I remember learning in my undergraduate control theory class that any "system" can be converted to any other "system". One of the examples we did was taking a mechanical system, which was a muffler, and converting it to an electrical system, which was an electrical circuit comprised of reactive and linear elements. Once it was in that form the frequency response was much easier to see. We got to see how a simple muffler was a lowpass filter, blocking high frequency gas movements which are easier to hear, and allowing low frequency gas movements to pass through, which allows the engine to breathe still.

That was when I realized how interconnected everything really is lol

Yes, that’s why electro-mechanical analogies are so common in engineering and physics. But it shouldn’t be too surprising that they can work as well as they do. There appears to be an elegant, underlying simplicity--or maybe "economy" would be a better term--in the ordering of the phenomenal world, and if there weren’t, then mathematical models could hardly describe and even predict so many of its relationships.

The 1D mathematical models describing the unsteady gas exchange characteristics of ICEs still in wide use reply on a system of non-linear hyperbolic differential equations, which can complicate analyses, so various simplified methods have been developed that have applications in acoustic modeling of systems, such as the lumped parameter/lumped element method.

I mentioned the electrical analogy to acoustic theory in my post, but only in passing. Thanks for bringing it up in more detail.

Impedance translation and waveguide circuits can be used to model an equivalent circuit of a Helmholtz resonator (for example) which sounds like what you did in control theory class. These can be very good for determining the response of resonators, and a lot of work has been done in this direction.

A HR can also be considered by the analogy of a sprung mass, where fluid mass in the HR neck is represented by a mass and the compressible volume of the flask is the spring. Newton’s second law of motion can be applied (a = Fnet/m, a = x’), mx’ + kx=0, to describe the equilibrium of the forces of the system. The solution to this equation will be f = 1/(2π)(K/m)^1/2, where m is the mass of the fluid in the HR neck and f is the resonance frequency of the resonator. After further manipulation the equation becomes the familiar f = c/(2π) [A/(VL’)]^1/2.

It's acoustic wave frequencies and wavelengths moving through a gas as the supporting medium that are blocked or allowed in these acoustic filters. It's a distinction between energy and matter, but an important one.

In ICE intake and exhaust systems, there i is superposition of acoustic and finite amplitude pressure waves. Acoustic waves have small amplitudes and little effect on the gas particulate medium, but finite waves can be strong enough to develop shock fronts and have significant effect on the medium (e.g. displacement of gas). This is where acoustic theory begins to break down and 1D (and 3D) analysis becomes necessary.