PHYSICAL CHARACTERISTICS OF SPEECH AND MUSIC 359 



Acoustical Power of Speech Waves 



Keeping this picture before us, as to the physical composition of 

 speech, and its kinematic nature, let us now consider some statistical 

 averages. If ten different persons spoke the sentence discussed above, 

 there would be a considerable range of differences in the frequencies 

 and intensities used to transmit it through the air. To get a typical 

 cross-section of American speech, it would require at least 100 such 

 sentences pronounced by at least 5 men and 5 women. This would 

 involve the analysis of 18,000 fundamental sounds besides the transi- 

 tions between them. Also, as was seen from the oscillograms given 

 above, the wave form changes even where it is ideally supposed to 

 be constant so that three or four sample waves from each steady 

 state condition should be analyzed to find the components in each 

 sound. Thus, we have the problem of recording and analyzing about 

 70,000 such waves. To analyze such a wave by the usual academic 

 methods, namely, to plot the wave to a definite scale and then analyze 

 it into its components by means of a Henrici or similar analyzer, would 

 require at least two or three hours. So such a job for analyzing only 

 the steady-state part of speech would require about 210,000 hours, or 

 100 years working seven hours a day for 300 days per year. In other 

 words, such a method of attacking the problem is altogether too slow. 

 To find the average intensities and frequencies involved in con- 

 versational speech, much more powerful methods for obtaining 

 statistical averages were adopted. 



There is a to and fro movement of the air particles simultaneously 

 with the alteration of the air pressure. When the source is so far 

 away that the disturbance can be considered as a plane wave, then 

 the following relations exist between the pressure p, the displacement 

 y, the velocity v, and the acceleration a of a layer of air particles, and 



the frequency of vibration — , namely, 



yco 



voi = a, (2) 



p = rv, (3) 



where r is the radiation resistance of the air and is given by the product 

 of the air density by the velocity propagation of the wave. The 

 intensity / of the sound at any point is the power passing through a 

 square centimeter of the wave front and is given by 



7=^- (4) 



r 



