472 



Comparative Animal Physiology 



tion, the resulting wave of motion will be found to be the algebraic summa- 

 tion of this fundamental and one or more of its multiples. The multiples of 

 the fundamental are referred to as "harmonics." In this manner improper 

 adjustment of the anatomical components of the ear (e.g., loose coupling 

 of middle ear bones; unequal tension on the ear drum or basilar membrane, 

 or any other elastic structure) could give rise to harmonics when the stimulus 

 consists of a pure tone. 



The intensity of sound waves is defined as the rate of flow of energy 

 through a unit area of the medium. Except for a few unusual conditions 

 (especially those in which standing waves occur), the energy of a sound 

 wave is proportional to the square of the root-mean-square value of the al- 

 ternating pressure. The human ear is responsive to a very wide range in 



PARTICLE DISPLACEMENT 



y = ,1 sin (o/ 



PARTICLE VELOCITY 



INSTANTANEOUS PRESSURE 



p = Aiaf'i sin (u>t + 90") 



TIME 



Fig. 153. Curves showing various aspects of plane progressive sound waves, together 

 with their equations, in which y=displacement; A=amplitude; w=angular velocity= 

 2 TT X frequency; trzitime; p,=velocity of particle; }9=alternating pressure; Po=;density 

 of air; c=:velocity of sound. From Stevens and Davis.^" 



the energy of stimulation, and for convenience in expression and in plotting 

 of data the scale used is logarithmic. A difference of one log unit (base 10) 

 in energy is called a bel, and a difference of one-tenth log unit a decibel. 



The decibel (abbreviated db) is thus defined as ten times the logarithm 

 of the ratio of two energies, but it can also be applied to two pressures, velo- 

 cities, currents, etc., which are related to energy by a square law. The number 

 of decibels in the ratio of two sound pressures thus become 20 times the loga- 

 rithm of the ratio. The number of decibels (N) relating two energies (E) 

 or two pressures (P) is therefore 



N = lOlogjEi^ 20 log P' 



On an energy scale a tenfold increase is 10 decibels, but on a pressure scale 

 a tenfold increase is 20 decibels. 



The ear can withstand a sound which has a million million times as much 



