64 ANALOGIES 



Therefore, the current transmission will decrease with increase in fre- 

 quency as shown by the characteristic of Fig. 4.5//. 



The reactance of the compliance of the mechanical system, Fig. 4.5F, 

 is inversely proportional to the frequency. Therefore, at low frequencies 

 the compliance will remain comparatively stationary and the behavior 

 will be the same as a directly coupled system. At high frequencies the 

 velocity (motion) of the compliance will be the same as the input velocity 

 and there will be very little velocity transmitted to the load. The velocity 

 transmission characteristic of this system is shown in Fig. 4.5/7. 



The acoustic system, Fig, 4.5G, consists of a pipe with an enlarged por- 

 tion forming an acoustic capacitance. At low frequencies the reactance 

 of the acoustic capacitance is large compared to the impedance of the pipe 

 and the sound flows down the pipe the same as it would in the absence of 

 the enlargement. At high frequencies the reactance of the acoustic capaci- 

 tance is small compared to the impedance of the pipe and the sound is 

 shunted out by the enlargement. Since the reactance is inversely propor- 

 tional to the frequency, the volume current transmission will decrease with 

 frequency as shown by the characteristic of Fig, 4.5//. 



D. Inductance and Capacitance in Series^ in Shunt with a Line and the 

 Mechanical and Acoustical Equivalents. — Figure 4.5/ shows an inductance 

 and capacitance connected in series across a line. The mechanical and 

 acoustical equivalents are shown in Figs. 4.5/ and 4.5K. At low frequen- 

 cies the three systems behave the same as Figs. 4.5E, 4.5F and 4.5G and 

 there is very little attenuation. At high frequencies the systems behave 

 the same as Figs. 4.5^, 4.55 and 4.5C and there is very little attenuation. 

 At the resonant frequency of the inductance and the capacitance the im- 

 pedance is zero. Therefore, there is no current transmission at this fre- 

 quency. At the resonant frequency of the mass and compliance. Fig. 4. 5/, 

 there is no velocity transmitted because the impedance of the resonant 

 system is zero. At the resonant frequency of the Helmholtz resonator 

 forming the branch of the pipe line in the acoustical system of Fig, 4.5Ky 

 there is no volume current transmission because the " incident " volume 

 current " pumps in and out " of the resonator. The transmission char- 

 acteristics of the three systems of Figs. 4.5/, 4.5/ and 4.5K are shown in 

 Fig. 4.5/:. 



E. Inductance and Capacitance in Parallel, in Shunt with a Line and the 

 Mechanical and Acoustical Equivalents . — Figure 4.5M shows an induc- 

 tance and capacitance connected in parallel across a line. The mechanical 

 and acoustical equivalents are shown in Figs. 4.5A^ and 4.50. At low fre- 

 quencies the systems behave the same as Figs. 4.5^^, 4.55 and 4.5C and 



