Attenuation Constant of Plane Wave in a Tube : Acoustic Characteristic Analysis of Silencing Systems Based on Assuming of Plane Wave Propagation with Frictional Dissipation Part 1

Abstract

The sound pressure distribution of standing waves and the attenuation characteristics of plane waves in a straight tube with a solid end are derived as a function of attenuation constant δ, using the fundamental equation which holds for plane waves propagating in a tube with frictional dissipation. Calculated results of the acoustic characteristics are given as a function of the non-dimensional attenuation coefficient η, which is fixed by the attenuation constant δ times length of tube l. The attenuation constant δ are measured by using these acoustic characteristics of plane waves in a straight tube with frictional dissipation. The experimental results of attenuation constants δ regress to the approximate equation, which is derived from a fundamental equation. The calculated values of attenuation constant δ by regression formula are compared with the experimental results, and they are found to be in good agreement. From these results, the following facts are confirmed that the attenuation constant δ is given as a function of a sound wave length and Reynolds number which is fixed by the inner diameter of a tube, kinematic viscosity and the sound velocity, and that the attenuation constant δ can not be negligible for the acoustic characteristics of resonance frequency ranges in a tube system.