MBASUEEMENT OF NOISE KAYE 



169 



THE DECIBEL 



We are now aware of the area of auditory sensations which we 

 have to mensurate, and we have to decide what is to be our " yard- 

 stick " or " degree." Our task is to try to correlate aural loudness 

 with physical intensity or energy; and already we have seen that 

 while the sensation of loudness advances, as it were, by simple addi- 

 tion, the energy level increases by leaps and bounds on a scale which 

 extends over almost astronomical magnitudes. This is a cumber- 

 some relation, and it is clear that there will be a real convenience in 

 adopting a scale of ratios of energy for our purpose. A similar need 

 which arose in telephone engineering was met by the introduction of 

 the " bel," a name chosen in honor of Alexander Graham Bell, the 

 inventor of the telephone. One " bel " expresses a tenfold increase 

 of power or energy ; in other words, two intensities in the ratio r : 1 

 differ by (log r) bels.* It has been generally agreed to adopt the 

 bel for acoustic requirements also, or rather the "decibel" (db.), 

 since the " bel " is a little too large for the purpose. We thus have 

 the following tabular relation : 



It will be realized that this scale of decibels is in no sense physio- 

 logical but is based wholly on intensity as measured by physical 

 methods. The scale has, however, the specific advantages — 



(1) Of being a rough fit with the aural scale of loudness sensation. 



(2) That experiment shows that the decibel, as above defined, cor- 

 responds approximately to the least perceptible change in loudness of 

 a sound of medium loudness under average conditions. In actual 

 fact the loudness step in question is sometimes a little more and 

 sometimes a little less than a decibel (ranging from 0.2 to 9 db.) 

 according to the frequency and the location in the auditory sensation 

 area. 



We are now in a position to set up a definition of the sensation 

 level of a pure note of specified frequenc}'' in physical terms. Our 

 " degree " will be the decibel, our " zero " the threshold of audi- 

 bility for that frequency, and the sensation level of a pure sound 



* Logarithms are to base 10. 



