Numerical and experimental study of finite-amplitude standing waves in a tube at high sonic frequencies

Abstract

Finite-amplitude standing waves in an air-filled tube are studied numerically and experimentally. The standing wave is excited at one end of the rigid-walled tube and a rigid cap is assumed at the other end. The one-dimensional nonlinear second order wave equation is solved numerically using a finite element algorithm based on the Bubnov–Galerkin method. Viscous and thermal losses at the walls of the tube are taken into account. An experimental setup is developed for the study of standing waves at high sonic frequencies. The acoustic field is measured along the tube axis with a fine calibrated probe. Experimental data of pressure distributions for the fundamental frequency (9.5 kHz) and the second harmonic (19 kHz) are compared with the numerical results, as a function of the tube length.