Axisymmetric Propagation of a Spherical N Wave in a Cylindrical Tube.
TEXAS UNIV AT AUSTIN APPLIED RESEARCH LABS
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An experimental and theoretical study of the propagation of a spherical N wave in a rigid cylindrical tube is presented. Both source, an electric spark, and receiver, a very wideband condenser microphone, were located on the tube axis. Spark energies of between 0.04 J and 2.3 J were used. The received signal is a series of pulses. The first pulse is the direct N wave, which travels straight down the axis. Subsequent pulses represent waves reflected from the tube wall their waveforms vary they are not N shaped. There is, however, a shape repetition every fourth reflected wave. A theoretical analysis of the problem was based on a solution of the linear wave equation for a dissipative medium. The solution, expressed as a ray expansion, indicates that the variation in pulse shape for low energy sparks is due primarily to focusing of the reflected rays each time they cross the tube axis Each focus is accompanied by a 90 degree phase shift of the components making up the pulse. It was also found that atmospheric absorption and microphone directivity have important effects on the shapes of the received pulses. Both analytical and numerical methods were used to compute individual pulse waveforms from the theoretical results. For low spark energies 0.1 J computed and measured waveforms are in good agreement. For higher spark energies 0.1 J the shapes of the measured waveforms are altered by finite amplitude effects, and the simple linear theory is no longer sufficient to explain the results. A numerical propagation algorithm, which includes nonlinear propagation distortion, has been proposed. A qualitative rendering of the algorithm accounts reasonably well for the observed changes in wave shape. Author