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albega
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Homework Statement
An infinite string is made of three sections, a single intermediate section of length a and density p1 between two semi-infinite sections of density p2.
A wave of frequency f is incident on the intermediate section. If a is an integer multiple of the wavelength in that section, show that the incident wave is not reflected.
Determine the amplitudes of the forward and backward traveling waves in the intermediate section in terms of the incident amplitude
Homework Equations
I can work out the amplitude and relfection coefficients as
r=k1-k2/k1+k2, t=2k1/k1+k2
in terms of wavenumbers (k1 is the incident wavenumber).
The Attempt at a Solution
In terms of showing the lack of reflection:
k1=k2 gives r=0. However that would imply no change in wavespeed across the boundary, so as the densities aren't equal, the tensions would have to be different, but I think they are the same. I think I'm misunderstanding something...