54 MATTER WAVES: SOUND AND ULTRASOUND 



high frequencies for soft tissue and even at low frequencies for dense tissue 

 such as bone. Truly elastic tissues simply reflect incident matter waves. 



The absorption coefficient for molecular absorption (k) is well known for 

 air and water: 



3vp 



-> c _p °v jc 



^ P ^ V 



where /is the frequency (cps) of the impinging wave, v the velocity (cm/sec), 

 p the density (g/cm 3 ), rj the viscosity (dyne sec/cm 2 ), A" 7 the heat conductiv- 

 ity (cal/sec deg cm), and the c's are the specific heats (cal/deg g) at constant 

 pressure, P, and constant volume, V. Hence the energy absorbed per centi- 

 meter of penetration of the impinging wave increases linearly with the vis- 

 cosity or "stickiness" of the medium and with its thermal conductivity; in- 

 creases very rapidly with increasing frequency; but decreases with increas- 

 ing density. 



For water, which is a sufficiently good approximation to soft tissue for 

 present purposes, k/f 2 = 8.5 x 10" 17 sec 2 /cm. For air the value is 1000 

 times higher, because although rj is 50 times smaller for air than for water, 

 v is 4^2 times smaller and p is 1000 times smaller. For liquids only the first 

 term (the frictional or viscous one) is important; for gases both are im- 

 portant. Therefore it is useful to aerate a tissue before sonic therapy is ap- 

 plied, because absorption is higher. 



Since reflection increases with increasing frequency, the method of appli- 

 cation is important. In the absence of reflection, the above expressions 

 describe the situation well. Direct application of the vibrator to the tissue 

 assures this. However, if the sound is beamed through air, the situation is 

 quite different: reflection occurs. 



Quantitative studies on tissues are only recent. The general rule which 

 has emerged is as follows: Beamed through air, sound of high frequency suf- 

 fers little absorption, and little damage results. The depth of penetration 

 increases with increasing frequency. Most (>95 per cent) of the incident 

 energy passes right through, or is reflected. Some of Von Gierke's figures 

 (1950) are: 5 to 6 per cent absorbed at 100 cps; 0.2 to 4 per cent absorbed 

 at 1000 cps; and <0.4 per cent absorbed at 10 kc. Beamed through liquid 

 or solid, ultrasonic radiation is easily controlled and its absorption pre- 

 dicted. More will be said about this later, in the section on therapy. 



SENSITIVITY OF A DETECTOR, AND THE WEBER-FECHNER LAW 



It is a fact that whether or not a receiver will detect a signal depends upon 

 how much the signal differs from the background noise. The dependence is 



