Lets say we have a system of four 8 ohm drivers on the same baffle connected as two serial pairs, paralleled. The resulting system would be eight ohms but +6db. What would happen if you created four of these systems and then connected the four systems together the same way the individual drivers were - in two serial pairs, paralleled.
A. Would the resulting system of 16 drivers be 8ohms and +12db?
B. Can we keep doing this ad infinitum, gaining more sensitivity while maintaining the same power load as one driver or am I missing something?
A. Would the resulting system of 16 drivers be 8ohms and +12db?
B. Can we keep doing this ad infinitum, gaining more sensitivity while maintaining the same power load as one driver or am I missing something?
I'd agree.
As you use more and more drivers, the power going to each driver starts getting smaller and smaller,
If you keep using the same output power. The drivers wil one day stop working because of insufisiant power going to each one of them.
but thats only reality
in a perfect world, yes, you could do that to infinity.
I am not an engineer, so I cannot give you an exactly perfect answer. I can only give examples to impart a sense of the scale of things.
There are two ways of going about this. First is to download the % efficiency to conversion chart from www.trueadio.com.
The second is to go by the following formula from the Adire website. Here it is:
http://www.adireaudio.com/tech_papers/spl.htm
Thanks to Pete Mazz for the reference.
SPL = 112 + 10 * log( n0 ), where n0 = % efficiency.
We have a speaker with an efficiency of 6.27%. What is it's efficiency?
112 + 10Log .00627 = 99.97 dB @ 1W/1M.
From this formula, we see that a 100 dB @ 1W/1M speaker is only 6.27% efficient.
I have read of horns that are 50% efficient. The reason they are so efficient is that they are so very large compared to the wavelengths of sound they are expected to carry. A 100 Hz wavelength is 11.25 feet long. A horn to carry that wavelength should be that length on each side-assuming it is a square mouth.
The more speakers you add in series/parallel configuration, the more the size of the wall of speakers you are building begins to take on the dimensions of a horn mouth. Thus, the efficiency rises accordingly.
Where does it stop? I don't know. Somewhere before 100% efficiency, that is for sure. But if 50% efficiency is achievable-and horns prove that it is-then maybe it doesn't make that much difference.
Consider:
100% efficient = 112 dB @ 1W/1M
50% efficient = 108.9 dB @ 1W/1M
The difference between 50% and 100& efficient is only 3.1 dB. Not enough to worry about, except for the satisfaction of finding out how far things can be taken.
There are two ways of going about this. First is to download the % efficiency to conversion chart from www.trueadio.com.
The second is to go by the following formula from the Adire website. Here it is:
http://www.adireaudio.com/tech_papers/spl.htm
Thanks to Pete Mazz for the reference.
SPL = 112 + 10 * log( n0 ), where n0 = % efficiency.
We have a speaker with an efficiency of 6.27%. What is it's efficiency?
112 + 10Log .00627 = 99.97 dB @ 1W/1M.
From this formula, we see that a 100 dB @ 1W/1M speaker is only 6.27% efficient.
I have read of horns that are 50% efficient. The reason they are so efficient is that they are so very large compared to the wavelengths of sound they are expected to carry. A 100 Hz wavelength is 11.25 feet long. A horn to carry that wavelength should be that length on each side-assuming it is a square mouth.
The more speakers you add in series/parallel configuration, the more the size of the wall of speakers you are building begins to take on the dimensions of a horn mouth. Thus, the efficiency rises accordingly.
Where does it stop? I don't know. Somewhere before 100% efficiency, that is for sure. But if 50% efficiency is achievable-and horns prove that it is-then maybe it doesn't make that much difference.
Consider:
100% efficient = 112 dB @ 1W/1M
50% efficient = 108.9 dB @ 1W/1M
The difference between 50% and 100& efficient is only 3.1 dB. Not enough to worry about, except for the satisfaction of finding out how far things can be taken.
Four speakers in a line will not give you the 6 dB increase in sensitivity. There will be an increase, but not as much as 6 dB.
To get the 6 dB increase in sensitivity, the speakers must be in roughly square arrangement. Something like:
OOO
OOO
OOO
Not
O
O
O
O
O
O
Of course, they must be as close as possible, very near touching, for the 6 dB benefit. Sixty-four 6.5" speakers should give you the benefit you mention when they are in an arrangement roughly 52" by 52".
To get the 6 dB increase in sensitivity, the speakers must be in roughly square arrangement. Something like:
OOO
OOO
OOO
Not
O
O
O
O
O
O
Of course, they must be as close as possible, very near touching, for the 6 dB benefit. Sixty-four 6.5" speakers should give you the benefit you mention when they are in an arrangement roughly 52" by 52".
Funny thing about line arrays, though, is that it is written that when you walk away from them, a line array decreases only 3 dB every time you double the distance from them. So if you are standing 1 meter from the speakerwhich is playing at 96 dB, and move to a position 2 meters away, the SPL will be 93.
A normal speaker or squarish array deceases 6 dB every time you double the distance. So at some distance from the speaker, assuming it is outdoors or in a large hall, the line array gives you more sound!
A normal speaker or squarish array deceases 6 dB every time you double the distance. So at some distance from the speaker, assuming it is outdoors or in a large hall, the line array gives you more sound!
Everything presented is valid as long as certain assumptions are maintained. Just to keep everyone’s perceptions clear about what is being said, it is necessary to understand that efficiency is related to power, and sensitivity is related to SPL at a point in space. The graph referred to by Kelticwizard (I couldn’t find it) has to qualify a conversion from efficiency to SPL by a radiation pattern. This is referred to in the Adire Audio link, but not explicitly defined.
If you ASSUME a driver is radiating at a frequency where the driver can be considered a point source, it can be said to be radiating omni-directionally (equal in all directions) into a 4-PI Sheridan sound field (Full Space). This is automatically theoretical in most case because there will be, at least the ground to block one of the directions, but for the sake of this discussion, we’ll continue. The output from such a driver can be measured at a point in space x meters from the driver to be, let’s say, 0db(ref). This becomes our reference measurement. If we now take the same driver with the same input power and frequency, and move it to the ground level, it will be radiating into a 2-PI sound field or half space. Now if we take the same measurement at x meters, the SPL is now +6db.
Is the driver more efficient? Is the driver more sensitive?
The answer is no on both questions. Small equations for efficiency (on which many of the graphs and such on the subject since Small, are based) ASSUMED a 2-PI sound field. So if a low frequency measurement is made in a semi-reverberant room, Small equations will have to be adjusted dramatically. The same situation is the case for the classic baffle step problem. The drivers efficiency or sensitivity doesn’t change, but the relative sound field it is radiating into does change and certainly the SPL at a point in space changes.
I hope I didn’t confuse the issue.
Rodd Yamashita
If you ASSUME a driver is radiating at a frequency where the driver can be considered a point source, it can be said to be radiating omni-directionally (equal in all directions) into a 4-PI Sheridan sound field (Full Space). This is automatically theoretical in most case because there will be, at least the ground to block one of the directions, but for the sake of this discussion, we’ll continue. The output from such a driver can be measured at a point in space x meters from the driver to be, let’s say, 0db(ref). This becomes our reference measurement. If we now take the same driver with the same input power and frequency, and move it to the ground level, it will be radiating into a 2-PI sound field or half space. Now if we take the same measurement at x meters, the SPL is now +6db.
Is the driver more efficient? Is the driver more sensitive?
The answer is no on both questions. Small equations for efficiency (on which many of the graphs and such on the subject since Small, are based) ASSUMED a 2-PI sound field. So if a low frequency measurement is made in a semi-reverberant room, Small equations will have to be adjusted dramatically. The same situation is the case for the classic baffle step problem. The drivers efficiency or sensitivity doesn’t change, but the relative sound field it is radiating into does change and certainly the SPL at a point in space changes.
I hope I didn’t confuse the issue.
Rodd Yamashita
Roddy:
Thank you for your response.
So what you aare saying is, the "112 dB @ 1W/1M = 100% efficient" figure is valid only for a speaker outside, on a hard reflecting service?
If we put this speaker up against a very large wall 100 feet wide and 100 feet high, so that the ground and the wall form a 90 degree angle, then the rating gets upped to "118 dB @ 1W/1M"? Is that it? I have read that each additional wall you put a speaker next to increases it's SPL 6 dB.
Also, do you know of any practical limit that would prevent a squarish array of speakers, that keeps quadrupling in size, from increasing it's sensitivity at the rate of 6 dB per quadrupling until it comes very near 100% efficiency? Is there any practical reason it cannot achieve 85 or 90% efficiency?
Thank you for your response.
So what you aare saying is, the "112 dB @ 1W/1M = 100% efficient" figure is valid only for a speaker outside, on a hard reflecting service?
If we put this speaker up against a very large wall 100 feet wide and 100 feet high, so that the ground and the wall form a 90 degree angle, then the rating gets upped to "118 dB @ 1W/1M"? Is that it? I have read that each additional wall you put a speaker next to increases it's SPL 6 dB.
Also, do you know of any practical limit that would prevent a squarish array of speakers, that keeps quadrupling in size, from increasing it's sensitivity at the rate of 6 dB per quadrupling until it comes very near 100% efficiency? Is there any practical reason it cannot achieve 85 or 90% efficiency?
Don't forget phase cancellation folks - nobody seems to have mentioned it yet, but it's arguably the biggest single problem with spherical arrays, and also a significant problem in ensuring correct coupling in line arrays.
The Bessel array in reducing the level to drivers on the edge of the array is an attempt to address this in part.
I'd love to write more on this, but it's time to go and play football......
The Bessel array in reducing the level to drivers on the edge of the array is an attempt to address this in part.
I'd love to write more on this, but it's time to go and play football......
Hi Kelticwizard,kelticwizard said:
Yes, you pretty much have the picture. Double power is +6db so when you halve the radiating space you effectively double the power concentration (the same power into half the space is +6db SPL at a relative point in that space).
The practical limit comes in when the distance to the room boundaries (walls, ceiling, floor) and, as Redeye point out, the distance between the drivers are comparable to the wavelength of the frequency being reproduced. When this happens, all bets are off. The calculation of SPL at a point in space becomes a grad school advanced math or physics course.
Hey Redeye, is that the football with the pointy ends on the ball? No. Than it’s not football.
Rodd Yamashita
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