Do you think that a ribbon tweeter would start to approach the low diaphragm mass where the effect of Zm approaching Zr would start to be noticed in efficiency calculations ?But this is fun so let's take it to another level.
We can write the equation for driver velocity as
U = F /(Zm + Zr)
where Zm is the mechanical impedance of the driver and a function of the moving mass, Mms, mechanical resistance, Rms, and suspension compliance, Cms. Zr is the radiation impedance. F is the force applied to the driver by the motor. Now, for most drivers Zm is much greater than Zr and the driver motion is unaffected by the change in loading between 2 and 4 Pi. Therefore, as we have discussed, the volume velocity will remain essentially constant and the efficiency in 2PI will increase by 3dB. BUT, when we are dealing with very low mass devices, in the limit where Zm goes to zero, then for the same force applied to the driver doubling of Zr in 2Pi will result in making U lower by 1/2 and the radiated SPL in 4PI and 2Pi will then be constant when the same driving force is applied to the driver. Since the force is BL x I, constant force means constant current and the power dissipated in the voice coil will remain constant. Thus, with source of negligible Zm the efficiency in 2Pi will actually decrease by 3dB. So for a zero Zm source with constant power dissapated in the VC going from 4Pi to 2Pi results in no change in SPL, a 3dB (factor of 2) increase in Zr, and a 3dB decrease in efficiency.
I only throw this out because we have been saying that the volume velocity remains constant, but not addressed why that might be reasonable. (Actually I threw this out because it mucks things up so we can argue some more.)
After all its not uncommon for a ribbon with a similar radiating area to a 1" dome to have a diaphragm mass of 0.01 grams or less.
I've also seen it suggested that the main reason the CSD on a ribbon is usually so good is that the extremely low diaphragm mass to area ratio results in the resistive air mass load itself being the dominant damping factor acting on the diaphragm, which is not the case on a conventional much heavier diaphragm. Thoughts ?
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I wonder what the mass of this is, since we're fueling the debate and I love watching physicists banter.
Plasma Speaker / Singing Arc - Early Modulated Prototype - YouTube
Edit: better one
http://www.youtube.com/user/timetec#p/u/5/cEeWtBAE5LY
Hi, yes you did, but didn't say it's pretty much irrelevant directly enough IMO, 😉, rgds, sreten.
Though of course the facts should always speak for themselves, sometimes they don't.
We'll be on to electrostatic bass units anytime soon, way off topic.
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I only throw this out because we have been saying that the volume velocity remains constant, but not addressed why that might be reasonable. (Actually I threw this out because it mucks things up so we can argue some more.
I suspected as much!
Here is a good paper regarding efficiency build up with multiple woofers and the significance/insignificance of radiation resistance relative to mechanical impedances.
http://www.aes.org/tmpFiles/elib/20111116/6041.pdf
Gander and Eargle at JBL are looking at large concert arrays. Look at page 13 where they go into stacked subs. Its a bit like the 1 woofer/2 woofer conundrum. There conclusion is much like Keeles: Drivers add up as in-phase vectors on axis, but this seems to be a combination of increase true efficienecy at low frequencies (increased by what they call mutual coupling) and increased directivity index at the top end. They state that you can't get beyond about 25% efficiency because (presumably) at some point the acoustic impedance does become significant and additional woofers will start to see their cone motion drug down by the significant load of very high efficiency.
Regards,
David
I'm reading Beranek (found a copy on the web) and he seems to "believe in acoustic impedance".
A section on placing a loudspeaker near a number of boundaries (a la Allison): "If you wish a source to radiate as much power as possible in a "small" near rectangular room the best location for a sound source is in the corner at either the floor or ceiling level. Under this condition the acoustic impedance presented to the source is such to draw more power from it at low frequencies than if it were located elsewhere in the room. It seems that about eight times as much power (9dB more) is radiated from the loudspeaker at low frequencies if it is in the corner as compared with being in the exact center of the room." (Chapter 10)
Chapter 5 on acoustic components gives the acoustic resistance plots for the 3 cases of a circular piston in an infinite baffle, at the end of an infinite tube and a piston in free space. The first 2 plots are directly derived using equations including bessel functions (no measurements of pressure and velocity).
Chapter 8 goes into loudspeakers in enclosures. In his summary of closed-box baffle design, right after defining Sd, Cas, Mmd and other factors you are instructed to calculate the appropriate Rar and Xar (acoustical impedance quantities) for the system. In the examples section he uses the "piston in an infinte baffle" numbers for a "very large box" and then the "pisiton in the end of a long tube" numbers for the 8 cubic foot case.
I'm really starting to believe that the answer is that you can describe whats going on in a number of ways and as long as you come up with 6dB for the difference it will be hard to disprove the particular theory. For example, I think that an image model would be equally valid. Start with a woofer in free space (4 pi) and for the 2 pi case you can use the image model equivalent of a real woofer facing forward and the second image woofer facing backwards. At low frequencies the real and the reflected woofers add for +6dB, at higher frequencies the rear firing image woofer become progressively more directional and eventually adds nothing.
There... no acoustic impedance, just adding pressures.
David
A section on placing a loudspeaker near a number of boundaries (a la Allison): "If you wish a source to radiate as much power as possible in a "small" near rectangular room the best location for a sound source is in the corner at either the floor or ceiling level. Under this condition the acoustic impedance presented to the source is such to draw more power from it at low frequencies than if it were located elsewhere in the room. It seems that about eight times as much power (9dB more) is radiated from the loudspeaker at low frequencies if it is in the corner as compared with being in the exact center of the room." (Chapter 10)
Chapter 5 on acoustic components gives the acoustic resistance plots for the 3 cases of a circular piston in an infinite baffle, at the end of an infinite tube and a piston in free space. The first 2 plots are directly derived using equations including bessel functions (no measurements of pressure and velocity).
Chapter 8 goes into loudspeakers in enclosures. In his summary of closed-box baffle design, right after defining Sd, Cas, Mmd and other factors you are instructed to calculate the appropriate Rar and Xar (acoustical impedance quantities) for the system. In the examples section he uses the "piston in an infinte baffle" numbers for a "very large box" and then the "pisiton in the end of a long tube" numbers for the 8 cubic foot case.
I'm really starting to believe that the answer is that you can describe whats going on in a number of ways and as long as you come up with 6dB for the difference it will be hard to disprove the particular theory. For example, I think that an image model would be equally valid. Start with a woofer in free space (4 pi) and for the 2 pi case you can use the image model equivalent of a real woofer facing forward and the second image woofer facing backwards. At low frequencies the real and the reflected woofers add for +6dB, at higher frequencies the rear firing image woofer become progressively more directional and eventually adds nothing.
There... no acoustic impedance, just adding pressures.
David
Still fighting the good fight!
I don't think that anyone is saying that an impedance approach is WRONG. You can obtain the same correct result with it. However, acoustic impedance is a construct of pressure, particle velocity, density and radiation boundary conditions. Heck, all of that is really just a pile of averages of particle kinematic properties, but it is way too cumbersome at that level.
It is like the difference between C and assembly language. C compiles into assembly (well, machine code actually, but assembly is the human-friendly version of it). Take the multiplication operation. In C, you just multiply two variables and that's that. However, if the target device doesn't have hardware multiply support, then that multiply operation in C is actually a series of bitwise shifts and addition in machine code / assembly language. The assembly/machine code is what is really going on behind the scenes!
I don't think that anyone is saying that an impedance approach is WRONG. You can obtain the same correct result with it. However, acoustic impedance is a construct of pressure, particle velocity, density and radiation boundary conditions. Heck, all of that is really just a pile of averages of particle kinematic properties, but it is way too cumbersome at that level.
It is like the difference between C and assembly language. C compiles into assembly (well, machine code actually, but assembly is the human-friendly version of it). Take the multiplication operation. In C, you just multiply two variables and that's that. However, if the target device doesn't have hardware multiply support, then that multiply operation in C is actually a series of bitwise shifts and addition in machine code / assembly language. The assembly/machine code is what is really going on behind the scenes!
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Like one of the ways I've bandied about was a given stroke 'x' to fill the front hemisphere, repeat for the rear hemisphere. Case 2, same total stroke of 2.x this time all in the front hemisphere, which is 6dB.
My theory on analogising a speaker as a curent source is based on increasing output with a higher impedance. Of course I wouldn't want to take that into a discussion about horns.
My theory on analogising a speaker as a curent source is based on increasing output with a higher impedance. Of course I wouldn't want to take that into a discussion about horns.
Low bass energy radiates into 4pi space, hits the back wall and re-radiates into the room. The first step is called 'baffle step' and the second step is called room gain.
That's how I have always looked at it. The woofer does nor radiate into 4pi space because (in most cases) there is a wall behind it.
Terry
That's how I have always looked at it. The woofer does nor radiate into 4pi space because (in most cases) there is a wall behind it.
Terry
Its true that in the practical case our enclosed loudspeaker is usually in a real room, but we are trying to understand the ideal case of a loudspeaker on an infinite baffle or a loudspeaker on a finite enclosure, the so called diffraction effects of a baffle.
Outdoors buried in the ground vs. in a cabinet suspended well above the earth, if you will.
David S.
Indeed! (and thanks for the small concession).
Calling it a construct seems a bit like saying: "Ohms law is okay, but impedance is just a concept while Volts and Amps are real. Isn't it?
When we leave the realm of pure physics and ask engineers to solve the problem, they (Beranek, Thiele) seem to gravitate towards equivalent circuits with acoustical impedance functions.
David S.
Things like pressure, temperature, density, velocity, etc are primitive variables. Impedance; acoustic, mechanical, electrical, fluid, is a derived quantity. It is a concepts.
Re ribbon tweeters, It is not so much that Zm is much smaller than Zr, but rather that the reactive part of Zm (mass reactants) is small so there is not much stored energy in the ribbon.
Going from full to 1/2 to 1/4 to 1/8 space limits dispersion, concentrating the fixed theoretical point source to a lesser radiation area, increasing “efficiency”.
In the real world of transducers, a driver’s efficiency is fixed, it’s radiation pattern is determined by cabinet location in relation to boundaries, cabinet design, the amount of cabinets, and the array shape and size.
A cabinet which has very high directivity is not more efficient than an omnidirectional radiator, but it is more sensitive on axis.
The “caveman” LF array Mark Gander & company measured in the late 1980’s seemed to be pushing the limit of 25% efficiency because the directivity was not very high.
Tom Danley came up with the Bdeap, which has significant directivity set up in half space, here is a quote from the Lab (Live Audio Board) Re: 4 Labhorns vs 2 or 4 Bdeap32
Reply #5 on: April 07, 2005, 11:20:52 am :
“In this case, the name means Boundary Dependant External Air Path. Pat pending.
My original intention was to make a small box that when combined with the Bdeap principal and a location (the appropriate distance) in a corner, one ended up with a 32Hz 1/8 space horn where much more than half of the total horn was in the external surroundings.
Ivan who posted about having installed many of the Bdeaps, was the one I think who decided to try them stacked up 2 on 2 outdoors.
In that configuration, the external air path was in the shape of a 180 degree conical horn (made of one face of the enclosures). In this configuration, this external horn has a faster expansion rate (higher cutoff) than when in a corner but is still a useful setup.
The 180 degree horn provides a LARGE forward directivity automatically and the result was that when measured at 10 meters (a distance which is –20 dB from 1 meter), a stack of 2 on 2 has a midband sensitivity of about 97.5 dB 1 W @ 10M.
With an equivalent on axis sensitivity of 117.5 dB 1W 1M, this configuration does get “loud” as well as being “quiet” on the back side of the array.
The only down side of this arrangement is the low cutoff is raised significantly in this configuration.”
I’ll leave it to you physics types to convert an on axis sensitivity of 117.5 dB SPL with 1 electrical watt at 1 meter to an efficiency %, but as you said in post #23:
“As a side note, a good number to remember is that 1 acoustic watt is 109dB at 1 m (omni source) and 112dB for a half space hemispheric source. Always 3 dB apart.”
Of course, the conversion of on axis sensitivity to efficiency is impossible to do without knowing the directivity vs frequency.
There are no transducers in enclosures that are truly omni except at VLF, rendering an exact figure for baffle step compensation an academic exercise.
Always enjoy reading your posts !
Art Welter
This discussion reminds me of the story of the blind men trying to describe an elephant by touch...
Hi,
Yes there are in the case of small speakers away from walls (for imaging)
where you do see the full baffle step occurring, typically takes from the
low one hundreds up to around 1K, you get a full 6dB baffle step, and
typically a further baffle peak of around 2dB at the top end to boot.
(only a sphere with a tiny driver gives a the classic 6dB transition)
5" unit on a 8" x 14" baffle (ZaphAudio ZMV5)
Its not academic and the speakers are omnidirectical below ~ 100Hz.
Room gain arrives too low to help, but can bolster the bass roll if the
speaker is designed with a slow bass roll-off to properly utilise it.
rgds, sreten.
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Hi,
I'm not sure, Zaph uses SoundEasy, but the baffle step sims in different
designs appear to be different, e.g. this looks very different to the above :
Zaph Audio -SR71 bass/mid unit and central / offset tweeters
rgds, sreten.
While I was at KEF we had the large room for impulse testing speakers on a hydraulic pole. We also had a baffle flush in the walls for driver curves. The room was 10 meters on a side, so the driver could be in a 10 x 10 meter baffle with a pretty good clear time window before the first reflection.
I remember taking some measurements ona B300 (12") and taking off axis curves every 10 degrees from 0 to 90. For the same woofer in a medium sized box you would expect a little bit of rolloff down to a very low frequency as you moved off axis. Even at 50 Hz I typically saw a few dB of drop at 90 degrees.
In the infinite baffle (wall) this is not the case. From 20 up to 1kHz (as I recall) there was absolutely no drop from 0 to 90 degrees, when measuring in the baffle. So, significant LF directivity mounted in the box. Essentially no LF directivity in an infinite baffle.
Is it the box that creates the directivity?
Glad my other posts haven't "put you to sleep".
David S.
Hi,
I'm not sure, Zaph uses SoundEasy, but the baffle step sims in different
designs appear to be different, e.g. this looks very different to the above :
Zaph Audio -SR71 bass/mid unit and central / offset tweeters
rgds, sreten.
The free Baffle Diffraction Simulator is a pretty cool tool, considering the price. I too have wondered about its accuracy. Has anyone done a comparison of its modeled predictions and the actual measured response? Probably not since the test environment needed to do an honest measurement is costly enough that the tester probably isn't bothering with free tools anyway!
SoundEasy kicks butt because it takes a digitized driver response curve and applies all the simulated frequency response effects to it to give a plot reflecting the actual driver's output. For $250 it seems to me to be a darn good deal, too.
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