Loudness is measured in decibels (dB), which is calculated using a logarithmic formula comparing sound intensity (I) to a reference intensity (Io). If intensity doubles Io, it is 3 dB higher; if intensity is 100 times Io, it is 20 dB higher. A sound that is 50 dB higher than the reference has an intensity 100,000 times greater than Io.

1. Decibels
Loudness is measured in decibels and calculated by means of the formula
o
I
Db 10log
I
 
=  ÷
 
, where “I” stands for sound intensity and “ Io” for the arbitrary
reference taken as hearing threshold.
Examples:
→If I = Io then o
o o
II
10·log 10·log 10·log1 10·0 0db
I I
   
= = = = ÷  ÷
   
→If I = 2Io then o
o o
2II
10·log 10·log 10·log2 10·0'3 3db
I I
   
= = = ÷  ÷
   
;
That is to say, should intensity double the reference level then it is 3 db higher.
→If I = 100Io then o
o o
100II
10·log 10·log 10·log100 10·2 20db
I I
   
= = = = ÷  ÷
   
Should intensity be a hundred times greater then it is 20 db higher.
→
o
o
x·I 50
50db 10·log 10·logx logx logx 5
I 10
 
= = ⇒ = ⇒ = ÷
 
⇒ x = 105
= 100000
50 db means that sound intensity is one hundred thousand times greater than
reference.