Does/can physical audio theory exist? I've been wondering,

Since some sound generating physical phenomena have been physically modelled as physical modelling synthesisers,

Does there exist a "physical audio theory" (or scientific subdomains fit for belonging to "physical audio theory"), which is like a subfield of applied mathematics or physics that describes the theory of sound generators, propagation and such. For example, the Karplus-Strong algorithm and its analysis would belong there and it would be presented as a derivation of string physics. Sure there's the physics of sound under physics, but I have not seen a coherent mathematical theory on "physical modelling synthesis", even if "physical modelling synthesis" could perhaps be laid out as mathematical formalisms, e.g. as an "applied linear algebra" body of theory. It seems like much of audio DSP is just scattered information.

For those interested, I also think there are at least some books concerning "physical audio theory", an example would be this book:

https://mitpress.mit.edu/books/designing-sound

It does contain chapters that predominantly analyze natural phenomena or "sound generating settings" and try to translate those into expressions in mathematics, using concepts from physics. The derivations don't differ that much from e.g. typical engineering analysis. Much like the Karplus-Strong algorithm was developed by analyzing string instruments.
Physics-based sound synthesis is a pretty multidisciplinary topic.  Quoting from the preface of Physical Audio Signal Processing: 


  [T]he material of this book is multidisciplinary, building on results
  from physics, musical acoustics, psychoacoustics, signal processing,
  control engineering, computer music, and computer science. Such
  diversity is typical of applied research.


It wouldn't really make sense to have it be some kind of subfield of math or physics; computer graphics is in a similar position.  Physics-based sound synthesis is mainly numerically simulating a physical model.  The trick, as usual, is making approximations to arrive at something reasonably efficient while not losing too much of what is important.  This is how fields like psychoacoustics and computer science come in.  There isn't a mathematical theory that will tell you what approximations won't produce unpleasant sounds and will run efficiently on a SHARC DSP.  The constraints are too ad-hoc.  Of course, you can put the constraints of a particular problem into a general mathematical theory of approximation and optimization to help derive solutions.