256 



AUDITORY BIOPHYSICS 



curve accurately you move to the right a distance X centimeters in T 

 seconds, or you move a proportional less distance x in t seconds, such 

 that 



x t 



X = T 

 Then 



x 



y = A sin 2-w - 

 y X 



would describe a wave motion in which X represents the displacement 

 equal to one wavelength. 



The radius of the reference circle has the same magnitude as the 

 amplitude A ; it is the maximum value that y attains in the wave motion. 

 It is also half the distance from crest to trough of the wave, or half the 

 perpendicular distance over which the particle m vibrates. 



Frequency 



The number of cycles or complete vibrations made by the vibrating 

 particle in 1 second is its frequency. 



1 



n = — 

 T 



where T is the period or time necessary for the particle P to move around 



the reference circle. 



The phase angle is the angular position of the particle on the reference 



circle with respect to its initial position measured from the x axis in 



a counterclockwise direction. In 

 Fig. VII-1, for example, the par- 

 ticle P 2 is out of phase with P 6 ; 

 its phase angle is 180°, i.e., P& is -n 

 radians out of phase with P 2 - In 

 a similar manner P3 is out of phase 

 with P7. Note their relative posi- 

 tions on the sine-wave curve. 



Longitudinal Waves 



When the line of vibration of 

 the particle is in the same direc- 

 tion the wave is traveling, the 

 result is what is called a longi- 

 tudinal wave. The oscillatory dis- 



Fig. VTI-2. Acoustic waves are leav- 

 ing the hole in the baffle board. Com- 

 pressions and rarefactions of the air are 

 shown as shaded and unshaded areas. 



