The Analogous Acoustical Impedance for Discontinuities and Constrictions of Circular Cross Section

The impedance introduced by an abrupt change of circular cross section of a tube has been examined. It is shown that in the case of an ideal viscousless fluid the effect of the discontinuity is to introduce an inductance in series with the acoustical transmission system. The discontinuity inductance has been determined as a function of the ratio of the tube radii and has been plotted for different values of this ratio. The problem of a small tube or constriction inserted between two larger tubes has also been treated. It is shown that the constriction inductance is equal to the sum of the discontinuity inductances of each end taken separately to a very good approximation. The constriction inductance can be considered as a correction term to be added to the analogous acoustical inductance of the tube and can be interpreted physically as an increase in the equivalent length of the tube.