Math check?
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hdnrs
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

godfrey
diyAudio Member

Join Date: Nov 2009
Location: Cape Town
Quote:
 Originally Posted by hdnrs Sub SPL: (2.83v/1m): 85.6 db
You'd get the same SPL with 1/10th of the power if you used a sub with 95.6dB sensitivity. See below.

Quote:
 Originally Posted by hdnrs Input power (power draw @ battery) = output (amp) power / 86% -Output Power should be ~86% of the input power
Yes, that's right.

Quote:
 Originally Posted by hdnrs DB @ distance = (DB@source - (20 * log(distanceFromSource/1m)))
Yes, that's right.
e.g. At 10m, there's a 20dB reduction. At 2m, the reduction is about 6dB.

Quote:
 Originally Posted by hdnrs 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
No, totally wrong.
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.

Quote:
 Originally Posted by hdnrs Input Power Output Power db (@source) @2m @3m @4m (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 [snip]
Sorry, no idea what that's about.

hdnrs
diyAudio Member

Join Date: Jun 2013
Quote:
 Originally Posted by godfrey No, totally wrong. 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)
Thank you, looking back on my reference material, I see I mistook double for 2x.

Quote:
 Originally Posted by godfrey Sorry, no idea what that's about.
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, 04:53 AM #4 hdnrs   diyAudio Member   Join Date: Jun 2013 Oops I mistook double for +2
hdnrs
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.
Attached Files
 snd.txt (1.1 KB, 4 views)

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