STATIONARY WAVES 



13 



D. Ratio of the Absolute Magnitudes of the Particle Velocity and the Pres- 

 sure in a Spherical Sound Wave. — From equations 1.40 and 1.43 the ratio 

 of the absolute value of the particle velocity to the absolute value of the 

 pressure is given by 



Ratio = 



Vl + /^V 



pckr 



1.45 



The ratio in equation 1.45, for various distances from the center in a 

 spherical wave system, as a function of the frequency is plotted in Fig, 1.3. 



5 6 r 89|q2 5 3 4 5 6 7 89|q3 



FREQUENCY IN CYCLES PER SECOND 



'lO* 



Fig. 1.3. Ratio of the absolute magnitude of the particle velocity to the pressure in a spherical 

 sound wave for distances off, |, 1, 2 and 5 feet from the source. (Courtesy of The Blakiston 

 Company from Olson and Massa, Applied Acoustics.) 



1.6. Stationary Waves. — Stationary waves are the wave system re- 

 sulting from the interference of waves of the same frequencies and are 

 characterized by the existence of nodes or partial nodes. 



Consider two plane waves of equal amplitude traveling in opposite direc- 

 tions; the velocity potential may be expressed as 



= [cos k{ct — x) + cos k{ct -\- x)] 1.46 



The pressure in this wave system from equations 1.19 and 1.21 is 



p = ~ P Yf ^ ^^'^^ ^^'" ^^^^ — x) + sin k(ct + x)] 1.47 



p = IkcpA [sin kct cos kx] 1 .48 



