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Old 09-10-2010, 01:35 AM   #1
Big Daddy Big Daddy is offline
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Default SPL Versus Distance and Power

SPL VERSUS DISTANCE

Generally speaking, the sound pressure level in free field such as an anechoic chamber drops by 6dB everytime you double the distance from the source. The actual levels depend on the sensitivity of the source (louspeaker). The formula to calculate the SPL as a function of distance is as follows:

SPL2 = SPL1 + 20*log(R1) -20*Log(R2)

where:

R1 = The original reference distance, normally 1 meter
R2 = The desired new distance from the source
SPL1 = The original reference dB level, normally the sensitivity of the speaker
SPL2 = The new dB level at the new distance

The formula to calculate Power as a function of SPL is as follows:

P2 = P1 * 10^((dB1-dB2)/10)

Where:

dB1 = The original SPL, normally the sensitivity of the speaker
dB2 = The reduced SPL level as a result of increasing distance
P1 = The original power needed to obtain the sensitivity, normally 1 watt
P2 = The power needed to maintain the original SPL, normally the sensitivity level

The following tables demonstrate the SPL as a function of distance for three hypothetical loudspeakers with sensitivities of 87dB, 90dB, and 95dB. The yellow column shows approximately how much power you will need to maintain the original SPL. The included graphs clearly demonstrate that the relationships between SPL, distance, and power are exponential.











SPL VERSUS POWER

To calculate the sensitivity of a speaker, 1 watt of test signal is send to the speaker in an anechoic chamber and the output is measured at 1 meter. If the power is doubled, the SPL output will increase approximately by 3dB. The relationship between SPL and power is as follows:

dB2 = dB1 + 10 * Log(P2/P1)

where:

P1 = 1 Watt
P2 = The value of P1 multiplied by 2, 4, 8, etc.
dB1 = 87, 90, or 95, depending on the speaker's sensitivity
dB2 = The new SPL level as a result of doubling the power

The following tables and graph demonstrate the relationship between SPL and power. As before, this relationship is exponential.







You can find a calculator and additional information at the following site:

http://www.sengpielaudio.com/calculator-distance.htm

Last edited by Big Daddy; 10-24-2011 at 06:02 AM.
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Old 09-10-2010, 02:36 AM   #2
SammyG SammyG is offline
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So if that's correct, essentially you'd have to double the wattage per meter to keep the speaker sensitivity rating?
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Old 09-10-2010, 02:45 AM   #3
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Quote:
Originally Posted by SammyG View Post
So if that's correct, essentially you'd have to double the wattage per meter to keep the speaker sensitivity rating?
Yes and no. Keep in mind that the relationship is exponential and not a straight line. Also, these numbers are in free field (anechoic chamber) without any reflections.

I am currently constructing another table that shows the relationship between power (watts) as a function of distance, taking sensitivity into consideration. Be patient please.

Last edited by Big Daddy; 10-24-2011 at 05:53 AM.
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Old 09-10-2010, 02:47 AM   #4
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Thanks BD, can't wait to see the other table. Thanks in advance!
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Old 09-10-2010, 04:01 AM   #5
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I created a new table and a graph of power as a function of SPL and added them to post #1. Hopefully, I haven't made any mistakes. I am too tired now. I will worry about checking them later.
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Old 09-10-2010, 10:24 AM   #6
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I remember this graph (or some of it) in another sticky. However, I like the fact that you started a new sticky just for SPL in regards to distance/power. Thank you Big Daddy!
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Old 09-11-2010, 12:28 AM   #7
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Quote:
Originally Posted by Fors* View Post
I remember this graph (or some of it) in another sticky. However, I like the fact that you started a new sticky just for SPL in regards to distance/power. Thank you Big Daddy!
Thanks Fors.

I don't believe you have seen any of these tables or graphs before. I created them yesterday. There is a small sensitivity table in the https://forum.blu-ray.com/speakers/7...ng-factor.html thread. That is an approximation table and may be partially similar to the last table in post #1.
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Old 09-11-2010, 12:45 AM   #8
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Quote:
Originally Posted by Big Daddy View Post
Thanks Fors.

I don't believe you have seen any of these tables or graphs before. I created them yesterday. There is a small sensitivity table in the https://forum.blu-ray.com/speakers/7...ng-factor.html thread. That is an approximation table and may be partially similar to the last table in post #1.
Reminds me of my Navy course Math for SIGINT. I had the very same formula. Very intense course - but you do know that you are saying :cool
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Old 09-11-2010, 12:55 AM   #9
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Quote:
Originally Posted by prerich View Post
Reminds me of my Navy course Math for SIGINT. I had the very same formula. Very intense course - but you do know that you are saying :cool
I took all my math courses in the 20th century when Math was still cool and there was no iPod to distract you.
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Old 09-11-2010, 01:18 AM   #10
LordoftheRings LordoftheRings is offline
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Quote:
Originally Posted by Big Daddy View Post
I took all my math courses in the 20th century when Math was still cool and there was no iPod to distract you.
That puts you way ahead of the pack!
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Old 09-11-2010, 01:28 AM   #11
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Originally Posted by LordoftheRings View Post
That puts you way ahead of the pack!
Unfortunately, too many young people only care about excitement and consider math courses booooooooooooooooooooring.
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Old 09-11-2010, 02:41 AM   #12
LordoftheRings LordoftheRings is offline
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Quote:
Originally Posted by Big Daddy View Post
Unfortunately, too many young people only care about excitement and consider math courses booooooooooooooooooooring.
Yup, I was one of them back then!
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Old 09-11-2010, 03:14 PM   #13
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"Generally speaking, the sound pressure level in free field such as an anechoic chamber drops by 6dB everytime you double the distance from the souce."

Just a brief change of subject, but kind of along the same line. The 6dB rule applies not only to audio, but the entire RF spectrum well up into the microwave region and above. This is one of the reasons that it really does not matter all that much how far the distance is between the transmitter and the receiver assuming all the losses are "free space" losses (no ground obstructions). The drop is 6dB every time you double the distance. So a 100 mile path has only 6dB more loss than a 50 mile path. 20,000 miles has only 6dB more loss than a 10,000 mile path, and so on. If you can avoid ground obstructions (a high antenna for one) you can communicate a long, long way. Avoiding ground obstructions is not all that feasible on earth (except mountain top to mountain top), but point the antenna towards the sky and the "sky is the limit" (within reason).
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Old 09-11-2010, 03:34 PM   #14
prerich prerich is offline
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Quote:
Originally Posted by Big Daddy View Post
I took all my math courses in the 20th century when Math was still cool and there was no iPod to distract you.
Same here!!!!
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Old 04-18-2011, 05:55 AM   #15
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The question is, what happens in a normal room? I've heard a suggestion that 3db rather than 6 is more typical in a room. Another thing I'll have to try out (not that hard to test).
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Old 04-18-2011, 02:06 PM   #16
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Quote:
Originally Posted by paulspencer View Post
The question is, what happens in a normal room? I've heard a suggestion that 3db rather than 6 is more typical in a room. Another thing I'll have to try out (not that hard to test).
In a typical home theater room, there are way too many reflections from everywhere and every room is different. As a result, I am not sure we can generalize about all rooms. I have never tested this in a room, but the 3dB assumption may not be bad.

There are too many obstructions in most rooms and it is not easy to test this. You need a relatively large room without too many furniture and other obstructions in it. Also, I am sure the typical $50 SPL meters are accurate enough to show the effect reliably for very short distances.

If you ever perform the test, please let us know about the results.
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