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When a Gaussian pulse propagates through a barrier its velocity is taken to be that with which the peak moves. When a uniform amplitude pulse propagates its velocity is taken to be that of the front of the main part of the pulse. By using a method due to Brillouin (1960) it is shown that the uniform amplitude pulse has quite different velocity characteristics from that of a Gaussian pulse, and indeed it propagates with a constant velocity-which is more in keeping with physical intuition.
K W H Stevens (1980) studied this question.
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