X. ULTRASONIC VIBRATIONS .'U 1 



6. Absorption and Scattering 



Wlienever a sound wave traverses a medium, there is naturally 

 some loss of energy to the particles of the medium. While these 

 losses may be separated into various types, it will suffice here to con- 

 sider all losses together. These losses will generally appear as heat 

 and raise the temperature of the medium. 



In all cases, the sound intensity, 7o, of a plane sound wave de- 

 creases in a liquid by passage over a distance d to the value 



I = he-'"'^ (11) 



where a is the over-all amplitude absorption coefficient of the me- 

 dium. Theory has shown that the absorption coefficient varies di- 

 rectly as the square of the frequency. Wliile some deviations from 

 this law have been found, it is the general practice to list the value of 

 a/P that is more a characteristic of the material than a. A list of 

 values of oc/P for some common materials is shown in Table II. 

 These values may be assumed to hold approximately over a fairly 

 large range of frequencies. The absorption coefficients of many more 

 materials and mixtures have been investigated and listed b}'^ Willard 

 (23). 



TABLE II 

 Sound Amplitude Absorption Coefficients of Various Liquids 



' (.a/P) X 10» 



Material cm. "'sec* 



Carbon disulfide 74 



Glycerol 26 



Benzene 8.3 



Carbon tetrachloride 5.7 



Chloroform 3.8 



Kerosene 1.1 



Toluol 0.9 



Acetone . 64 



Water (distilled) 0.33 



To calculate the distance over which half the energj'' is lost, we 

 merely place I = 3^/o and then 2adi/^ = In 2 = 0.693 or: 



d,/. = 0.693/2« = 0.347/a 



In the case of benzene at 950 kilocycles, for example, a/P = 8.3 X 

 10~^^ a = 0.0075 cm.~' and so d./, = 46 cm. In other words, the 



