Wave propagation in a non-uniform string

Abstract

In this article I present the behavior of the reflection and transmission coefficients of a pulse at a joint between two strings with mass densities µ1 and µ2. The joint is made of a string segment with mass density varying linearly from µ1 to µ2. It will be shown that the reflection of the pulse at the joint depends largely on the ratio between the pulse width and the length of the joint. Analogies with other physical systems such as antireflection coatings and tsunamis will be considered briefly. Keywords: wave, pulse, string, non-uniform, inhomogeneous, discontinuous, anti-reflection, anti-reflective, tsunamis, pulse energy.Neste artigo mostro o comportamento dos coeficientes de reflexão e transmissão de um pulso propagando através de uma emenda entre cordas com densidades de massa µ1 e µ2. A emendaé um segmento de corda com densidade de massa variando linearmente desde µ1à µ2. Será mostrado que a reflexão do pulso na emenda depende sensivelmente da razão entre a largura do pulso e o comprimento da emenda. Discutirei brevemente analogias com outros sistemas físicos como camadas anti-refletoras e tsunamis.