CORRECTIVE NETWORKS 65 



the transmission is small. At high frequencies the systems behave the 

 same as Figs. 4.5E, 4.SF and 4.5G and the transmission is again small. 

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

 ance is infinite. Therefore, the shunt circuit introduces no attenuation 

 at this frequency. At the resonant frequency of the mass and compliance 

 of Fig. 4.SN the input to the spring does not move. Therefore, the sys- 

 tem transmits the same as a directly coupled system. At the resonant 

 frequency of the Helmholtz resonator, Fig. 4.50, there is no volume cur- 

 rent flowing into the resonator from the line because the input acoustic 

 impedance is infinite. Therefore, the sound is transmitted down the pipe 

 the same as in the absence of the resonator. The transmission charac- 

 teristic of the three systems of Figs. 4.5M, 4.5N and 4.50 is shown in 

 Fig. 4.5P. 



F. Inductance in Series with a Line and the Mechanical and Acoustical 

 Equivalents. — In Fig. 4.6A an inductance is connected in series with a 

 line. If the impedance of the inductance is small compared to the input 

 and output impedances the attenuation introduced by the inductance will 

 be small. If the impedance of the inductance is large compared to the 

 input and output impedances the current transmission will be small. Since 

 the impedance of an inductance is proportional to the frequency the trans- 

 mission will decrease with frequency as shown in Fig. 4.6D. 



In the mechanical system of Fig. 4.65, if the mass reactance is small 

 compared to the load or driving impedance, the addition of the mass will 

 cause very little reduction in the velocity transmitted to the load. If the 

 mass reactance is comparatively large the mass will remain practically 

 stationary and the velocity transmitted to the load will be small. Since 

 the mechanical impedance of a mass is proportional to the frequency, the 

 velocity transmission will decrease with frequency as shown by the char- 

 acteristic of Fig. 4.6D. 



The acoustical system of Fig. 4.6C consists of a pipe with a constriction 

 which forms an inertance M. At low frequencies the reactance of the 

 inertance is small compared to the impedance of the pipe and the inertance 

 introduces very little attenuation. At high frequencies where the react- 

 ance of the inertance becomes large compared to the impedance of the 

 pipe, the volume current transmission through the inertance will be small. 

 Since the acoustic impedance of an inertance is proportional to the fre- 

 quency, the volume current transmission will decrease with frequency as 

 shown by the characteristic of Fig. 4.6D. 



G. Capacitance in Series with a Line and the Mechanical and Acoustical 

 Equivalents. — In Fig. 4.6E a capacitance is connected in series with a line. 



