SY,
with Your assumption of "acoustically close" Your number of +6dB increase in output power is correct but You haven`t explained what is "mutual coupling" and where the increase in sensivity actually comes from.
What You have explained is where the +3dB of acoustic output power comes from while doubling the speakers input-power.
What is still missing is an explanation where the additional +3dB for a total of +6dB in acoustical power output comes from.
It is true that two "closely spaced" speakers driven by the same (frequency and phase) signal yield +6dB power output
but the "mutual coupling" effect is included in this result.
and the mutual coupling effect itself depends of:
a.) signal frequency
b.) distance of drivers and drivers dimensions
The above two statements are actually one and the same thing and have nothing to do with acoustical power output increase due to the mutual coupling effect.
Your first example is obviously for the case of feeding two drivers each with a seperate amp. True, the output voltage of each amp may be the same, but in order to drive a speaker You`d need current too. Hence You`d need another time the current for driving the second speaker.
The second example is for two drivers parallel wired on one amp. Due to half the speakers total impedance the amp now delivers twice the current. The effect is the same as the foregoing (*unless that now You have only one amp. which has to supply double the current, whereas before You had two amps each one delivering one time the current for driving each one of two speakers).
In both cases You have doubled (+3dB) the acoustical ouput-power by means of doubling the drivers electrical input-power. Therefore there is still no actual increase in sensivity.
Remains the question where does the increase of the additional +3db (for a total of +6dB) acoustical output-power of 2 "closely" spaced drivers come from?
You guess it, from the "mutual coupling" effect.
Mutual coupling is an enterily acoustical thing and in order to better understand and to visualize its effects, IMO it really helps to leave aside changes in SPL-output due to amplifier/speaker interface related effects of parallel or serial wiring, or multiple amp feeding multiple drivers.
In contrary to changes in SPL output due to different wiring of driver/amplifier interface, the mutual coupling effect leads to a "true" increase in sensivity (power-input versus power-output) as You get more than double (up to 4 times = +6dB) acoustical output-power with only double (+3dB) electrical input-power.
I always need a real life analogy to better understand those kind of things. Once I came up with something which helped me to visualize the mutual coupling effect - maybe it helps You too:
Imagine a person with an umbrella pushing/pulling it back and forth in front of his body, moving a certain amount of air - just like a speaker driver does.
Now a second person with the same umbrella enters the picture, doing the same and moving the same amount of air - but far away from the other person, let`s say 20 meters away.
The two persons together move twice the amount of air as each one of them.
As there are two persons with two umbrellas, each one has to deliver one time the power to move his umbrella which is the analogy to two speakers each one driven by it`s own amplifier.
The parallel wiring of two speakers on one amp. would correspond to one person moving the two umbrellas at the same time (veerrrry long arms supposed) .
Both variations finally would lead to the same conclusion regarding input-power versus output-power: doubling the (input)-effort/power to move/drive two umbrellas/speakers for double the output.
Now imagine the 2 persons moving further and further together still pushing/pulling their umbrellas like speaker drivers.
I think it`s now easier to imagine that depending of the distance at which the two persons are still seperated and the frequency of the movement (both move them at the same frequency and in phase of course) that the umbrellas begin to have some kind of influence one on the other. Below a certain distance and below a certain frequency, the total amount of moved air begins to exceed the total amount of moved air as when both persons would be still far away from each other.
How comes?
At low frequencies where a driver does not yet beam but radiate in all direcions (4phi radiation) there are air-waves bent around the drivers circumference.
When both persons/umbrellas are close together the air which is bent around the umbrellas (drivers) circumference cause to move additional air which is located "inbetween" the distance from one umbrellas outer circumference to the other and this air literally gets "sucked" back and forth by and according the umbrellas movement. It could be also explained as one umbrella would produce pressure on the other.
This causes to "mutual couple" a certain amount of (additional) air to the amount of air which both umbrellas would move if they were still seperated (far away from each other). In a more technical language this is often called an increase in (mutual) radiation impedance.
This effect sort of increases the "radiation area" of two closely spaced umbrellas. Applied this to two speaker drivers they give more than double the acoustical ouput due to more than doubling the effective radiation area (while input power is the SAME and as can be seen has nothing to do with this).
The max. gain of mutual coupling effect on acoustical power output of two closely placed drivers is +3db but only when they are not more than 1/4 wavelength apart. With raising frequency or increasing drivers distance this gain of power output goes from +3dB against zero.
BTW:
Here a link to another DIY-Audio.com thread regarding the topic of mutual coupling:
Multiple Drivers to Increase Efficiency
Assuming the voltage output of the amplifier doesn't sag when the second speaker is attached in parallel, the amplifier, it's power output and the delivery thereof to the one or two speakers in question have absolutely nothing to do with this. It's a red herring.
This is just a baffle step discussion in disguise.
The entire 6db of gain comes from the fact that each of the two speakers is effectively radiating into half space instead of a single speaker radiating into whole space.
This is just a baffle step discussion in disguise.
The entire 6db of gain comes from the fact that each of the two speakers is effectively radiating into half space instead of a single speaker radiating into whole space.
The crucial word is displacement.
So that the second surface area (or driver, or umbrella) moves at all (and with the same displacement as the other one) You have to put in something and that`s the (doubled) electrical power we were already talking about.
Otherwise there would be surface area (or a driver, or an umbrella) without moving.....
That's right, but for the same input voltage, you still get double the pushed air volume. It's awfully easy to confuse sensitivity (the relevant parameter here) with efficiency (irrelevant here). If you keep power constant, you only get a 3dB gain. There was a very nice article about this by Koonce in Speaker Builder a few years back- I'll see if I can dig it up.
Like we talked in this thread, I would like to see where is the limit in the theory.
http://www.diyaudio.com/forums/showthread.php?s=&threadid=50867
AFAIK, it would take quite a big line array to beat a horn loaded design. On the other hand, a horn loaded line array could be quite funny.
http://www.diyaudio.com/forums/showthread.php?s=&threadid=50867
AFAIK, it would take quite a big line array to beat a horn loaded design. On the other hand, a horn loaded line array could be quite funny.
RHosch said:
Sure, look at it this way.
Remove the room from consideration.
Speaker A is attached to the middle of an acoustically transparent curtain (red line) 100 yards on a side which is hanging in free space. Speaker B is attached to the other side of the curtain.
Speaker A only is turned on and is playing a 10Hz tone which is witnessed by W. Speaker A is radiating into whole space.
Speaker B is then switched on and plays the same tone at the same level effectively solidifying the curtain as far as speaker A is concerned. Speaker A is now radiating into half space and the witness sees a 6db increase in SPL.
Attachments
Sensitivity is important because speakers are usually driven by voltage sources and one is usually interested in matching sensitivities in a multi-way system. You can just as easily say that there's a 3dB gain in efficiency, then let the reader figure out that paralleling the drivers and driving them with a voltage source gets him a 6dB gain in output. That leads to all kinds of fun as the reader gets an extra 3dB he wasn't expecting and gets to ask about it in an Internet forum.
Bill Fitzpatrick said:
Interesting, but what about the case of two side by side speakers? That's the case I had in mind, and it didn't seem to fit your half-space explanation. However, in the bigger picture "mutual coupling" I suppose could be looked at in that way, as two side by side drivers would still create an effective "invisible barrier" between them.
lets get away from the non-existant space and how about lets try a closed environment.
Let us look inside an acoustic suspension enclosure. Take for instance a 100liter box with two drivers. At first let us neglect one driver and calculate the pressure increase INSIDE the box with the driver displacing one liter of air inside the box
Using the gas law equations
P1(V1) = P2(V2)
101.3kpa(100L) = P2(99L)
P2= 102.32323232kpa
Now we will add the other driver and both will displace one liter apeice.
101.3kpa(100L) = P2(98L)
P2 = 103.367kpa
Now that seems pretty linear to me.... if displacing two liters would have made ~104kpa I'd rest the case of mutula coupling.... but it doesnt.
Bill your idea seems to be the best explination so far
Let us look inside an acoustic suspension enclosure. Take for instance a 100liter box with two drivers. At first let us neglect one driver and calculate the pressure increase INSIDE the box with the driver displacing one liter of air inside the box
Using the gas law equations
P1(V1) = P2(V2)
101.3kpa(100L) = P2(99L)
P2= 102.32323232kpa
Now we will add the other driver and both will displace one liter apeice.
101.3kpa(100L) = P2(98L)
P2 = 103.367kpa
Now that seems pretty linear to me.... if displacing two liters would have made ~104kpa I'd rest the case of mutula coupling.... but it doesnt.
Bill your idea seems to be the best explination so far
I think cocolino is trying to say that the mutual coupling is an external effect from the drivers point of view. The drivers push the same volume, but due to mutual coupling some extra air gets into motion as well. If this is true, mutual coupling would increase the efficiency (sensitivity as well, because the same voltage would give more spl?) of the driver system.