I haven't seen a direct treatment of this question before, but it does seem dumb to ask, but I'm going to ask anyway.
Are frequencies <100hz omnidirectional because the wavelength at the cone is so long that the wave simply propagates in all directions due to its size?
Or, it is because low frequencies can't really be blocked by reasonable thicknesses of normal cabinet materials? It seems 16mm of solid wood is just barely good enough to get -60dB at 100hz, and it gets worse the lower you go.
Or is it both?
I'm a crazy person so I'm wondering if you could make a more cardiod-type speaker by simply making really thick concrete enclosures, or something similarly impractical. I am not sure if that would solve anything in terms of LF directivity, which is why I'm asking.
Are frequencies <100hz omnidirectional because the wavelength at the cone is so long that the wave simply propagates in all directions due to its size?
Or, it is because low frequencies can't really be blocked by reasonable thicknesses of normal cabinet materials? It seems 16mm of solid wood is just barely good enough to get -60dB at 100hz, and it gets worse the lower you go.
Or is it both?
I'm a crazy person so I'm wondering if you could make a more cardiod-type speaker by simply making really thick concrete enclosures, or something similarly impractical. I am not sure if that would solve anything in terms of LF directivity, which is why I'm asking.
Dipoles (OB) and planar speakers generally have something approaching a cardioid radiation pattern at low frequencies.
Sheer size: ~34400/pi/100 = ~109.5 cm/43.11" diameter growing exponentially larger with decreasing frequency, so 50 Hz is 2x larger, 25 Hz 4x, so while a large baffle can maintain ~180 deg @ 100 Hz it takes a short wall for 50 Hz and a relatively large one for 25 Hz.
Mostly it’s the wavelength. As Allen says cabinets are a separate problem
It’s not really the size of the cone, it’s the size of the baffle.
It’s not really the size of the cone, it’s the size of the baffle.
I have an "obsolete" 1936 house with 1" thick plaster (think mortar) walls, not drywall. Outside the wall the speakers back up to, my house emits a lot less bass on 1 to 10 W music than those sheet metal boxes (cars) driving by buzzing and humming. The speaker manufacturer (Peavey) says in their test setup my SP2(2004) speaker drops 28 db from 60 hz to 30 hz. They measure 1 m away in the front with pink noise source. In my living room with the speaker backed up against this hard wall, on a white noise sample from 6' away, my cardioid microphone shows a 3 db drop from 60 hz to 30 hz. So yes, a hard concrete (plaster) wall 14' wide 11' tall forces the sound out front where I want it. I also get some reflection from the partial back wall 14' from the front of the speakers. In the middle of the back wall there is an open double doorway to the dining room & kitchen.
Such a hard back wall setup is not used on stage shows, because the hard brick or concrete wall at the back of the stage (if one) leaves no room for the scenery. Also the sound man doesn't want the backing music bleeding into vocalist microphones, so the speakers are usually in front of the stage, not the back. Hence PA speakers need "baffle step correction" because most of the bass leaks out the back as much as it projects out the front. Baffle step correction is a bass boost in the crossover.
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Baffle step correction is not to correct for leakage out of the back of the speaker, but because the wavelengths at high frequencies become small compared to the baffle and therefore louder in the forward direction. This is what is referred to as the 4pi (full space 360 degrees), to 2pi (half space 180 degrees) transition. The driver and baffle begin to "beam" to the front like a flashlight at high frequencies, when wavelengths are small and fully supported by the baffle.
Small wavelengths relative to the baffle cannot wrap around and radiate in all directions. Conversely, at low frequencies the wavelengths become much longer and larger than the baffle, so they lose the support of the baffle and begin to wrap around the speaker, eventually becoming omnidirectional at very low frequencies. A 50hz wavelength is 270 inches long, 500hz is 27 inches and 5000hz is 2.7 inches. A driver will become directional and start to beam when it's width is around 1/3 of the wavelength it's producing.
Small wavelengths relative to the baffle cannot wrap around and radiate in all directions. Conversely, at low frequencies the wavelengths become much longer and larger than the baffle, so they lose the support of the baffle and begin to wrap around the speaker, eventually becoming omnidirectional at very low frequencies. A 50hz wavelength is 270 inches long, 500hz is 27 inches and 5000hz is 2.7 inches. A driver will become directional and start to beam when it's width is around 1/3 of the wavelength it's producing.
Baffle step correction boosts the low frequencies so they are as loud as the high frequencies supported by the baffle and radiating in the forward direction. It's a gradual transition from omnidirectional at low frequencies to straight ahead at high frequencies in the case of a speaker in a box.
More about quasi cardioid pattern of dipole sub in u shaped damped enclosure
http://musicanddesign.speakerdesign.net/NaO-II-U-frame.html
http://musicanddesign.speakerdesign.net/NaO-II-U-frame.html
Yeah, what I said. The bass goes to the back of the cabinet same as the front. 4 pi space includes the back of the cabinet. People love their jargon, can't live without it. .
If you made the back of a speaker cabinet out of 4" of concrete, at the front of an open stage it wouldn't do any good for cardioid bass because the wavelength of the reflector would be only 28" or so. Bass would still wrap around back. My 14' plaster wall behind the cabinet approaches a half wavelength of 39 hz.
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Maybe in a really poor cabinet. Or can you show otherwise? Certainly the longer wavelengths will wrap around the cabinet, which will mean that there is almost as much bass behind as in front.
The cardioid bass trick is currently popular in PA work, and it is effective at keeping bass energy off the stage. Three subs in a line on behind the other with proper spacing and delay does it. It can be done with two, but three works much better.
It's basically a matter of wavelengths, and what they can bend around.
For dipoles or cardioids, its still basically the above, but with added phase summations that either reinforce or cancel radiation in particular directions.
For dipoles or cardioids, its still basically the above, but with added phase summations that either reinforce or cancel radiation in particular directions.
Right. My concern was that those new to speaker building would be confused and think that bass "leaking" through the cabinet to the rear was the issue.
If anything, no matter how robust you build a cabinet, internal resonances and bass are going to "leak" back out through the very thin cone and be more pronounced to the front. One of the main reasons I prefer building boxless speakers, such as dipoles and cardioids.
I understand what was trying to be relayed in relation to a speaker being placed close to a rear wall to support low frequencies in a live music production, it was just a bit confusing to someone who may be new to this field.
I believe the OP was just trying to understand the reason low frequencies become omnidirectional and was likely referring to a common aperiodic or vented closed box speaker and I wanted to make it very clear.
Also, the only dumb question is one that is never asked; we were all neophytes at one time and I appreciate those that took the time to clear up muddy water for me.
Jason
Yes, the associated physics is that of "diffraction".
Long wavelengths (bass frequencies) bend or "diffract" round loudspeaker enclosures more than short wavelengths (high frequencies).
Thanks all, this is very helpful and I think I am beginning to appreciate the impact of diffraction at low frequencies. Maybe one way to think about it is the entire cabinet effectively begins to look like a spherical point source compared to wavelengths of 10-20+ feet. In which case, the wave isn't going to be bouncing off of the outside of the cabinet at all.
I'm interested because it would be nice to be able to build a speaker with some directivty low down like the D&D 8C or whatever, but I'm not eager to prototype a ton of tuned vents or build a complex and highly expensive 4-way rear-firing woofer type of thing. My hope was there could be some significant benefit to just making really heavy cabinets, but it seems like that would have a marginal impact and outside the cabinet is where the action is.
I'm interested because it would be nice to be able to build a speaker with some directivty low down like the D&D 8C or whatever, but I'm not eager to prototype a ton of tuned vents or build a complex and highly expensive 4-way rear-firing woofer type of thing. My hope was there could be some significant benefit to just making really heavy cabinets, but it seems like that would have a marginal impact and outside the cabinet is where the action is.
All of this would seem to suggest that rear-firing ports about a foot from a wall should work fine, correct?
D
Deleted member 375592
It is a tiny bit more complicated. The case of only speaker cone moving is a theoretical one. In reality, the speaker cabinet is moving too, and the floors it sits upon, and the walls, and the neighbors will yell indiscriminatorily because they are driven nuts by your bass obsession.
The force applied to the cabinet is the same as to the cone, the acceleration is Bl*Imax/M. Say, M=20kg; Pmax=500; Bl=12N/A; R=4; a=sqrt(Pmax/R)*Bl/(M*pi^2) =0.68g; Note that peak cone acceleration (m=0.2kg) is ~100 times more, like 70g. You need to use proper vibration isolation, tuned to, say, 2Hz, to decrease "a" by 100, best-case, and an MSc in mechanics to use such isolation properly. Otherwise, the cabinet will vibrate with the floor, which has a huge radiation surface and all simplified models will go kaboom (and measurements too).
Yes, there is a significant benefit in decorating the subwoofer cabinet with lead and stones ... up to the floor's bearing capacity.
The force applied to the cabinet is the same as to the cone, the acceleration is Bl*Imax/M. Say, M=20kg; Pmax=500; Bl=12N/A; R=4; a=sqrt(Pmax/R)*Bl/(M*pi^2) =0.68g; Note that peak cone acceleration (m=0.2kg) is ~100 times more, like 70g. You need to use proper vibration isolation, tuned to, say, 2Hz, to decrease "a" by 100, best-case, and an MSc in mechanics to use such isolation properly. Otherwise, the cabinet will vibrate with the floor, which has a huge radiation surface and all simplified models will go kaboom (and measurements too).
Yes, there is a significant benefit in decorating the subwoofer cabinet with lead and stones ... up to the floor's bearing capacity.