Reciprocity Theorem in practice

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In keeping with the newly and clearly re-written forum principles, I would like to start a new thread about the Reciprocity Theorem, because it is starting to be off-topic on another sub thread.

The Reciprocity Theorem goes back to Huygens (light) and Helmholtz (my personal hero) and Lord Rayleigh (for sound). It states that a point source of sound and a point source of pick-up (like a small mic) can be interchanged in location and the mic would read the same.

For setting up speakers, it means you could put your sub where you sit and search around the room with a mic to find a location that gives best results. Then you would put the sub in that best location. At least that's the generic way to put it. (The alternative is, of course, the old way we've always done it: move the sub around to possible new locations and keep the mic stationary where your head would be.)

Some people think that is great idea and are strong advocates (in the other thread, "I made a sub, it sucks.."). It means you don't have to move your sub around, just your mic. Makes good sense setting up for a show in a large arena with large speakers and you are just trying to get the general freq response about right in the listening area.

Others are thinking of typical modest music rooms at home where the room modes are strong and the sound varies a lot when the mic (or your head) is moved one foot. In such a room, you might wonder how your ported sub is changed by playing while hanging in mid-air over your listening chair and pointing in various wrong directions and how that relates to a small mic in an open space near the wall where you are going to re-locate your sub.

Who has experience with Reciprocity Principle testing and in what kind of setting?

Ben
 
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1)It means you don't have to move your sub around, just your mic. Makes good sense setting up for a show in a large arena with large speakers and you are just trying to get the general freq response about right in the listening area.

2)Others thinking of typical modest music rooms at home where the room modes are strong and the sound varies a lot when changed one foot, might wonder how your ported sub is changed by playing while hanging in mid-air over your listening chair and pointing in various directions and how that relates to a small mic in an open space near the wall.
Ben,

1) When setting up for a show in a large arena, the set up area is almost always defined by sight lines, and the mains speaker system is flown to cover the seating area. Subs may be flown or deployed on the arena floor, or both, but the array tends to be determined by design considerations, as the placement options are generally fairly limited due to stage, set, lighting and audience positions. The subs and mains need to be fairly close to each other, or timing and phase issues become problematic, with the sound quality in the crossover region varying widely through the coverage area.
2) Ported or most any small room size subs are pretty much omni- directional at sub frequencies, so other than pointing the sub at a carpeted surface to lessen harmonic distortion or upper out of band peaks, not much to consider as long as you have placed the sub properly in the listening position to insure reciprocity.

Placing a large, heavy sub properly in the LP may prove to be more difficult than moving it around to the available acceptable locations, and of course putting a sub that relies on walls or corners as part of the design won't give a representative reciprocity sitting on a couch ;^).

Art
 
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Yes, reciprocity works well for low frequencies. What doesn't work so well is putting the sub driver where you head would normally be located when sitting in the listening location! Sometimes that is not easy if your sub is large and heavy. But it is possible to substitute a smaller sub that still has enough bass extension since that will be easier to place 4 feet off of the ground.
 
...and of course putting a sub that relies on walls or corners as part of the design won't give a representative reciprocity sitting on a couch
Wrong! That would violate reciprocity, the very property that we are using for the measurement.

What happens is that the microphone gets boundary reinforcement from the walls or corners just like the sub would while the sub does not when placed at the listening location. That's reciprocity in a nutshell right there.
 
Charlie,

Regarding the usual bass reflex or sealed sub, I am in agreement with you 100%.

However, if one eliminates the mouth horn portion of a corner horn by taking it out of the corner, it's frequency response will be radically altered, the Fc raised, it will no longer be the cabinet it was designed as. To properly work with that type of horn in reciprocity, you would have to replace the missing corner at the LP, which is not going to happen ;^).

Same applies to an open baffle sub- if the open baffle is put very close to a wall, it no longer is an open baffle, it becomes a sort of bass reflex or transmission line, as in the case of the corner horn, the wall becomes part of the cabinet.

IIRC, the OP has both of these "exceptions to the rule" in his listening room.

Art
 
OK, I agree on the above points but I did not see those type of systems mentioned in the opening post. It seems you have some insight or inside information on Ben's collection! I was considering the more typical sealed, ported, or PR loaded type of subwoofer. Thanks for mention the issues with the other types of systems. It's good to note that here.
 
All subs are gigantically influenced by their proximity to walls and floors (as the sim programs incorporate), even if omnidirectional, diffraction ignored. So hanging it in the air where your head would be changes the sub output a lot.

We can't talk about sitting the sub roughly where you sit since the sound changes foot by foot. What is the "point source" of a big ported cabinet, not to mention all the other kinds of cabinets?

And reciprocally, we can't talk of putting the mic where the sub will be moved to because the sub is 6 cu feet.

So putting the sub where your head would be and putting a big box where your little mic was is not sensible reciprocity even if easy to pronounce in words.

On the other hand, trying your sub in a new location and keeping the mic where your head would be is a model that is easy to fulfil.

B.
 
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Have to disagree again on your doubts about reciprocity. When you exchange the two (sub and mic), at low frequencies they exchange reinforcement so the result is the same. Also, hauling your sub around the room (multiple moves) is more difficult than moving it one time to the "head" position. Moving a mic around is much easier IMHO. You simply need to put the mic approximately in the position where the driver is located (e.g. above the floor). I think that this will be the case even with a ported sub. The port and driver should be near each other and not 6 feet apart...

But, sure, if you want to move the sub around and measure at the listening location that should work very well. That has nothing to do with reciprocity, however.
 
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Have you done it yourself? If so, how and what were the results?

Yes, I used this with a sub in the past and it worked well - about 10-12 years ago. The sub measured about 1x2x4 feet and has two 12's and an 18" PR. I had to put it up on a table to put it about where my head was located when sitting on a sofa. Then I did measurements with ARTA of the in room response, moving the mic to positions I thought might be reasonably good until I got one that looked relatively smooth. Then I moved the sub there. But come to think of it I did not make a "confirming measurement" with the sub in the final position and the mic back at my listening location... But it did sound fine to me. That system is, unfortunately, long gone and I don't even live in that place anymore.
 
Thanks, I really am going to have to try it for myself, I'm aware that the method is widely advocated but I have niggling doubts about it. I'll have to build a simple monopole sub to play with, would probably be best? At the moment I have stereo U-frame subs and they have to stay pretty much where they are.
 
I'll have to build a simple monopole sub to play with, would probably be best? At the moment I have stereo U-frame subs

The object of moving your sub(s) around is to find a location where the room modes and the characteristics of THAT sub in THAT location sum to some "house curve" you like, as referenced to your normal listening chair and ear height.

Once when we were painting the music room, I tried 14 sub positions for my compact but fabulous AR-1 (1956)*, using the conventional method, not the not-often-heard-of Reciprocity method. Substantial differences and substantial improvement from worst to best location.

So there's no value for you in taking any sub box at hand for testing by hanging from a rope from your ceiling** where your head will be later. That has little to do with the synergy you are trying to achieve with your actual system subs.

B.
*and the other sub was very different, as per the value of heterogeneity in setting up subs
**for the test (Reciprocal or conventional) to be valid, you must leave your listening chair in its usual location; that means hanging the sub from the ceiling; that doesn't matter as much in a large arena or in a recording studio where the listeners move about, but it does matter in your room at home
 
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I didn't intend to use it with the existing subs, I think this method can only work with a single sub? If at all. I'm intrigued to see if it works, as I said I'm doubtful but I'm finding it hard to say why, and no one seems to have come up with an explanation other than reciprocity theorem says it does
 
Here is data. The first picture shows two contrasting locations. Big differences, eh? Sure makes it look hopeless to imagine you could wrangle either of them with a passive crossover, even ones made custom for each.

The second picture shows what I'd call a useful looking location (not sure it is the one I ended up with for that speaker; looks like one of the curves from the first picture). Easy to work if you have DSP with a touch of EQ and smart choice of crossover frequency and slopes.

It would be nice to see data from all those posting their opinions here.

B.
 

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**for the test (Reciprocal or conventional) to be valid, you must leave your listening chair in its usual location; that means hanging the sub from the ceiling;
Or one could simply put a sub like your "compact but fabulous AR-1" on a milk crate on your chair, no rigging from the ceiling is required.

From experience, I can definitely say moving the mic 14 times would be a lot easier than moving the sub to 14 different locations, especially if you were to be thinking of possibly putting the sub in positions off the floor. That said, since you already lugged your AR-1 to 14 positions, no need to do any more work if you are happy with the response.
 
Let's take REW Room Simulation and check.

View attachment 633832
View attachment 633833


Very similar, isn't it?
Could you please explain what we are supposed to be looking at and what we might conclude? Are you saying that the simulation agrees with its own underlying theory? Or that the radiation resistance of being in the middle of the floor is not important (or reciprocated by the mic placement in the corner)?

Reciprocity Theorem is a math construct, proven in the manner of math theorems a few decades ago. As best as I can google, there are a number of researches published that - under the usual limited test circumstances - show it is valid for acoustics.

Also, it is seems to be applicable in special ways like mic calibration or figuring out where to put loudspeakers in car doors. I don't know if that validates using it for big speaker boxes in small rooms and other features of home music.

Not feasible for me to try Art's milk crate test just now*. But surely there have to be readers who can set up (and photograph) an REW comparison of standard and reciprocal measurements quickly?

B.
*Umm, my large DIY high-voltage electrostatic panels in the way
 
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Could you please explain what we are supposed to be looking at and what we might conclude?


As you can see there are two simulated frequency responses with reversed driver and listener positions.

Are you saying that the simulation agrees with its own underlying theory?


Underlying math with some kind of integrals/differentials/rotor divergences and etc must do their work, but it's better one time to compare similar graphs than much time to see the complicated formula.

;)

IMG_6411.GIF
 
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Could you do a similar reversal simulation where one of the positions isn't in a corner?



Let's try.

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Being a DIYers or engineers we couldn't believe strong math, especially if it provides repetitive results corresponding with real measurements. (Or even this math is created to correspond with experimental).

But the most valueable ability is to show results in intuitive and clearly understandable way.
 
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