A string of impedance ends in a two-layer stack

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Superposition, boundaries and interference · Superposition, boundaries and interference

Modes, Packets and Media, Ch Reflection, transmission, matching and tunnelling at boundaries

Problem

A string of impedance

Z_0=1.0\,\mathrm{kg\,s^{-1}}

ends in a two-layer stack. The first layer met by the wave has impedance

Z_A=1.5\,\mathrm{kg\,s^{-1}}

and is a quarter of a wavelength thick in its own material; behind it, a layer of impedance

Z_B=2.0\,\mathrm{kg\,s^{-1}}

is an eighth of a wavelength thick in its own material; the stack is backed by a long string of impedance

Z_{\rm L}=4.0\,\mathrm{kg\,s^{-1}}

. ((a)) Find the input impedance

Z_{\rm in}

presented at the front of the stack. ((b)) Find the fraction

R

of the incident power reflected, and compare it with the bare join of

Z_0

directly to

Z_{\rm L}

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