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Inverse square law in smaller spaces
Inverse square law in smaller spaces
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Old 16th May 2018, 01:48 PM   #1
jf4828 is offline jf4828
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Default Inverse square law in smaller spaces

So I'm trying to determine SPL requirements for a PA system in a small room where maximum listening distance is about 40ft. The room is approximately 40ft by 60ft with speakers playing into the 60ft length. I'd like to get up to 100dBA safely at 40ft from speakers. Using inverse square law I'd need a speaker to play approximately 122dB at 1 meter to meet these requirements. Not a huge deal but I'm hoping to go pretty deep in bass with space limited mains and it's easier to cost effectively spec a system just shy of 120dB at 1 meter. Not at all looking for speaker recommendations, I'd just like to understand my real SPL requirements. Do room reflections add much to the SPL at higher frequencies. I have a handle on room gain for low frequencies.... My weekly need is really 95dBA but want some headroom.....

Last edited by jf4828; 16th May 2018 at 02:01 PM.
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Old 19th May 2018, 01:09 AM   #2
JMFahey is offline JMFahey  Argentina
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Inverse square Law applies fully in open, unobstructed space, which is not your case.
You have a quite small, reverberant room, where any sound will start bouncing from walls, floor and ceiling and quickly create a stable reverberant field.
Canīt vemture a number but consider 2 factors working on your behalf:
* at low frequencies, as you noticed, large wave but relatively unabsorbed Bass will be bounced back into the room and be quite louder than expected in an open field.
* this will not happen at high frequencies but since they are very directional, they are definitely NOT radiating uniformly into a 360 degree sphere by any means but most probably concentrating on a narrow, say 60 degree or so beam, so *within* that beam they may be easily be , say, 10dB louder at a distance than expected if they were truly omnidirectional.

So in both cases I guess that you may ease your source SPL requirement by as much as 10dB ; say 6 dB to be very conservative.
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Old 19th May 2018, 03:21 PM   #3
TBTL is offline TBTL  Germany
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Don't forget to factor in the crest factor of music.
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Old 22nd May 2018, 03:41 PM   #4
brig001 is offline brig001  United Kingdom
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Best bet would be to test it. Borrow or hire something and measure it for yourself. Even if the system is smaller than you require, you can still apply the same scaling.
So, if you get 100dB at the speakers and 80dB at your preferred listening distance, you will always need 20dB more at the speakers than at the listening position.

If your home stereo is reasonably loud, you could test using that

Brian
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