I recently starting thinking about loudspeaker systems with large/wide baffles. One concept that inevitably comes up is of the "infinite baffle". Strictly speaking, an infinite baffle is... well, infinite in extent, a plane. But is this really a helpful definition? What does this really mean for a practical loudspeaker.
Let's start with some thought experiments. What does the infinite baffle do? It subdivides the "space" into which the loudspeaker is operating. For example, you can start with "free space". This is something like being magically suspended in the air, infinitely (!) far away from any boundary. Now let's introduce a plane - the earth. Even if you don't believe in a flat earth, it's flat enough to be planar. Just by doing this the "space" that the air that the loudspeaker is operating into has been "halved". There is the "infinitely" large earth below, and the "infinitely" large atmosphere above. On the surface of the earthly plane, you are now in what is called "half space". Further boundaries can subdivide this space into smaller and smaller sections. Each time the space is halved, the sound pressure that is generated by a source is doubled, increasing by +6dB.
Getting back to the infinite baffle, if the baffle is also "infinite" then the baffle acts as one of these dividing planes. Think of an infinitely large open field, containing an infinitely tall and wide box with a driver installed on one side and "close" to the ground level. Of course this is just a thought experiment so far. No such real speaker exists. But if it did, the speaker's infinitely large baffle would increase the sound pressure by 6dB.
Now let's move from the theoretical world of infinite things to the human-sized world with real dimensions. What does an "infinite baffle" really mean? For the answer it seems that we can turn to Olson's well known 1951 article "Direct Radiator Loudspeaker Enclosures" for a clue. You can find it online. For simplicity let's consider his spherical enclosure. The diffraction signature of the sphere transitions smoothly through a 6dB rise as frequency changes from low to high (see Olson's text). The middle of this rise (the +3dB point) is often referred to as the "baffle step" frequency. It's essentially where the "baffle" (in this case a sphere) is starting to become "infinite-like" to sound. I say this because, just like the +6dB increase from an infinite plane, the sound pressure asymptotically reaches +6dB at high frequency. This is the case for any shape, not just for the sphere, in the high frequency limit.
So it seems like we can propose an answer to the question:
When may a baffle be considered infinite?
as
No less than the +3dB baffle step frequency.
I'd like to start a discussion about this topic here. Also, I would like to hear people's thoughts about the reason why the baffle step even exists. For example, Olson's experiments used a very small diameter source so that the radiation it produced would have very low directivity (e.g. like an omnidirectional source). Therefore, there is a component of the sound wave that is traveling parallel to and just above the baffle towards its edge. When the distance is small compared to the wavelength, we get the familiar cabinet diffraction effects. But it seems that for large distances, even though the edge of the baffle is still there, diffraction "disappears" and the baffle acts like an "infinite" baffle at that frequency as long as the distance is "large enough". This means that a relatively modest baffle can still be an "infinite" baffle at high frequencies. But what is the physics that is responsible for this? Because edge diffraction will be weak or absent at high frequencies and large baffle size, this will have some consequences for the radiation pattern of the loudspeaker to the sides and rear because these areas will only receive sound produced by the (front mounted )source via diffraction.
I think there are some interesting consequences to these ideas that are related to loudspeaker design and I hope there can be a in depth discussion about the points I have raised above.
Let's start with some thought experiments. What does the infinite baffle do? It subdivides the "space" into which the loudspeaker is operating. For example, you can start with "free space". This is something like being magically suspended in the air, infinitely (!) far away from any boundary. Now let's introduce a plane - the earth. Even if you don't believe in a flat earth, it's flat enough to be planar. Just by doing this the "space" that the air that the loudspeaker is operating into has been "halved". There is the "infinitely" large earth below, and the "infinitely" large atmosphere above. On the surface of the earthly plane, you are now in what is called "half space". Further boundaries can subdivide this space into smaller and smaller sections. Each time the space is halved, the sound pressure that is generated by a source is doubled, increasing by +6dB.
Getting back to the infinite baffle, if the baffle is also "infinite" then the baffle acts as one of these dividing planes. Think of an infinitely large open field, containing an infinitely tall and wide box with a driver installed on one side and "close" to the ground level. Of course this is just a thought experiment so far. No such real speaker exists. But if it did, the speaker's infinitely large baffle would increase the sound pressure by 6dB.
Now let's move from the theoretical world of infinite things to the human-sized world with real dimensions. What does an "infinite baffle" really mean? For the answer it seems that we can turn to Olson's well known 1951 article "Direct Radiator Loudspeaker Enclosures" for a clue. You can find it online. For simplicity let's consider his spherical enclosure. The diffraction signature of the sphere transitions smoothly through a 6dB rise as frequency changes from low to high (see Olson's text). The middle of this rise (the +3dB point) is often referred to as the "baffle step" frequency. It's essentially where the "baffle" (in this case a sphere) is starting to become "infinite-like" to sound. I say this because, just like the +6dB increase from an infinite plane, the sound pressure asymptotically reaches +6dB at high frequency. This is the case for any shape, not just for the sphere, in the high frequency limit.
So it seems like we can propose an answer to the question:
When may a baffle be considered infinite?
as
No less than the +3dB baffle step frequency.
I'd like to start a discussion about this topic here. Also, I would like to hear people's thoughts about the reason why the baffle step even exists. For example, Olson's experiments used a very small diameter source so that the radiation it produced would have very low directivity (e.g. like an omnidirectional source). Therefore, there is a component of the sound wave that is traveling parallel to and just above the baffle towards its edge. When the distance is small compared to the wavelength, we get the familiar cabinet diffraction effects. But it seems that for large distances, even though the edge of the baffle is still there, diffraction "disappears" and the baffle acts like an "infinite" baffle at that frequency as long as the distance is "large enough". This means that a relatively modest baffle can still be an "infinite" baffle at high frequencies. But what is the physics that is responsible for this? Because edge diffraction will be weak or absent at high frequencies and large baffle size, this will have some consequences for the radiation pattern of the loudspeaker to the sides and rear because these areas will only receive sound produced by the (front mounted )source via diffraction.
I think there are some interesting consequences to these ideas that are related to loudspeaker design and I hope there can be a in depth discussion about the points I have raised above.
I've been curious about the Cornu spirals, with that big square baffle with a small driver dead center. I'd assume this design also does the "bifurcation", as no sounds radiate out the back. (At least...not supposed to).
So maybe that design solves both > +3db baffle step and the bifurcation of the sound?
An OB for example could(?) meet the baffle step requirement part, but also has some back radiation - no bifurcation.
So maybe that design solves both > +3db baffle step and the bifurcation of the sound?
An OB for example could(?) meet the baffle step requirement part, but also has some back radiation - no bifurcation.
Charlie, doesn't baffle step have to do with wavelength and baffle size? In which case a 20hz tone would have no loss in forward energy if produced on a 60 foot wide/tall baffle ... as your example of a high frequency produced on a baffle larger than the wavelength. If the baffle is smaller than the wavelength being produced you'll see a reduction in forward energy.
The meeting of front and back waves adds as much as subtracts.
The further out you go, the less "meat" there is to interact front and back. Both the front and back have already gone on to power the room, with less to meet the opposite wave.
Unless you love circular baffles with a small cone driver smack in the middle, the effect is smeared according to the distances.
Easy to day-dream about logical analyses of dipoles until you try to figure out how to analyze what's really happening with the wave bouncing off the back wall.
Something about non-infinite baffles that just irritates people. Seems natural to criticize them. Dunno why. Maybe because most people think it ain't a speaker if it isn't in a very solid box - except for ESL enthusiasts, of course.
B.
The further out you go, the less "meat" there is to interact front and back. Both the front and back have already gone on to power the room, with less to meet the opposite wave.
Unless you love circular baffles with a small cone driver smack in the middle, the effect is smeared according to the distances.
Easy to day-dream about logical analyses of dipoles until you try to figure out how to analyze what's really happening with the wave bouncing off the back wall.
Something about non-infinite baffles that just irritates people. Seems natural to criticize them. Dunno why. Maybe because most people think it ain't a speaker if it isn't in a very solid box - except for ESL enthusiasts, of course.
B.
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One instructional exercise I think, is to quantify the directivity of a speaker in a room at wavelengths that are significant to the room. Then to step back from this.
I'd also like to clarify something, although CharlieLaub has made it clear what he is talking about, and as important as that is... Traditionally an infinite baffle refers to the separation of front and back radiation using an enclosure which is a significant portion of Vas or larger, such that it's internal volume has little effect on Q.
I'd also like to clarify something, although CharlieLaub has made it clear what he is talking about, and as important as that is... Traditionally an infinite baffle refers to the separation of front and back radiation using an enclosure which is a significant portion of Vas or larger, such that it's internal volume has little effect on Q.
SF Stradivari has some virtues, and kimmosto has done a similar project and I understand that he was quite happy with it
KS-483
Sound stage is stable but not razor-sharp when listening distance is more than 230 cm. Shorter distances with thick carpets on the floor create very sharp and detailed stereophonic illusion. Size of instruments and vocalist is a bit bigger than average. I feel sound stage as high, although most of the lower frequencies lie down. Maybe bigger projection of images make also sound stage higher. Images from upper mid are projected above tweeters' level. Tilt angle changes elevation of these images.
KS-483
Sound stage is stable but not razor-sharp when listening distance is more than 230 cm. Shorter distances with thick carpets on the floor create very sharp and detailed stereophonic illusion. Size of instruments and vocalist is a bit bigger than average. I feel sound stage as high, although most of the lower frequencies lie down. Maybe bigger projection of images make also sound stage higher. Images from upper mid are projected above tweeters' level. Tilt angle changes elevation of these images.
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A good question. There is an excellent explanation in the Kolbrek-Dunker Horn Book Ch-14 for direct radiators.
I would add a further restriction to the thought experiment. The radiator is an ideal piston membrane radiating from only 1 side. Extending AllenB's suggestion.
IMO the baffle always has potential for reflection and diffraction. The 6dB gain (ie. 4Pi=>2Pi space) is from "in phase" reflection off the baffle. The amount of baffle diffraction (2Pi->4Pi radiation impedance change) depends on the baffle geometry and frequency. Since all the effects superimpose, their relative contributions will change with frequency. As the frequency increases the driver gets more directional and radiates more "plane like" waves so less pressure at the baffle edges and lower diffraction contribution. As the driver gets smaller the directivity effect starts at higher frequencies. So Olson's little (7/8in) driver would never be directional in his test range. Which makes sense if you are testing baffle shape diffraction.
Charlie -> Are you trying to find how big the baffle should be ? or at what frequency you should start using your drivers to minimize diffraction? I am willing to contribute simulation cycles to test some thought experiments.
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It's more appropriate to consider the large baffle as a waveguide, as there is no separation to cause a wave to be reflected.
The wave is being supported(not allowed to dissipate), resulting in higher pressure along the wavefront.
If there were reflection there would be cancellation at practical baffle sizes.
The wave is being supported(not allowed to dissipate), resulting in higher pressure along the wavefront.
If there were reflection there would be cancellation at practical baffle sizes.
Wouldn't wavelets on the wavefront at a distance from the baffle reflect and there's no cancellation because they would support the wavefront? They're "in phase" as Don put it.
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Don't the wavelets define the wave front? Isn't a wavelet simply a mathematical tool which allows simultaneous time and frequency analysis?
Yes they are a tool, but observation of wave phenomena supports their existence, that's enough, or do you mean something else?
That might have confused the issue, but Huygen's principle applies to all waves. There are some youtube videos (of course) Huygens’s Principle: Diffraction | Physics II