Driven oscillating nonlinear acoustic waves

A computational investigation has beenconducted for a weakly nonlinear model of acoustical plane wave propagation in a cylindrical tube. Atthe left end a harmonic driving actuator excites standing waves in the tube with a solid wall at the righthand end. For driving frequencies a little higher thanthe frst resonance frequency of the simple waveequation, neglecting nonlinearities and dissipation,we observe formation of oscillating shock waves inthe weakly nonlinear model. A little above the second harmonic frequency of the simple linear waveequation we observe two counter propagating shockwaves in the tube. Increasing the driving frequencyfurther the oscillation mode turns into two parallelpropagating shocks. A Hamiltonian energy analysisis included, which demonstrates balance between theenergy input from the driver and the dissipation of thewave dynamics.