CHAPTER VIII 



SIMPLE-HARMONIC WAVES. DIFFRACTION 



76. Spherical Waves. Point-Sources of Sound. 



From this point it is convenient to consider specially the 

 case of simple-harmonic vibrations. In problems relating to 

 the impact of sound waves on obstacles, or their transmission 

 by apertures in a screen, and so on, the results will vary in 

 character with the pitch, the determining element being the 

 relation between the wave-length and the linear dimensions of 

 the obstacles, &c. 



It will be desirable, for the sake of conciseness, to use 

 imaginary quantities somewhat more freely than in the pre- 

 ceding chapters. Thus we assume that the velocity-potential 

 < varies as e int , or e ikct , where 



..................... (1) 



if X be the wave-length of plane waves of the same period 2?r/n. 

 The general equation of sound waves ( 70 (4)) therefore be- 

 comes 



Vty + Afy = ...................... (2) 



In the case of plane waves whose fronts are perpendicular 

 to the axis of x, we have 



+"*-<> ..................... < 3 > 



the solution of which may be written 



<f> = Ae- ikx + Be ikx , ..................... (4) 



or <f> = C cos kx + D sin kx, ............... (5) 



