Decibel

Small page dedicated to this issue as most people are not used to it and it is widely use in audio .
Why do we need the dB , because the ear is extremely sensitive and in audio we relate to our ears .
Oure hearing has a range from 0 to 125 dB , below 40 dB its bearily audible and above 105dB it gets painfull , and above 115 dB (sustained period ) there is permant damage done .

2 different dB calculations :

voltage comparisons and power comparisons , don't mix them up they are different

voltage :

formula : difference in dB = 20 LOG U1/U2

example :

my amplifier has a test tone of 1KHz 1V RMS fed to it and i measure at the output 20V RMS
since I want to test its bandwith I increase frequency to 20 KHz and I remeasure voltage at the output (I keep same input voltage ) and lets say I measure 10V RMS

so how many dB have I lost : 20 LOG 20/10 = 6 dB

Power wise :

Amp delivers to an 8 ohm load 50 watts , I change the load and I get 100 watts

Difference = 10 LOG 100/50 = 3dB increase in power

Small Table for easy comparisons

dB	Voltage U1/U2	Power P1/P2

0	1	1
3	1,41	2
6	2	4
9	2,82	7,95
12	4	15,8
15	5,62	31,6
20	10	100
30	31,6	1000

Practical use :

You want to buy speakers , and you are aware about sensitivity issues , and you wonder if the speakers will work powerwise with you're amp ? I'll make a few assumptions that I think apply to almost all : max listening volume 102dB this is very loud and has ample margin for the high end listener .

Where you to buy an electrostatic speaker 82dB/w/m you would need 20dB of amplification or 100watts at least
If you buy 90dB/w/m direct radiating dynamic speakers you need about 12dB or 15,8 watts of power
And a 93dB/w/m would just require 7,95 watts of power .