflection and the "phantom source" I have mentioned before. But it's not clear whether that is just a guess/model of the diffraction process or the established physics of it. So I am still trying to get to the bottom of it...
Anyway, the thesis is a good review and shows the weaknesses of the various diffraction models that are discussed. Get it here:
Tore Skogberg - Loudspeaker Cabinet Diffraction
Attachments
Regarding phantom source, I'd imagine the particles moving will influence the nearby particles to the velocity vector direction mostly, but the particles aren't perfectly aligned so to speak so they will have their vector pointing a bit different direction than the particle influencing them (anyone playing billiards?🙂. This makes the point source radiate as sphere, right? Baffle boundary impedance will reflect about half of the air particles (which propagate along the baffle) to an angle that is mostly to the direction away from the sound source and away from the baffle, some even almost 90 degrees out from the baffle, where they reflected particles soon meet the particles already moving that way (without reflecting from the baffle) and constructively add and there hence a 6db "lobe"? This happens everywhere when a particle influences another, so practically continuously along the baffle.
But there at the baffle edge boundary sudden impedance change will send a lot of particles back to the direction of the source as well, as any direction actually (some go through that impedance boundary and some bounce back). A phantom source. Now at this point there is less than half of the particles heading to the baffle boundary since only part propagated forward (past the baffle) and part of them headed back (back along the baffle). Still following?🙂 When there is less particles heading to the baffle boundary ready to reflect and add to the lobe the addition isn't 6db anymore but something less. Also past the baffle edge, there isn't any (or only very little) particles reflected from the baffle (or enclosure) boundary there isn't any addition to the lobe there, which makes the "step". Still haven't imagined how the frequency relates with all this. It might be that the impedance boundary size will have different effect with different frequency, an acoustically significant obstacle as it is often written.
Edit. I might speak with wrong terms since I'm scratching this from back of my head, but maybe it still gives some thoughts to you.
But there at the baffle edge boundary sudden impedance change will send a lot of particles back to the direction of the source as well, as any direction actually (some go through that impedance boundary and some bounce back). A phantom source. Now at this point there is less than half of the particles heading to the baffle boundary since only part propagated forward (past the baffle) and part of them headed back (back along the baffle). Still following?🙂 When there is less particles heading to the baffle boundary ready to reflect and add to the lobe the addition isn't 6db anymore but something less. Also past the baffle edge, there isn't any (or only very little) particles reflected from the baffle (or enclosure) boundary there isn't any addition to the lobe there, which makes the "step". Still haven't imagined how the frequency relates with all this. It might be that the impedance boundary size will have different effect with different frequency, an acoustically significant obstacle as it is often written.
Edit. I might speak with wrong terms since I'm scratching this from back of my head, but maybe it still gives some thoughts to you.
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Surely someone somewhere has made a model of air either in reality or in a computer, similar to this Longitudinal wave | physics | Britannica but in 2 or 3 dimensions? How hard can it be? Wouldn't it be useful?
Even a 3D model would have its limitations. Earlier, I said that air molecules oscillated around their 'stationary' positions.
A realistic model of longitudinal wave motion, in any dimension, would have to take into account that air molecules have no stationary positions.
The molecules of air in typical room conditions are travelling randomly in all directions with average speeds similar to that of a rifle bullet (close to 1,000 mph).
The wave motion has to be superimposed on that choatic collection of molecules. It might be quite a challenge to simulate that!
Just goes to show how poor most models in physics are at representing reality.
A realistic model of longitudinal wave motion, in any dimension, would have to take into account that air molecules have no stationary positions.
The molecules of air in typical room conditions are travelling randomly in all directions with average speeds similar to that of a rifle bullet (close to 1,000 mph).
The wave motion has to be superimposed on that choatic collection of molecules. It might be quite a challenge to simulate that!
Just goes to show how poor most models in physics are at representing reality.
So the wave motion is largely independent of the molecular motion, makes you wonder how the wave is actually carried, and it can be carried on the wind too. 🙂
Ah yes, you immediately referred to the 2D animation. I simply wondered why you asked for another one.
The wave motion of sound is totally dependent on the simple harmonic motion of the molecules - the bulk motion of the molecules is irrelevant.
I asked for a model of the air, and whether it would be useful, it isn't is it? From your previous reply that would seem to be the case.