As far as I know, the intensity of wave reflection at a boundary between two media, for normal incidence, is always governed by the ratio of the wave speeds in the two media. This holds if the wave is a scalar $\Psi$ with a requirement that $\Psi$ and $\Psi'$ both be continuous at the boundary. It also holds in somewhat different contexts such as an electromagnetic wave or a wave in the Schrodinger equation, if you reinterpret things slightly and allow for an ambiguity in the sign of the reflected amplitude.
So I was perplexed to come across this statement about mercury delay lines in old computers:
Mercury was used because the acoustic impedance of mercury is almost exactly the same as that of the piezoelectric quartz crystals; this minimized the energy loss and the echoes when the signal was transmitted from crystal to medium and back again.
The speed of sound is very different in mercury and quartz. Attempting to resolve my confusion, I dug up this article at UNSW, which defines an acoustic impedance $Z$ and a specific acoustic impedance $z$, the latter being a property of the medium alone. ($Z$ depends on both the medium and the cross-sectional area.) I also found this pdf file from Aalto University giving a quantitative treatment of reflection.
The Aalto article gives convincing physical arguments that the continuity requirement is the following: (1) the pressure has to be continuous, and (2) the normal component of the particle velocity has to be continuous. Based on this, they derive equations for reflection and transmission that look like the usual ones, but that use the ratio of $z$ rather than $c$. (They call it $z_c$.) They also say that
"In fact, also the characteristic impedance is continuous at the boundary (see this by comparing the pressures and particle velocities on both sides)"
This seems logical, and although I'm not sure whether their term "characteristic impedance" refers to what UNSW call $Z$ or what they call $z$, in fact, it seems to me that $Z_1/Z_2=z_1/z_2$, since the two only differ by a factor of the cross-sectional area $A$, which is equal for the two media at the boundary.
But wait, this implies that all media have the same $z$ at a fixed frequency, which is surely false since $z$ is a property of the medium. This is a contradiction.
(1) Can anyone help me clear up this contradiction?
(2) Are there some circumstances when acoustic reflection depends on the velocity $c$ and some in which it depends on $z$? E.g., would it be one or the other depending on whether it's a small-area port between two large volumes, or something like that? Or was I simply wrong in my expectation that it would depend on $c_1/c_2$?