Small-Signal Impedance of Short Tubes

Abstract

Relations expressing the acoustic inertance and resistance of short open tubes in terms of kva are reviewed. The tube radius is a; kv is the complex wave number for viscosity waves. Analogous relations giving the acoustical impedance of a cylindrical cavity in terms of kTa, where kT is the thermal wave number, are considered. Viscous and thermal losses have sometimes been incorrectly separated in the literature. Past measurements, showing disagreement between theory and experiment for small kva, are cited. New measurements of inertance and associated resistance, in the range of |kva| from 1 to 77, are reported. The method of standing wave analysis used. In some instances the inertance tube is incorporated in an adjustable-cavity resonator. Inertance values after end corrections agree with theory within 2.5 percent. Corrected resistance values generally agree with theory within 3 percent for |kva| < 10. Greater discrepancies for larger values of kva are attributed to excessive losses in very short cavities. Consideration of present results together with published data for larger values of kva indicates close agreement of theory and experiment for a range of kva extending at least from unity to several hundred.