304 EARLE C. GREGG, JR. 



wavelengths in liquids (V ~ 1200 m./sec.) range from 6 to 0.0012 cm. 

 and in solids (7 ~ 4000 m./sec.) from 20 to 0.004 cm. 



It is important to remember that the velocity of propagation is 

 a physical constant of the medium while the wavelength and fre- 

 quency are not. For example, if a sound wave travels from one 

 medium with a given velocity and to a second medium with another, 

 only the wavelength will change, since the frequency is determined by 

 the sound source and the velocity by the physical constants of the 

 media. Other phenomena, such as reflection, occur at boundaries 

 between media but these will be treated later. Table I contains a 

 list of commonly used materials and their velocities of propagation. 

 More complete lists are in Bergmann (2) and Hiedemann (3a). 



2. Pressure 



Since a sound wave in a medium consists of the individual parti- 

 cles in a regular, defined motion, it is possible to treat the wave as an 

 alternating pressure phenomenon rather than a particle displacement 

 as long as the physical constants of the medium are taken into ac- 

 count. By comparison with simple harmonic motion, we may say 

 that the sound pressure variation with time at any point in a medium 

 is: 



p = Psin (2x/0 (4) 



where p is the instantaneous pressure at any time, t, and P is the 

 pressure amplitude or maximum pressure obtained at a given point. 

 This pressure variation may be either positive or negative, so that 

 in a given medium two points one-half wavelength apart have a pres- 

 sure differential of twice the maximum pressure. It is the large 

 pressure and pressure differentials that account for many biological 

 and chemical actions of ultrasound. 



To convert particle displacement into pressure amplitude re- 

 quires a knowledge not only of the physical constants of the medium, 

 but also of the type of sound wave present. 



3. Types of Sound Waves 



In general, if a vibrating piston is a source of sound in a medium, 

 the character of the sound wave is determined by the ratio of the 

 wavelength of the sound in the medium to the dimensions of the 

 piston (3, p. 108; 1, p. 147). If the wavelength is very large com- 



