The Propagation Characteristic of the Sound Wave in a Viscoelasticity Sound Tube

Damping in acoustics means sound absorption. In this paper, a theoretical analysis of the one-dimensional wave propagation in the damping medium is discussed. First, it is shown that density in complex number is derived by adding the viscous damping force and the inertial force of the fluid. This results in that the propagation velocity and the wave number are also complex numbers, and the imaginary part of the complex wave number is always negative. Therefore, distance decay occurs in the damping medium. In case of undamped medium, natural modes are formed while traveling wave and the reflected wave are superimposed in one-dimensional acoustic tube. Both the eigenvalues and natural modes are real numbers. If the damping is assumed to be Rayleigh damping, complex eigenvalues and real natural modes occur. However, if the excitation vibration pattern is not valid, natural mode is never excited. So, excitation vibration pattern is considered to excite the natural modes. Numerically calculations are achieved in different two ways of measuring propagation speed. One is time decay of damped natural mode, and the other is distance decay of forced vibration.