72 



ANALOGIES 



Equations 4.66, 4.67, 4.68, 4.69, 4.70 and 4.71 show that the systems of 

 Fig. 4.9 are low pass filters transmitting currents, velocities or volume 

 currents of all frequencies lying between and the cutoff frequency /c 

 where /c = coc/Itt. 



E. High Pass Wave Filters. — Electrical, mechanical and acoustical high 

 pass wave filters are shown in Fig. 4.10. 



The impedance of the series arm in the three systems 



1 



Z£l 



\__ 



Zmi — ■ ^ 

 1 



Zai 



Jo:Ca 



4.72 

 4.73 

 4.74 



HI 



Ih 



s 



ELECTRICAL 







MECHANICAL 







ACOUSTICAL 



Fig. 4.10. High pass wave filters. (Courtesy of The Blakiston Company from Olson and 



Massa, " Applied Acoustics.") 



The impedance of the shunt arm in the three systems is 



Zm2 = j<jiin 



ZA2 = JOJM 



The limiting frequencies are given by 



— = and — = — 4 



Z2 22 



From the constants of the system, 



ZiE 1 



4.75 

 4.76 

 4.77 



Z2E 

 ZlM 

 ZiM 



LCe^c 



1 



mCu^c 



= 0, when coc = <» 

 = 0, when coc = oo 



4.78 



4.79 



