I : 2/ Sound and the Ear 7 



and the velocity of sound propagation c, the wavelength may be deter- 

 mined by the relationship 



X = - (2) 



The wavelength is important in discussing diffraction, a phenomenon 

 common to all wave-motion. Diffraction patterns are significant when 

 the wavelength is comparable to the object the sound wave encounters. 

 At shorter wavelengths, specular reflection and shadows are produced, 

 whereas at longer wavelengths, the wave is transmitted as though the 

 object were not there. 



In air, a low tone of frequency 35 cps has a wavelength of about 10 m, 

 which is comparable in size to a house. At the other end of the human 

 audible range, a frequency of 9 x 10 3 cps (9 kc) has a wavelength of 

 about 3 cm which is small compared to a person's head. Thus, the 

 lowest audible frequencies will be diffracted around a house; in other 

 words, the sound waves at these lowest frequencies will appear to bend 

 around most obstacles. This makes it difficult to localize the source of 

 the very low frequency tones below 100 cps. Conversely, the highest 

 audible frequencies will form sharp shadows around small objects; the 

 source of a 5-10 kc tone is easy to locate. At frequencies around 1 kc, 

 the wavelength is comparable to the head. The diffraction pattern 

 has the effect of increasing the amplitudes at the ear above those in the 

 incident wave. 



This increased amplitude makes the sounds near 1 kc seem extra 

 loud. 1 The loudness is not simply determined by the particle velocity v 

 or the displacement in the incident wave. Rather, the loudness is most 

 readily related to another physical characteristic, the sound pressure 

 amplitude. The latter and not the particle velocity or displacement is 

 actually measured in most acoustic experiments. The sound pressure p 

 is defined as the difference between the average (or equilibrium) pressure 

 P and the instantaneous total pressure, P; that is, 



P = P-Po (3) 



Diagrammatically, one may represent this as shown in Figure 2. The 

 acoustic pressure p is a scalar which will vary with both position and 

 time. 



Two waves of the same amplitude but traveling in opposite directions 

 give rise to what is known as a standing wave pattern. Under some con- 

 ditions, the wavelengths correspond to the characteristic dimensions of 



1 Other effects discussed later in the chapter also contribute to the increased 

 loudness of sounds at 1-3 kc. 



