Scattering at Impedance Changes

When a traveling wave encounters a change in wave impedance, scattering occurs, i.e., a traveling wave impinging on an impedance discontinuity will partially reflect and partially transmit at the junction in such a way that energy is conserved. This is a classical topic in transmission line theory [299], and it is well covered for acoustic tubes in a variety of references [301,372]. However, for completeness, we derive the basic scattering relations below for plane waves in air, and for longitudinal stress waves in rods.

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Subsections

• Plane-Wave Scattering
  • Scattering Solution
  • Reflection Coefficient
  
  
• Plane-Wave Scattering at an Angle
  • Reflection and Refraction
  • Evanescent Wave due to Total Internal Reflection
  
  
• Longitudinal Waves in Rods
• Kelly-Lochbaum Scattering Junctions
• One-Multiply Scattering Junctions
• Normalized Scattering Junctions
• Junction Passivity

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.