Your electrical analogy is good, and your observation that a pressure
microphone reveals nothing of impedance is correct. Boundaries do make a
local change in impedance, which, like impedance changes in an electrical
transmission line, cause reflections. In acoustics, a horn shaped
structure, with gradual change in cross section, is used for impedance
matching between driver and open air for example; without the horn
structure the driver would couple very poorly to open air.
In addition to pressure microphones there exist velocity or pressure
gradient microphones in both the very old ribbon microphone type and
modern MEMS versions, which can for example distinguish between sound
reflecting from a surface and sound originating from vibration of the
surface where a pressure microphone cannot. There was an article on this
in Sound and Vibration Magazine a while back which I cannot find now, but
I recommend the (free) magazine to anyone interested in acoustics:
http://www.sandv.com
As to the degree in acoustics, you could get the equivalent of two
semesters of grad level acoustics by reading Physical Acoustics by
Blackstock, a former acoustics prof who put about 40 years of acoustics
teaching experience into this book, which focuses on the physics of sound
more than engineering applications like Acoustical Engineering by Olson,
and unlike Olson presumes a basic understanding of partial differential
equations. As far as I know Blackstock is the only acoustics book author
who completely derives the wave equation for sound in an ideal gas from
basic principles of conservation and continuity, with all assumptions
fully justified.
Having now extolled the virtues of Blackstock's book several times now I
suppose I should admit to having worked as a 'student observer' in his
acoustics lab at U of Rochester in the summer of '68, collecting data on
several entertaining shock wave and non-linear propagation experiments.
Glen