Nonlinear Oscillations of Acoustic Shock Waves in a Cylindrical Tube

We investigate nonlinear and dissipative acoustic waves in a tube driven by a sinusoidal driver at one end and impossing a fixed wall boundary condition at the opposite end. For driving amplitudes close to resonances in the tube, we have found multiple oscillating shock waves in a weakly nonlinear thermoviscous acoustic model. For slow off resonance driving, we observed a nearly linear oscillating ground state superimposed by bursts of oscillating schock waves. The small amplitude nearly harmonic oscillations xare slow, whereas the oscillating shock waves exhibit fast propagation back and forth in the tube.