Anechoic Coating Project: Report on the Determination of Acoustic Properties of Materials by Propagation of Waves in Water Filled Tubes

摘要

The first part concerns itself with the development of the wave equation in its general form. In order to apply the wave equation to the analysis of sound waves in water filled tubes, the equation is converted from Cartesian to cylindrical coordinates. It is then shown that the wave equation is separable and that its solution may be represented as the product of four distinct functions, each related to only one variable. The general solution to the wave equation is then shown to be a complex waveform being simultaneously propagated along the longitudinal and radial axes of the tube as well as in the theta-space. It is shown that the wave equation reduces to a plane wave, that is, one which is propagated along the longitudinal axis of the tube only. It is further shown that, as the radial waves form a discontinuous series of frequencies, a certain minimum frequency must not be exceeded in order to maintain plane monochromatic waves. The final part deals with the application of theory to sound waves in water filled tubes.