302 EARLE C. GREGG, JR. 



range. While these new effects are due primarily to the higher fre- 

 quencies (or smaller wavelengths), many — particularly the biologi- 

 cal, metallurgical, and chemical actions — have become evident only 

 because of the relative ease of producing extremely large amplitudes 

 of sound at those frequencies. While the wavelength undoubtedly 

 plays a role in biological reactions, a direct correlation has not yet 

 been established, and the mass of evidence today indicates that one of 

 the most important parameters is the sound intensity. 



1. Frequency, Wavelength, and Amplitude 



Whenever a sound wave travels through a given medium, the 

 individual particles of the medium, in the simplest case, execute 

 simple harmonic motion. That is, each particle vibrates back and 

 forth in a manner similar to a mass on a spring. If the direction of 

 vibration of the particles is in the direction of propagation of the 

 sound, the vibration is said to be longitudinal. If at right angles to 

 the direction of propagation, the vibration is transverse. Liquids and 

 gases can support only longitudinal vibrations while solids may sup- 

 port both. If the motion is simple harmonic, the maximum dis- 

 placement of each particle from its rest position is called the amplitude 

 and the number of total excursions per second is known as the fre- 

 quency. 



For simple harmonic motion, the time dependence of the particle 

 displacement is said to be sinusoidal and may be represented mathe- 

 matically as : 



X = A sin (27r/0 (1) 



where A is the amplitude or maximum displacement, / the frequency, 

 t the time at which the particle is observed after having passed through 

 a rest position, and x the displacement of the particle from its rest 

 position. The usual units are time in seconds, frequency in cycles 

 per second, and amplitude in centimeters. From the above, it also 

 follows that the particle velocity and acceleration are: 



V = 2TrfA cos (27r/0 (2) 



a = -iTT^fA sin (27r/0 (3) 



In the discussion above, consideration was given only to the mo- 

 tion of each individual particle referred to its rest position. When a 

 sound wave traverses a medium, each particle affects the others so 



