Was reading this again because I want to build a sealed subwoofer using mutual coupling to give a boost in the right area (when they start rolling off). I've never found an equation that tells you how to know this. I do believe the effect starts at 1/2 wavelength and you get a full +3 db at less than 1/4 wave spacing.
BTW the right way to look at this is that the extra efficiency is always there but just somewhat "covered up" by the drivers being out of phase until they are sufficiently close.
About 4' of 5' apart seems about right to boost below about 50 hz
BTW the right way to look at this is that the extra efficiency is always there but just somewhat "covered up" by the drivers being out of phase until they are sufficiently close.
About 4' of 5' apart seems about right to boost below about 50 hz
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Hi Polkhigh,
FYI: Easy Reading at:
Loudspeaker and Headphone Handbook - Google Books
Read:
1.4.6….Page 24 and 25
and 1.4.7
then go to Ekv 1.32---->
Read from Page 20 to 26
1.4.3 Power output of two sources-radiation impedance considerations
Ekv 1.31…..1.3.2
b
thanks I'll have to look at that. It seems obvious that say you have four sealed subs. You want to set the distance between them so that any two are within a 1/4 wave distance of the -3 db point, and then all four are within a 1/4 wave distance of the -6 decibel point. My own tests with dual sealed subs have produced really good sound quality that is very adaptable to room gain.
Tapering off of the coupling effect
This works because the speakers aren't very efficient to begin with.
For those wondering about the conservation of energy.
As you get more and more woofers, the coupling effect tapers off.
So you might get +3dB free efficiency for the first pair, then +2.5dB, then +2dB and so on as you keep doubling woofers.
One obvious reason for this is that the multiple woofers take up more space and are thus farther away and can't couple as well.
But even if you could create a big bass tunnel to try and couple all the drivers close, the acoustic pressure each cone exerted on another would eventually restrict cone motion. A bit like the cramming multiple speakers into a small box analogy. The more impedance matched a woofer is to the air to begin with, the more pronounced the effect.
Let's say one woofer increase the air pressure by a pascal from ambient (about 12 grams of resistive force to an 18"), another woofer nearby can easily keep increasing the pressure to two pascals and the motors can easily handle the 24 grams of force. (There is probably far more resistance created by cone inertia, suspension losses and by the woofer box air than the air it radiates into) It loads down the cone of the other speaker and increases the work done on the air by the speaker. A bass speaker can just as easily move with two pennies on it as with one, but eventually the back pressure applied to the cone will restrict its motion in the case of multiple 18" firing into a car cabin.
This works because the speakers aren't very efficient to begin with.
For those wondering about the conservation of energy.
As you get more and more woofers, the coupling effect tapers off.
So you might get +3dB free efficiency for the first pair, then +2.5dB, then +2dB and so on as you keep doubling woofers.
One obvious reason for this is that the multiple woofers take up more space and are thus farther away and can't couple as well.
But even if you could create a big bass tunnel to try and couple all the drivers close, the acoustic pressure each cone exerted on another would eventually restrict cone motion. A bit like the cramming multiple speakers into a small box analogy. The more impedance matched a woofer is to the air to begin with, the more pronounced the effect.
Let's say one woofer increase the air pressure by a pascal from ambient (about 12 grams of resistive force to an 18"), another woofer nearby can easily keep increasing the pressure to two pascals and the motors can easily handle the 24 grams of force. (There is probably far more resistance created by cone inertia, suspension losses and by the woofer box air than the air it radiates into) It loads down the cone of the other speaker and increases the work done on the air by the speaker. A bass speaker can just as easily move with two pennies on it as with one, but eventually the back pressure applied to the cone will restrict its motion in the case of multiple 18" firing into a car cabin.
The simple answer as to why there is a +3db increase in efficiency is IMO the extra magnets. Extra magnets increase efficiency (to a point of course).
The reason it only works within 1/4 wave distance is simply that as the two sources get farther apart they are out of phase. There can actually still be a coupling effect at farther distance at certain angles.
What you're describing in your post is more what would happen in a small space at insane volume levels, where there is too much kinetic energy in the air. Mutual coupling diminishes mostly because of electrical reasons that some people here understand better than me.
The reason it only works within 1/4 wave distance is simply that as the two sources get farther apart they are out of phase. There can actually still be a coupling effect at farther distance at certain angles.
What you're describing in your post is more what would happen in a small space at insane volume levels, where there is too much kinetic energy in the air. Mutual coupling diminishes mostly because of electrical reasons that some people here understand better than me.
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Having a stronger magnet (along with lighter, lower resistance coil wire) does improve efficiency, as does having a lighter cone, fewer suspension/spider losses and also an amplifier with a lower input impedance.
But this is not the main reason related to multiple speakers and air coupling. First you have to understand that most of the energy cost of the speaker is in moving itself e.g. you'd use only slightly less power if you used your speaker in the vacuum of space. (Assuming an infinite baffle because compressing air in an enclosure accounts for a high energy cost too compared to work done on the outside air).
Now understand that to double the air pressure a speaker has to move about twice as much (for small signal levels not engine cylinder or bicycle pump level pressures). This requires 4 x the amplifier power because the cone velocity is twice and the resistive forces are also around twice and power is force x velocity.
Two speakers in close proximity can also double the air pressure compared to one. And this only uses twice as much power as one to create 4 x the sound energy. Of course, the back pressure on the cones is now twice that of on one speaker, because one speaker created a pressure wave that tries to push back on the cone of the other speaker, and the voice coil of the other speaker has to push the cone against the original air AND the pressure wave from this speaker. (You can see that the sound waves from a woofer will be able to set the cone of a close by un-powered woofer in motion out of phase)
Again, the extra amplifier power used to push against this pressure wave is negligible as most of the energy is spent moving the speaker itself. Say I want to move a pile of apples to the top of a hill. It's a bit like comparing the energy I use to run up and down a hill carrying 2 apples at a time vs carrying one apple. I only use slightly more energy carrying two apples at a time but I get twice as many apples to the top. In this case the apples are air atoms and I am the big heavy speaker cone.
You can also see from the apples analogy that there is a peak in efficiency somewhere between making hundreds of trips up and down a hill with only a single apple each time and struggling and straining with several times my bodyweight worth of apples. So you can't just keep doubling efficiency forever, but it can be quite useful for snagging some extra output, especially as I like a lot of bass.
But this is not the main reason related to multiple speakers and air coupling. First you have to understand that most of the energy cost of the speaker is in moving itself e.g. you'd use only slightly less power if you used your speaker in the vacuum of space. (Assuming an infinite baffle because compressing air in an enclosure accounts for a high energy cost too compared to work done on the outside air).
Now understand that to double the air pressure a speaker has to move about twice as much (for small signal levels not engine cylinder or bicycle pump level pressures). This requires 4 x the amplifier power because the cone velocity is twice and the resistive forces are also around twice and power is force x velocity.
Two speakers in close proximity can also double the air pressure compared to one. And this only uses twice as much power as one to create 4 x the sound energy. Of course, the back pressure on the cones is now twice that of on one speaker, because one speaker created a pressure wave that tries to push back on the cone of the other speaker, and the voice coil of the other speaker has to push the cone against the original air AND the pressure wave from this speaker. (You can see that the sound waves from a woofer will be able to set the cone of a close by un-powered woofer in motion out of phase)
Again, the extra amplifier power used to push against this pressure wave is negligible as most of the energy is spent moving the speaker itself. Say I want to move a pile of apples to the top of a hill. It's a bit like comparing the energy I use to run up and down a hill carrying 2 apples at a time vs carrying one apple. I only use slightly more energy carrying two apples at a time but I get twice as many apples to the top. In this case the apples are air atoms and I am the big heavy speaker cone.
You can also see from the apples analogy that there is a peak in efficiency somewhere between making hundreds of trips up and down a hill with only a single apple each time and struggling and straining with several times my bodyweight worth of apples. So you can't just keep doubling efficiency forever, but it can be quite useful for snagging some extra output, especially as I like a lot of bass.
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Two acoustical reasons:
One rason why mutual coupling has diminishing returns for more and more speakers is because as you stated, the waves can become out of phase.
The other reason is that sound energy radiates under the inverse square law so as the speakers are moved apart, one speaker with its sound wave no longer exerts as much back pressure on the other speaker. If you moved the speakers to be one wavelength apart, they would be back in phase but the added distance would reduce the transmitted back pressure each speaker sends each other. The combination of phase plus distance forms this decaying roller coaster type graph of mutual coupling's effective distance.
One electrical reason is that like an electric motor, a loudspeaker is most efficient at converting power into sound when there is a certain amount of load on the cone. As you keep doubling up speakers (maybe you confined them in the sidewalls of an open ended tube to reduce inverse square law effects, and you time delayed the drivers closest to the end of the tube to reduce out of phase effects), the load on each cone increases. There comes a point when it is hard for the speaker cone to move.
This varies from speaker to speaker. In most cases, the load on the cone on the side of the air we hear is almost always too little but it could be too much if you tried to build a really high compression horn and load it with a guitar speaker with a tiny coil.
One rason why mutual coupling has diminishing returns for more and more speakers is because as you stated, the waves can become out of phase.
The other reason is that sound energy radiates under the inverse square law so as the speakers are moved apart, one speaker with its sound wave no longer exerts as much back pressure on the other speaker. If you moved the speakers to be one wavelength apart, they would be back in phase but the added distance would reduce the transmitted back pressure each speaker sends each other. The combination of phase plus distance forms this decaying roller coaster type graph of mutual coupling's effective distance.
One electrical reason is that like an electric motor, a loudspeaker is most efficient at converting power into sound when there is a certain amount of load on the cone. As you keep doubling up speakers (maybe you confined them in the sidewalls of an open ended tube to reduce inverse square law effects, and you time delayed the drivers closest to the end of the tube to reduce out of phase effects), the load on each cone increases. There comes a point when it is hard for the speaker cone to move.
This varies from speaker to speaker. In most cases, the load on the cone on the side of the air we hear is almost always too little but it could be too much if you tried to build a really high compression horn and load it with a guitar speaker with a tiny coil.
It sounds like you're thinking about it more as a physical movement of the air, like the way that a turbine or piston moves air. Sure there is fluid dynamics involved but its not really what's going on with mutual coupling. I used to think so but have changed my mind.
Mutual coupling is very predictable with distance and angles, and its clearly a matter of being in phase or not. If it was about the efficiency of moving air then you would still have some effect for sounds that aren't within 1/2 wave. Further it would vary greatly with total volume but coupling doesn't.
The magnet strength doubles relative to signal strength and this increases efficiency. But then you also have more cones to move? So how does that work? The reason is that the excursion and velocity of each cone goes down. So magnet strength effectively doubles. But then doubling magnet strength begins to diminish after a certain point as well.
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Well technically a speaker doesn't technically blow air from one place to another like a fan does (cheap reflex ports aside), but it does push against air and the force it creates against air resistance pressurises the air in front of the speaker and the wave radiates away at the speed of sound, the pressure getting weaker as the wave disperses.
As a sound wave propagates through free space air, the pressure vs distance forms a sinewave that decreases in amplitude inversely proportional to the distance you travel. You will get some reinforcement if sources are 1, 2, 3 wavelengths apart but only at certain positions and the reinforcement won't be as much because the pressure waves have tapered off in intensity over distance and don't provide much back pressure on the other speaker cone.
An out of phase wave actually "pulls" on the other speaker's cone or more accurately the higher pressure behind the speaker pushes it forwards in the direction it was wanting to go anyway. The result is the speaker doesn't have much of anything to push against and it can't generate air pressure. It's like when you go to use a public restroom and you push on the door and someone inside pulls on the door at the same time and you say "uhhh" as you stumble forwards and regain your balance.
Total volume increases the back pressure on each woofer and extra actual sound energy is gained, but the ratio of extra energy gain is conserved.
The force a speaker coil exerts is equal to the current I x the field/coil strength in BL of the loudspeaker. That's why you often see N/A by BL figures in Thiele Small parameter specifications. It means Newtons per Ampere of current. A Newton is the force required to accelerate a kilogram at 1m/s^2. It is about 100 grams in Earth's gravity. Which is equal to the length of voice coil in metres x the density of the magnetic field in Teslas, so the unit also works out as a Tesla Metre.
But as the coil moves in the magnet it generates a back voltage in the coil which is the BL x the coil velocity in metres per second at that point in time. (Assuming the coil moves 90 deg to the magnetic field which it does in a speaker). This voltage is in opposite to the amplifier phase and effectively reduces the amount of power the coil sees (increasing its impedance).
Doubling the magnet strength works up to a point just as using a coil of wire material twice as conductive, but half as thick and twice as many turns.
You would get twice as much force on your cone but as soon as it started to move, and slightly more than twice as much back voltage (because the cone also moved a bit more due to the double motor strength) and the two would cancel out. The energy loss is in the suspension and spider resistance and air resistance slowing the cone. Also the resistance of the coil wire and if you achieved a superconducting coil, it would be the resistance of the output of the amplifier. No matter how strong the magnet is or conducting the coil, you will always be fighting mechanical losses and the air resistance is the useful bit that creates the sound. Ideally you want it to dwarf the other losses.
The displacement of each cone doesn't decrease significantly if each driver is individually powered (until efficiency gain plateaus).
Unless you are talking about sharing power between multiple speakers, but then the force on each cone goes down, but with multiple speakers you are effectively reducing the mechanical and electrical losses by reducing current and reducing mechanical Rms with lower cone velocities. With series parallel drivers let's say 4, each run of wire goes through two speakers so BL doubles as the length of wire in the two speakers is added. The other run doesn't count towards BL any more than thicker coil wire but it does halve Re. So BL doubles with 4 speakers. Current to each speaker halves so force in coil halves. So for the same power you are applying twice as much force to a cone 4 x as big and heavy which moves it half as much. It displaces twice as much air and therefore increases air pressure by twice as much. This creates 8 x the air resistance on the total cone as it has 4 x the area. As it is only moving half as much though it creates 4 x the acoustic power, yet mechanical and electrical losses are the same as one speaker.
To be honest I found this last point hardest to answer as I didn't quite get what you are saying.
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Alright, I'm certainly not an expert and not sure that I care enough to seriously debate this. But consider this. Two 8" drivers playing a 12 khz sine wave spaced 4 feet apart. If you stand exactly equidistant between them there will be a +3 db bump.
Now why is there this narrow area of coupling? The drivers are completely beaming at this point and far apart, so the sound waves from each driver aren't affecting the other one. So the effect isn't from the interaction of the drivers with each other. Its inherent to the sound from the drivers themselves being in or out phase.
I believe the same signal split results in less excursion but the extra push from the extra magnet adds a +3db boost. This is what I was getting at before but probably could have said it better. Some people here probably know the equations for excursion and cone velocity relative to signal.
Btw there is nothing inherently better about using multiple identical drives. IMO its a bit of a gimmick. Array type speakers shape the response and limit room interaction and so can be good for projecting sound over distance. So they have their place when properly designed, but most typical sized rooms don't need them.
Now why is there this narrow area of coupling? The drivers are completely beaming at this point and far apart, so the sound waves from each driver aren't affecting the other one. So the effect isn't from the interaction of the drivers with each other. Its inherent to the sound from the drivers themselves being in or out phase.
I believe the same signal split results in less excursion but the extra push from the extra magnet adds a +3db boost. This is what I was getting at before but probably could have said it better. Some people here probably know the equations for excursion and cone velocity relative to signal.
Btw there is nothing inherently better about using multiple identical drives. IMO its a bit of a gimmick. Array type speakers shape the response and limit room interaction and so can be good for projecting sound over distance. So they have their place when properly designed, but most typical sized rooms don't need them.
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Well technically it will be a +6dB although you'll have to get exactly in the right spot as the wavelength is just over an inch at this frequency. The coupling is from the pressure of one wave adding to the pressure of the other wave as they collide at the same time.
In other regions there will be a cancellation because the pressure of one wave will enter the partially evacuated air of the other wave, creating normal atmospheric pressure. The average energy increase is +3dB just from there being two sources of sound energy even though they aren't loading each other significantly.
Stronger magnets reduce the amount of current required in the coil for the force produced. Exactly the same result as more turns of thinner but more conductive wire have the same effect by increasing the length of wire in the coil (assuming both coils weigh the same). This is good because current creates both heat in the coil and the amplifier outputs, neither of which are perfect conductors. For series parallel speakers N, the BL goes up by Sqrt(N) but Re (coil resistance) stays the same. So multiple coils are more efficient.
What would happen if I had a speaker with double the cone area and mass, and double the suspension stiffness and losses, but with the same magnet and coil as only one speaker? The acceleration on the cone would halve and thus assuming the same frequency, the speed the cone reached would be half which means the excursion would be halved.
Mechanical power losses in suspension would be proportional to speed squared but the suspension is twice as lossy so ultimately the power loss is halved. You might however have more thermal losses in the coil due to lower impedance from less cone motion creating a back voltage. The SPL vs voltage in would be about the same or 0dB compared to the original speaker though it's hard to see whether efficiency is gained or lost as it depends on the ratio of suspension losses and coil losses.
So with a speaker with a really underpowered magnet, you will gain 3dB by increasing BL by Sqrt(2) and keeping Re the same (the average of two drivers either in series or parallel).
TLDR, putting one magnet on a speaker cone twice as big and heavy won't change output much. Half displacement but twice area.
Putting two magnets/coils on a speaker cone twice as big and heavy is +3dB (judging from it being equivalent to two separate drivers)
So yeah you are sort of correct but it is surprisingly complicated to think through the why and I probably haven't been perfectly rigorous in my explanation and would need to study more about inductance and electromotive force for coils moving in magnets to work out the resistance of coils moving or being restricted from moving in magnetic fields with AC currents.
A simpler reason though for mutual coupling is that the ratio of air pressurised to mechanical and electrical losses improves with multiple speakers. 1 speaker moving twice as far has 4 x the losses and 2 x the sound pressure. 2 speakers have twice the losses of one and 2 x the sound pressure.
I think that's the answer right there. The workload is divided evenly among the drivers but the total BL of the system increases.
Because the magnet power generally dominates over the suspension in terms of force you get close to a doubling. It would be interesting to see if drivers with very low qms where the suspension dominates have less of a coupling effect. I would assume they do.
I also believe that the suspension have less of a drag on the moving parts per individual driver since the velocity and excursion are less. One thing about array type speakers is they do have an effortless quality to them. They're nice if you got a big room to put them in.
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Mutual coupling is not free output nor is it some mysterious unknown factor or unused performance capitalized, so much. It is two drivers acting as one and beaming as if double the size. this creates a 3db increase focused between them as a lobe rather than them combing. The energy from from two drivers in total does not change. It is the very same as a line array but in the simplest form. Another example would be that the same motor and magnet ...and power input...on a 15" speaker will generally have more output than a corresponding 12" despite all things being equal... but the 12" beams at a higher frequency.