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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
Fors* Fors* is offline
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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
Big Daddy Big Daddy is offline
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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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