Maybe someone could recommend a good and easy to understand book having a chapter about the addition of acoustical sources. This one, in french, is perfect for an initiation to acoustics, this is the kind of book one never regret to buy :
Initiation à l'acoustique : Cours et exercices (1Cédérom) - Antonio Fischetti - Amazon.fr - Livres
Maybe there is something equivalent in english.
And it is the cause of permanent confusion for so many people.
AndrewT's post make me think I could also have given the above calculations in Volts.
Yes.
The amps you are going to use are voltage sources, that means that their output voltage is independent of the load, be it open circuit, 16, 8 or 4 Ohm.
Was the earlier statement that two drivers need to be within 1/4 wavelength to gain the full +6 db sensitivity correct?
In that case, if two drivers are 17 inches apart the upper frequency at which you will start gaining less sensitivity would be ~200 Hz.
I wonder if anyone has a graph showing the boost relative to the fraction of the wavelength - is it correct to assume that as you reach 1 full wavelength apart you reach the minimum increased efficiency of +3 db? (Not taking into account loss of level at the listener's position due to distance from the driver).
In that case, if two drivers are 17 inches apart the upper frequency at which you will start gaining less sensitivity would be ~200 Hz.
I wonder if anyone has a graph showing the boost relative to the fraction of the wavelength - is it correct to assume that as you reach 1 full wavelength apart you reach the minimum increased efficiency of +3 db? (Not taking into account loss of level at the listener's position due to distance from the driver).
Any decent crossover simulator (like Bagby's PCD) will give a graph (or a series of graphs) to show the effect of driver distance vs wavelength. At 1/4 wave or less you should get full mutual coupling, as distance increases past 1/4 wave you will get less, and at some frequencies you will get interference (lobing, comb filtering, stuff like that).
With PCD you can investigate these effects including the ability to move the virtual mic location so you can view the lobing in the horizontal and vertical off axis too. And you can offset the relative distance of the two drivers back and/or forth in relation to the virtual mic too.
Basically PCD does exactly what you want to see, and you probably already use it. Just load one driver as a mid, and load another driver exactly the same as the first as a tweeter, don't add any filters of any kind, and look at frequency response on and off axis as you move the driver distances to any distance you like in relation to each other and the virtual mic. The graph you get is showing the mutual coupling (summed response) of those drivers at the virtual mic location.
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the 1/4 wavelength rule allows one to calculate the frequency below which full coupling is maintained. This gives the +3dB effect from the two drivers fed with the same total power compared to one driver fed with the same total power.
If the distance from centre to centre of the two drivers is increased to 1/2 wavelength, then the front radiation is stll +3dB
The side radiation suffers cancellation due to destructive interference of the two out of phase wavefronts. Perfect cancellation would give silence i.e. -1000000dB
As the spacing c/c gets bigger than 1/4 wavelength the width of the lobe gets narrower. This is often shown in a two way treble + mid where the forward lobe can be quite narrow and the nulls are effectively notches in the signal strength.
The same applies to big drivers sitting next to each other. At very low frequencies they are omnidirectional. At higher frequencies they start to lobe.
If the distance from centre to centre of the two drivers is increased to 1/2 wavelength, then the front radiation is stll +3dB
The side radiation suffers cancellation due to destructive interference of the two out of phase wavefronts. Perfect cancellation would give silence i.e. -1000000dB
As the spacing c/c gets bigger than 1/4 wavelength the width of the lobe gets narrower. This is often shown in a two way treble + mid where the forward lobe can be quite narrow and the nulls are effectively notches in the signal strength.
The same applies to big drivers sitting next to each other. At very low frequencies they are omnidirectional. At higher frequencies they start to lobe.
The attached figures show what others have described with words.
Attachment #1: Power gain for one source due to mutual coupling from another identical source. Upper X-axis scale shows ratio of spacing to wavelength.
Attachment #2: 2D polar response for 1/8 wavelength and 3 wavelength spacings.
Attachment #3: 3D polar response for 1/8 wavelength and 3 wavelength spacings.
In ideal free space (ie no room) when two identical sources are placed near each other:
- on-axis SPL will increase +6dB at all frequencies (compared to a single source).
- total radiated acoustic power increases +6dB at low frequencies transitioning to +3dB as wavelength gets small relative to the spacing, (compared to a single source).
The figures were taken from Section 1.4 in the “Loudspeaker and Headphone Handbook” which contains an excellent description and analysis of mutual coupling between sources including the effects on radiation impedance “seen” be the individual sources. In fact, the entire first chapter is a good introduction to basic acoustics relevant to loudspeakers as sources.
Currently this chapter is available for free preview at Google Books:
https://books.google.com/books?id=T...d headphones handbook mutual coupling&f=false
Attachments
Definitely not true. Corner positioning may not be the best for even distribution of bass as it focuses the central decay point at the most extreme position in your room, but it also provides 1/8th space containment of your bass, giving you a 9dB increase to sensitivity from the full space measurement. In other words, you get 8 times more efficient using a corner-loading than you would in free-space. That's almost twice the bass from the same sub just from a position change. If you have a set listening position or cluster of positions, distribution of bass does not need to be super even, and you can frequently get more bass to the locations you want at no detriment of inconsistency between positions. You may actually end up with more even sound depending on where the sub's location is in relation to the listening area.
Technically power is a product of voltage and current so a doubling of voltage is a quadrupling of power and current is part of the equation already. If you double your power to get an increase of 3dB, this includes the increase in current as well. While it may yield the result you're looking for, your math is flawed.
Sorry, misquoted the first response. It's still technically not true though. You've essentially listed the same change from 2 perspectives. Voltage remaining the same does not inherently produce a doubling of power. This relies on the change in current brought about by the change in impedance. In other words, only the output power from the amp changes, not the power delivered to each driver. Running a single 8-ohm driver with 8V of potential gives 8W of power. Driving a second 8-ohm driver with 8V also gives 8W of power, which combines to 16W total giving double the power, but this is still distributed between 2 drivers. The reason you can still get double the power at the same voltage is because you have double the current and half the impedance. The two 8-ohm drivers combine to produce a 4-ohm load on the amp, which will draw twice the current for the same voltage. This doubles your power from the amp for a 3dB boost, but it would be the exact same power boost as saying 2 drivers are driven by the same voltage. It's just ohms law. If you want a quadrupling of power you need both double the voltage and double the current (which happens naturally if impedance is the same).
Mutual coupling is a phenomenon that compounds on top of typical constructive and destructive interference. Yes, you get a 3dB boost to output based on the doubling of displacement using 2 diaphragms and motors, but this is not what mutual coupling attempts to describe. This is simply super-position and occurs at all frequencies regardless of distance of the diaphragms in relation to wavelength. If it did not, you would not hear a sound as louder if you have 2 speakers on opposite sides of the room. In order for mutual coupling to be both frequency and proximity dependant, it must be from another source. Also, as one or more of you have said incorrectly, doubling of current is the same as driving 2 drivers with the same voltage. The impedance drops according to laws of resistance and current increases from the amp to compensate for this decrease in resistance. Each driver still gets the same amount of power and current as well as voltage according to ohms law, so the doubling in output power or "acoustic power" is the same thing as the doubling in current. Current technically wouldn't double if they were on different amp channels but the effect would be the same so current doubling is the inherent necessity to produce the doubling in output/displacement.
Mutual coupling has to do with how the impedance of 2 drivers interact with each other. Specifically, how the mechanical air load impedance of each driver changes due to ther other. Mechanical air load impedance is the resistance of the elastic medium (air in this case) which induces a resistance to movement of the diaphragm. In other words, the difficulty to move air which induces a back EMF which varies with frequency. This value changes when multiple diaphragms are used as they affect one another. The movement of one diaphragm will produce a change in each other based on their distances as one wave will interact with the other diaphragm and visa-versa. The mutual air load impedance of the two drivers will be different than a single direct radiating piston, and this difference is what produces mutual coupling. This is also why doubling the surface area produces a reduction in the mutual coupling frequency by a ratio of the square root of 2. (radius in determining coupling based of diaphragm size is the root of the value of area).
The simple explanation is that the pressure on driver 2 induced by the movement/oscillation of driver 1 and vice-versa, causes a change in the mutual and self impedances of each driver coupling with the air (or other elastic medium) and produces a mutual coupling that translates to a boost in output when drivers are in-phase and spaced close in relation to the wavelength in question.
Mutual coupling has to do with how the impedance of 2 drivers interact with each other. Specifically, how the mechanical air load impedance of each driver changes due to ther other. Mechanical air load impedance is the resistance of the elastic medium (air in this case) which induces a resistance to movement of the diaphragm. In other words, the difficulty to move air which induces a back EMF which varies with frequency. This value changes when multiple diaphragms are used as they affect one another. The movement of one diaphragm will produce a change in each other based on their distances as one wave will interact with the other diaphragm and visa-versa. The mutual air load impedance of the two drivers will be different than a single direct radiating piston, and this difference is what produces mutual coupling. This is also why doubling the surface area produces a reduction in the mutual coupling frequency by a ratio of the square root of 2. (radius in determining coupling based of diaphragm size is the root of the value of area).
The simple explanation is that the pressure on driver 2 induced by the movement/oscillation of driver 1 and vice-versa, causes a change in the mutual and self impedances of each driver coupling with the air (or other elastic medium) and produces a mutual coupling that translates to a boost in output when drivers are in-phase and spaced close in relation to the wavelength in question.
First, cutting into half space from free space or full space would only produce a doubling (3dB increase in output), but this is assuming waves do not superimpose and still radiate outward. You're implying that the waves reflect off each other which is absolutely incorrect. You could get as much as a 3dB increase based on superposition assuming the waves would be in phase, but this has nothing to do with limiting the radiation space of the speaker/driver.
Sensitivity is the dBSPL produced per Watt of power delivered. Efficiency is the effective translation of energy used to create motion. You can have a very sensitive driver (able to produce 100dB @ 2.83V and 1 meter--2.83V is 1W at 8-ohms) that is incredibly inefficient (efficiency is typically between .5% and 2% of energy translated into sound). A driver with 1% efficiency can still have a sensitivity of 95dB compared to a 2% efficient driver that can have sensitivity of 85dB. Efficiency doesn't matter here because you still have to put 10x the wattage into the more efficient driver to get the same output levels. I think you have these terms backwards.
You've given an explanation, but it's completely false. Mutual coupling is caused by changes in mutual air load impedance changing due to one anothers interaction on each other. Containing sound to a space relies on reflection not pure superpositional interference (constructive or destructive) so it would be impossible for mutual coupling to exist due to half/full space interaction because sound waves cannot reflect off one another.
Larger Sd (postonic surface area) creates greater displacement, as well as more excursion (Xmax), both of which combine to create Vas as the displacement, but this is different from mutual coupling. Mutual coupling inherently has to involve multiple pistons. You're talking about changing the parameters of a single piston, not multiple. Also, a doubling of Vas producing a 6dB boost is not a useful value. Double displacement produces a theoretical 6dB boost to output, but it also changes your F3, and your Qts values so your curve is different, often producing more than 6dB increase near the F3 point (especially when Qts increases above .7). To discuss mutual coupling requires that the effect be unique to multiple drivers being used.
Only problem is due to the way cone diaphragms interact and the inability to fit in an infinitesimally small area, you reach a limit. Every time you double your driver count, you decrease your frequency point below which mutual coupling occurs by a ratio of the square root of 2 because you've increased your driver diameter. Additionally each time you add more drivers you increase the distance between them and push it closer to no longer being able to mutually couple. This does a few things. First, after the first additional driver, you have an increasingly uphill battle as you would have to go to 4 drivers to get the additional 3dB given by mutual coupling over 2 drivers (3db from 1 to 2 from mutual coupling). And again just 3dB from going to 8 drivers from 4 and so on. However, you get to a point where they simply combine rather than actually mutually couple, so you just get the boost of more surface area and motor strength. So a 100 driver setup vs a 50 driver setup would give you just 6dB boost, assuming they still mutually couple, and another 3dB due to power handling. This isn't advised though because so many sources will inevitably cause lobing and even comb filtering.
You actually only get a 6dB boost from mutual coupling rather than 9 in a 4-woofer cabinet because it's logarithmic. In other words doubling gives 3dB increase so adding a 3rd does not double from 2 to give a 3dB boost. Going from 2 to 4 does though. Since impedance is effectively the same in both a single woofer and 4 wired in series parallel (discounting mutual air load impedance that causes mutual coupling) you get the same output power from the amp, distributed 4 ways to the drivers. This means 6dB less power per driver, but combined to give a net 0dB gain from 4 drivers with 25% power each. This gives a net boost to sensitivity of 6dB given purely from mutual coupling. You should also get a big increase in power handling however, for an additional 6dB boost to max output based on the power handling of 4 voice coils being 4x greater. If you then have 2 of these quad subs right next to each other you should get the inherent 3dB boost due to double the surface area and power, but if your drivers are close enough together as well, you should get a mutual coupling boost of another 3dB on top of it for a total of 6dB.
Pano,
It is close to Halloween, the zombie threads come alive like cicadas on some somnambulant cycle that can't be tied to any semblance of our reality.
Hey, what's that knocking at my window- let's see, my 40V chain saw is charged, 3 spare batteries, one spare chain, five bolts in the crossbow, 400 rounds of 22 and 380 ammo-
+/- 3dB...
Actually, I find Chris responses quite enlightening.
Moreover, if people would first search the forum instead of starting new threads on topics that have been discussed before, wouldn't that:
- Improve the effectiveness and efficiency of searching the forum
- Conserve some server storage space?
I came across at least 4 threads on this topic, of which this is the most comprehensive.
Moreover, if people would first search the forum instead of starting new threads on topics that have been discussed before, wouldn't that:
- Improve the effectiveness and efficiency of searching the forum
- Conserve some server storage space?
I came across at least 4 threads on this topic, of which this is the most comprehensive.