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The bridge reflectance is needed as part of the loop filter in
a digital waveguide model (Chapter 6).
As derived in §C.11.1, the force-wave reflectance of
seen on the string is
![$\displaystyle \hat{\rho}_b(s) \eqsp \frac{R_b(s)-R_0}{R_b(s)+R_0} \eqsp \frac{s^2+\frac{1}{m}(\mu-R_0)s + \omega_0^2}{s^2+\frac{1}{m}(\mu+R_0)s + \omega_0^2} \protect$](img2010.png) |
(10.7) |
where
denotes the wave impedance of the ideal string, and
denotes the resonance frequency in
radians per second. The velocity reflectance is simply minus the
force reflectance (§C.11.1).
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