8 



Sound and the Ear /I : 2 



a physical system, and the phenomenon of resonance arises. This is 

 illustrated in Figures 3 and 4 for strings and organ pipes. Note that in 



each case a series of characteristic (eigen) 

 frequencies exists. Vibrations at these fre- 

 quencies are particularly easy to excite. The 

 lowest possible frequency is called the funda- 

 mental frequency or first harmonic. The next 

 highest frequency is called the first overtone. 

 If it is an integral multiple of the funda- 

 mental, it is called a harmonic. For example, 

 an overtone five times the fundamental is 

 the fifth harmonic. The standing wave 

 pattern in the outer ear is discussed further 

 in Section 4. 



It was noted above that the loudness of a 

 given pure tone is determined primarily by 

 the sound pressure amplitude. Often, 

 another physical term, intensity, is associated 

 with loudness. Intensity is the energy 

 transmitted across a unit area per unit time. 

 In practice, intensity is difficult to measure 

 and not too useful as a concept for studies of 

 hearing. For a plane wave, the intensity T 

 is related to the pressure by 



Time 



Figure 2. The dotted line 

 shows the average pressure P 

 and the solid line indicates 

 the absolute pressure P. The 

 difference between P and P 

 is the acoustic pressure p. 

 The maximum of p is A , the 

 acoustic pressure amplitude. 

 The figure is drawn for a pure 

 tone showing simple har- 

 monic dependence of p on 

 time. In general, the form of 

 p is more complex. An rms 

 value of/) can be specified but 

 not an amplitude for a com- 

 plex wave form. 



T = 



I 

 pc 



(4) 



where p is the root mean square (rms) 

 acoustic pressure, p is the density of the air, 

 and c is the wave velocity. For other wave 

 shapes, the expression is more complex 

 (although the term pc always appears). 

 The intensity for a given value of p varies 

 with the temperature, since pc also varies. 

 Loudness depends only on p, not on the 

 temperature. 



Instead of presenting data in terms of 



the rms sound pressure amplitudes, it is customary to use the sound 



pressure level L. This is defined by 



201og © 



db 



(5) 



