Acoustic Wave Filters: Attenuation and Phase Factors

Acoustic wave filters; attenuation and phase factors.---Theoretical discussion, The ratio of the rate of volume displacements in successive sections eY is equal to e^-αe^-iφ where α is the attenuation constant and φ the decrease in phase from section to section. If Z₁ and Z₂ are the impedances in the conduit and branch respectively, it is shown that in the region of no attenuation, cosφ=1+1/2Z₁Z₂ and φ changes from 0 to π, while in the attenuated region φ is either 0 or π and coshα=|(1+1/2Z₁Z₂)|, becoming infinite for the natural frequency of the side branch while φ passes discontinuously from 0 to π or π to 0. Experimental values of phase change φ. Sound from various points along the filter was transmitted to one ear and the relative phase was determined from the apparent direction of the phantom source. For a low-pass filter the values of the total change per section agree well with the theory except that the change occurs gradually instead of suddenly, but agreement was not found in the cases of the other two types.