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21st June 2013, 02:45 AM  #1 
diyAudio Member
Join Date: Jun 2013

Math check?
Hi,
I was hoping to get a little more info about how to use SPL. I am trying to create a portable sound system for various applications (battery powered, transportable via subway). I am concerned with size, weight, quality and throw (I hope that is the correct term). I have a variety of speaker / amp / battery solutions currently I am working on my subwoofer. Since sound level is measured at a reference point and SPL is measured at the source I wanted to try and work out power consumption vs. relative sound levels in order to approximate how my power source (i.e. battery) requirements and volume levels. Currently I am focused on using this outdoors. Here is what I suppose to be the relevant pieces of data Sub SPL: (2.83v/1m): 85.6 db Amp: 200 Watt RMS (Class D ~86% efficiency) Here is the logic used Input power (power draw @ battery) = output (amp) power / 86% Output Power should be ~86% of the input power db (@ source (i.e. 1m) ) increases 3 db for every 2 watts (output power) over SPL For the data below I used an increase of 9 db for every 6 watts DB @ distance = (DB@source  (20 * log(distanceFromSource/1m))) As taken from http://www.sengpiela...distancelaw.htm Is this correct ? Thanks (Watts) Watts (86% eff) 1 1 85.6 79.6 76.1 73.6 8 7 94.6 88.6 85.1 82.6 15 13 103.6 97.6 94.1 91.6 22 19 112.6 106.6 103.1 100.6 29 25 121.6 115.6 112.1 109.6 36 31 130.6 124.6 121.1 118.6 43 37 139.6 133.6 130.1 127.6 50 43 148.6 142.6 139.1 136.6 57 49 157.6 151.6 148.1 145.6 64 55 166.6 160.6 157.1 154.6 71 61 175.6 169.6 166.1 163.6 78 67 184.6 178.6 175.1 172.6 85 73 193.6 187.6 184.1 181.6 92 79 202.6 196.6 193.1 190.6 99 85 211.6 205.6 202.1 199.6 106 91 220.6 214.6 211.1 208.6 113 97 229.6 223.6 220.1 217.6 120 103 238.6 232.6 229.1 226.6 127 109 247.6 241.6 238.1 235.6 134 115 256.6 250.6 247.1 244.6 141 121 265.6 259.6 256.1 253.6 148 127 274.6 268.6 265.1 262.6 155 133 283.6 277.6 274.1 271.6 162 139 292.6 286.6 283.1 280.6 169 145 301.6 295.6 292.1 289.6 176 151 310.6 304.6 301.1 298.6 183 157 319.6 313.6 310.1 307.6 190 163 328.6 322.6 319.1 316.6 
21st June 2013, 03:19 AM  #2  
diyAudio Member
Join Date: Nov 2009
Location: Cape Town

You'd get the same SPL with 1/10th of the power if you used a sub with 95.6dB sensitivity. See below.
Quote:
Yes, that's right. e.g. At 10m, there's a 20dB reduction. At 2m, the reduction is about 6dB. Quote:
A 10dB increase requires 10 times the power. A 3dB increase corresponds to approx double the power. The formula is: dB = (dB @ 1 Watt) + 10 * log(power in Watts) If you put that together with the other formula, you find something useful: For a given SPL, the power required is proportional to the square of the distance. e.g. At 4 times the distance you need 16 times the power, for the same SPL. Sorry, no idea what that's about. 

21st June 2013, 03:42 AM  #3  
diyAudio Member
Join Date: Jun 2013

Quote:
Sorry I have never been able to post tables in forums... it always fails I'll need to recalculate it anyway. Thank you. for the info [TD]Input Power[/TD][TD]Output Power @ 86% eff [/TD][TD]db (@source)[/TD][TD]@2m[/TD][TD]@3m[/TD][TD]@4m[/TD] [/TR] [TR] [TD]1[/TD][TD]1[/TD][TD]85.6[/TD][TD]79.6[/TD][TD]76.1[/TD][TD]73.6[/TD] [/TR] 

21st June 2013, 05:53 AM  #4 
diyAudio Member
Join Date: Jun 2013

Oops I mistook double for +2

21st June 2013, 06:23 AM  #5 
diyAudio Member
Join Date: Jun 2013

Thanks I have corrected, it's clearly unfortunate that my sub has such a low SPL.
I've attached the calc table as a text file; I simply can't get the table function to work correctly. It's pretty simple, input power (drain), output power (less efficiency), current, db @ source, DB at distance in meters (2m, 3m, 4m, 5m). I thought it may be of interest to others. 
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