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(29) Wave Interference

# (29) Wave Interference - Wave Interf erence What is the...

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Wave Interference What is the relationship between traveling wave and standing wave solutions to the wave equation, ( 361 ), in an infinite medium? To help answer this question, let us form a superposition of two traveling wave solutions of equal amplitude , and zero phase angle , that have the same wavenumber , but are moving in opposite directions. In other words, (379) Because the wave equation, ( 361 ), is linear, the previous superposition is a valid solution provided the two component waves are also valid solutions: that is, provided , which we shall assume to be the case. Making use of the trigonometric identity (see Appendix B ), the previous expression can also be written (380) which is a standing wave [cf., Equation ( 362 )]. Evidently, a standing wave is a linear superposition of two, otherwise identical, traveling waves that propagate in opposite directions. The two waves completely cancel one another out at the nodes, which are situated at , where is an integer. This process is known as total destructive interference . On the other hand, the waves reinforce one another at the anti-nodes,

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