6 Sound and the Ear /I : 2 



This is known as a Fourier representation. In many cases, only a finite 

 or a discrete set of frequencies is necessary; then, we refer to the repre- 

 sentation as a Fourier series. Speech and the character of musical 

 instruments are determined by the frequencies present and their relative 

 amplitudes. In the most general case, the sound is represented by an 

 amplitude distribution which is a continuous function of frequency. 

 This amplitude function is called a Fourier transform. The amplitude 

 distribution for a sound "ee" is shown in Figure 1. 



/ 



\ * *•«=■>* * 7 — X 7 — 



_i L v i \ 1 \ *= — \- 



e 



C3 Co 



, C to 



^£ 



C <*- 



3 ° 



i5 





0.2 



0.5 1.0 



Frequency 



(b) 



2.0 



5.0 



10 kc 



Figure I. (a) Fourier Series. The complex wave form labeled 

 "sum" can be formed by adding relative amounts of four pure 

 tones shown, (b) Fourier transform (or spectrum). The 

 spectrum of the sound "ee" has the general form shown. The 

 Fourier transform is a complex number; only its absolute value 

 is shown. 



A term closely related to frequency is wavelength, A. This is the 

 distance between the two nearest wavefronts with the same displacement 

 and particle velocity in a plane sound field. If one knows the frequency 



