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24th May 2012, 03:28 PM  #1 
diyAudio Member
Join Date: Apr 2010
Location: Brisbane

3 dB
Like to start this thread to take away a lot of misassumptions about Voltages , Watts and the coupling of those lovely things to our human ears .
I read this forum almost daily and I’m still surprised ( but understanding ) members asking questions , that would be all “answered” under our human ear “3dB” rule . I can explain this Logarithmic stuff , but there must be a teacher out here on this forum that will do much better than me ! so come one , please explain the 10log and 20log stuff ! Cheers , Rens
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25th May 2012, 11:54 AM  #2 
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Join Date: May 2007

I'm not sure what you mean by the human ear "3dB rule".
Decibels are a way of describing ratios. Because adding and subtracting are easier for humans to do than multiplying and dividing, we make use of the properties of logarithms (which are the inverse of exponentials). The maths is taught in a high school near you. The Bel is simply the base10 log of a ratio. It was found to be inconveniently high a measure, so instead we use a tenth of a Bel  a decibel. To get a ratio in dB you take the log and multiply by 10. In electronics we are mainly interested in power ratios, so take the base10 log of the power ratio and multiply by 10. The result is the power ratio expressed in dB. Power goes like voltage squared. To square a number you double its log, so to get a power ratio in dB from a voltage ratio (e.g. a voltage gain) you take the base10 log of the voltage ratio and multiply by 20. This is only strictly correct if the same impedance is used, but there is a convention in electronics that when we are only interested in voltage gain we use dB anyway and ignore the impedance difference. So 6dB could mean a strict power ratio of 4, or it could mean a voltage ratio of 2. The context should make it clear which is meant. In the case of equal impedance the two ideas are the same. I don't know if this deals with your question, but it is an area where people seem to get confused and sometimes confidently assert wrong ideas which they have picked up. 
25th May 2012, 11:58 AM  #3 
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Join Date: May 2002
Location: The great city of Turnhout, BE

I had a column in one of the previous diyaudio newsletters explaining all this in somewhat more detail.
In case you missed it, it should still be on teh forum. Not sure what the '3dB ear rule' is  never heard of it. 3dB of course simply being the point where the voltage level has decreased by 3dB to 0.707 times the starting value. Is that what you mean? jan didden
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25th May 2012, 12:02 PM  #4 
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Join Date: Mar 2002

I think the ' rule ' is that 3db is the minimum audible
change in level.
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25th May 2012, 01:47 PM  #5 
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Join Date: May 2002
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That's not correct. There are documented tests that fractional dB differences are audible.
What may be meant is that 3dB difference is perceived as doubling of sound level (not sure it actually is though). Probably need to look up on the FletcherMunson or similar graph. jan
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25th May 2012, 02:01 PM  #6 
Did it Himself
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10dB is percieved as doubling of sound level.
3dB being the most commonly noticeable change is something I have heard said before. It's kind of a good step.
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25th May 2012, 03:08 PM  #7 
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Join Date: May 2007

3dB is half power, but I'm not sure what that has to do with ears.

25th May 2012, 03:27 PM  #8 
diyAudio Member
Join Date: Feb 2008

Phon curves are a better way to describe perceived sound level. 10 phon is a doubling, meaning from 10 to 20 there is a doubling, and from 70 to 80 ... and so on.
As it happens, 10 phon is 10 db @ 1 kHz. But not necessarily 10 dB at other frequencies.... Equalloudness contour  Wikipedia, the free encyclopedia
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25th May 2012, 10:02 PM  #9  
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Join Date: Mar 2002

Quote:
3db is 'measureable' as doubling of level, but is the (commonly) least perceptable change. Hence the logarithmic scale used.
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25th May 2012, 10:07 PM  #10 
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Join Date: Feb 2008

Wrong. Its easy to hear much smaller changes in level than 3 dB.
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