Natural Science Forum / Physics / Acoustics / September 2004

I recollect (but haven't verified) that Z1 = Z2 implies V1 = V2. Z1 ~=
Z2 implies a reflected wave at the boundary, which implies refraction at
non-normal incidence, which in turn implies that the velocities differ.

Jerry

The naive answer is that if the impedances are equal, Z1=z2, there
will be no reflection since it is the contrast in impedance that
spawns reflections. Impedance is given as

   Z = rho * c,

where rho is material density and c is speed of sound. Z1=Z2 with
c1 =/= c2 implies that the densities are related as

  rho1/rho2 = c2/c1.

Now, the slightly less naive answer (i.e. after having checked with
ch. 6.4 in Kinsler & Frey) is that for non-normal incidence, the
incidence angle does play a part in the reflection coefficient
via Snell's law

   sin(phi_1)/sin(phi_2) = c2/c1,

i.e. it is sufficient that the wave velocities are different, to
spwan a reflection.

So a partial answer to your question is that there is a reflection at
oblique incidence, so it is not impossible to detect the layering.
The obvious requirement to a measurement system is that it is
bi-static, i.e. the source and reciever are at different locations.

From there on, it is basically a question of dimensions. How large
is the tank or reservoior where these fluids are stored? How high
or low in the reservoir is the boundary expected to be? What
fluctuations do you expect on the boundary depth? How large is
the velocity contrast between the fluids? What frequency do you
intend to use for the transducer? How accurately do you need to
estimate the boundary? What source levels can you use? What is
the bacground noise? What echo levels do your reciever need to
detect returns? How many recievers do you have available? Can
you afford to make an array or do you have one single opportunity
to make an estimate?

The list goes on and on. You really need somebody to look more
closely into your particular problem and your particular setup.
The whole setup appears to be a bit too complex for relying on
help via USENET.

Rune