18 



Sound and the Ear /I : 3 



change of pitch is noticed. These difference limens for frequency 

 change are not independent of the sound pressure level. As the latter 

 is lowered, the size of the difference limen for frequency changes increases. 

 The presence of these finite steps, dignified by the term difference 

 limens, resembles the phenomena well known in many phases of 

 chemistry and physics, usually grouped under the classification quantum 



20cps 



lOOcps 



.Okc 

 Frequency 



Figure. 7. Equal loudness contours after the American Stand- 

 ards Association (1936). There is no general agreement on 

 the exact shape of these curves, but the general flattening at 

 higher sound pressure levels is always observed. After J. C. R. 

 Licklider, in Handbook of Experimental Psychology, S. S. Stevens, 

 ed. (New York: John Wiley & Sons, Inc., 1951). 



mechanics. Similarly, pure tone thresholds measured on individuals at 

 very low frequencies suggest some type of quantum effect. Quantum 

 effects do occur in acoustics, but the physical quanta of sound energy, 

 known as phonons, are far too small to associate them in any way with 

 hearing. Just as does the photon, the phonon has an energy, E, such that 



E = hv 



where h is Planck's constant and v is the frequency. A straightforward 

 calculation will show the reader that, even at the threshold of hearing, 

 a huge number of phonons must be reaching the ear each second, or 

 even each cycle. This number is so large that the phonon cannot be 

 responsible for the quantization observed in hearing studies. 



The hearing tests described in this section give no direct clues to the 



