DECIBEL SCALE 291 



of some germs which has multiplied itself 100,000 times. We may say 

 that its mass has increased in the ratio of 100,000 to 1 or 100,000 times. 

 Instead of expressing this ratio increase in such large numbers, we will 

 apply the decibel system of notation. The " germ gain " can be 

 expressed as follows: 



._ . , Total germs at the finish 



Germ gain = logi — — : : 



Total germs at the start 



/100,000\ 

 = log 10 I - — ) 



= 5 



In this notation we say that we have a germ gain of 5 bels or 50 db above 

 total germs at the start instead of a 100,000 ratio gain. 



If the group of germs continues to increase until a quantity 1,000,000 

 has been reached, the germ gain in decibels is 10 X log (1,000,000) = 60 

 db. Thus, the mass of germs has increased 900,000 units, while in the 

 decibel notation it has increased from 50 db above threshold to 60 db 

 above threshold, or a 10-db germ gain. In other words, as the level of 

 the germ mass rises, the additional germs needed to effect equal germ 

 gain increase is not the same, and an increasingly greater quantity of 

 germs is required to cause an equal germ gain increase. 



The American Standards Association [1936] adopted 10~ 16 watt/cm 2 

 as representing the lowest intensity that a 1000-cycle sound may have 

 and yet be just audible by a normal ear. This value is used as a stand- 

 ard reference level of acoustic power. 



If the intensity of an acoustic disturbance of 1000-cycle frequency 

 (Fig. VII-6) increases from 10 -12 watt/cm 2 to 10 -6 watt/cm 2 above 

 threshold, then in the decibel notation it has increased from an intensity 

 level of 40 db above threshold to an intensity level of 100 db above 

 threshold, or an intensity gain of 60 db has taken place. 



If the acoustic waves presented to the ear had a 100-cycle frequency, 

 the examination of Fig. VII-19 would reveal that the above intensity 

 gain would have carried the tone from threshold to the 97-db intensity 

 level. 



The decibel notation uses the average speech power as the zero decibel 

 level. The level of very loud speech would then be designated as +20 

 db, of weak speech as —20 db, and of a just audible whisper as —40 db 

 from this average speech power level. The speech power gain from a 

 whisper to very loud speech is therefore about 60 db. 



A change in power level of a sound by 1 db is approximately the small- 

 est that the ear can detect. This is known as the " sensation unit." 



