11:4/ The Absorption of Electromagnetic and Ultrasonic Energy 213 



an electrically conducting cytoplasm surrounded by a poorly conducting, 

 lipid membrane with a high dielectric constant. These electrical data 

 are interesting as physical properties of the cells but have not yet been 

 related in detail to the differences between cells. 



4. Ultrasonics 



Mechanical vibratory energy has the same end effect on cells and tissues 

 as does the electromagnetic energy discussed in the previous section of 

 this chapter, namely it heats them. The rate of heating is comparatively 

 small for low frequency mechanical vibrations. The frequency range 

 used for most heating studies is above the audible; it is referred to as 

 ultrasonic. The absorption of ultrasonic energy is not inherently 

 different from that of energy at audible frequencies. Some authors 

 refer to nonauditory uses of acoustics as "sonics," but in this text the more 

 common name "ultrasonic" is used. 



Ultrasonic vibrations, then, are the sound waves whose frequency is 

 above the audible range. The properties and mathematical descrip- 

 tions of audible sound waves in air are discussed in Appendix A. There, 

 it is emphasized that in air, sound waves are compressional waves 

 characterized by a sound pressure (also called acoustic pressure) p and a 

 local particle velocity v. The acoustic pressure p and particle velocity v 

 are propagated throughout the medium with a characteristic wave 

 velocity c. During the propagation, the wave may also be attenuated. 

 The properties of the medium can be summarized in a quantity analogous 

 to the electrical impedance, called the characteristic impedance Z. It is 

 defined for plane waves as the ratio 



z = ? 



V 



The real part of this impedance R represents the propagation of un- 

 attenuated sound waves. The value of R is given by the product pc, 

 where p is the density medium and c the velocity of sound. The 

 imaginary part of Z represents attenuation, that is, the absorption per 

 unit length. For many purposes, it is convenient to describe a medium 

 in terms of the real part of the impedance pc and the attenuation factor. 

 This pair of numbers is completely equivalent to Z. The attenuation 

 factor is the ratio by which the pressure amplitude is decreased in 

 traveling one unit distance. Often, the log of this ratio is given, expressed, 

 for example, as decibels/cm. (For a definition of decibels, see Chapter 1 .) 

 Absorption of ultrasonic energy by biological cells and tissues is more 

 complicated than similar absorption in a gas. In a solid or liquid, 



