REFRACTION AND DIFFRACTION 17 



velocity in the direction in which the sound is traveling. Making this 

 substitution in 1.58 the result is 



/o = °4^^^^V. 1.59 



V -\- W — Vs 



Equation 1.59 shows that the wind does not produce any change in pitch 

 unless there is some relative motion of the sound source and the observer. 



1.11. Refraction and Diffraction. — The change in direction of propa- 

 gation of sound, produced by a change in the nature of the medium which 

 affects the velocity, is termed refraction. Sound is refracted when the 



COOL AIR - LOW VELOCITY , WARM AIR - HIGH VELOCITY 



WAVE FRONTS, 



WAVE FRONTS" 

 HIGH VELOCITY COOL AIR - LOW VELOCITY 



SURFACE OF THE EARTH SURFACE OF THE EARTH 



Fig. 1.4. The refraction of a sound wave in air. 



density varies over the wave front. (See equation 1.15.) A sound wave 

 may be bent either downward or upward depending upon the relative 

 temperatures (densities) of the air,^ Fig. 1.4. The distance over which 

 sound may be heard is greater when the wave is bent downward than 

 when it is bent upward. The first condition usually obtains during the 

 early morning hours while the latter condition prevails during the day. 

 Diffraction is the change in direction of propagation of sound due to 

 the passage of sound around an obstacle. It is well known that sound 

 will travel around an obstacle. The larger the ratio of the wavelength 

 to the dimensions of the obstacle the greater the diffraction. The dif- 

 fraction around the head is important in both speaking and listening. 

 The diffraction of sound by microphones and loud speakers is important 

 in the performance of these instruments. The diffraction ^ of sound by a 

 sphere, a cube and a cylinder as a^ function of the dimensions is shown in 

 Fig. 1.5. These data may be used to predict the diffraction of sound by 

 objects of these general shapes. As, for example, the sphere may be used 

 to predict the diffraction of sound by the human head. 



^ For other phenomena of atmospheric acoustics such as the effects of wind and 

 temperature upon the propagation of sound waves and the applications to sound 

 ranging and signaling in air, see Stewart and Lindsay, "Acoustics," D. Van Nostrand 

 Co., New York City. 



2 MuUer, Black and Dunn, Jour. Acous. Soc. Amer., Vol. 10, No. 1, p. 6, 1938, 



