Why is #Acoustics sometimes hard to learn? A thread of thoughts provoked by revising my materials for two acoustics modules I'll be teaching in October.

First reason's positive: acoustics is amazing, the applications are really diverse so there's a lot to learn. Interesting = hard, or at least it's a subset. An obvious simplification if you're only interested in room acoustics is no good if you care about underwater acoustics.

Less positive: the terminology is clunky and misleading. Specific acoustic impedance isn't really specific, volume velocity isn't what it sounds like etc

Particular gripe: calling the (strong form of the) mass conservation equation the continuity equation, which conflates two kinds of continuity

Other terminology, while not actively misleading, is unhelpful e.g. Euler's equation (he did quite a few things!) versus 'inviscid momentum equation' (does what it says on the tin, even if the label's a bit long)

Even if we adopt more helpful terminology we have to tell our students what everyone else calls these things so they can engage with the field - it all gets in the way of actual understanding

Even everyday language can mislead; I used to keep catching myself saying and writing "when x = 0" or "where t > 1" until I (mostly) trained myself out of it.

There's another way in which the history of the subject casts shadows. Because the governing equations (for lots of useful applications) are so beautifully simple the subject became mathematically in a way that fluid dynamics, say, wasn't for students at the same level.

The wave equation has solutions out the wazoo and anytime you add two together you've got another - they breed like tribbles. Proving that solutions of the Navier-Stokes equaations even exist would get you a million bucks and lasting fame.

So, lucky acousticians, we've got lots of solutions, so we get all the maths that comes with them - Bessel functions, Fourier Transforms, complex representations and so on. All good stuff, but there's a danger that we let the maths to take care of the physics

That's not necessarily bad - the maths usually understands the physics better than I do. But it puts the cases that have analytic solutions on a pedestal, and discourages exploration of those that don't

That's why numerical codes (for those who can afford them) make such a difference - because they break that distinction. Take our old friend the baffled piston - the analytic solution only gives the near-field on-axis, but the whole near-field's really interesting.

Even the most basic 3D radiation problem, the pulsating sphere, doesn't have to wait till you can write the laplacian in spherical co-ordinates, instead you can ask why its low-frequency efficiency is different from its high-frequency efficiency

The maths shows you that it is, but doesn't tell you why, or that compactness doesn't depend on separability. For sure there's some physics in separability, but not as much as some people seem to think

Another side-effect of the traditional applied-maths treatment of acoustics is the tendency to want to build an invincible fortress of reason from the ground up. Or maybe that's my tendency.

Anyway, it's entirely understandable, even admirable, to want to develop things from an agreed starting point to the desired conclusion by unassaliable logical steps, as we would when reporting research.

But there's a danger of casting the student in the role of an extreme skeptic, who refuses to accept, say, the continuum hypothesis unless we can make it an inescapable conclusion.

We certainly want our students to be skeptical, but that doesn't make them 'reviewer 2', and casting them in an adversarial role by default isn't the best start to a learning relationship. There's a place for "it turns out that".

And since - news flash - computers exist, students can explore and visualise solutions they're given, even analytic ones, and may lear more from doing so than from learning how to obtain it from the boundary equations.

One more way that the past of the subject constrains he present is the assumed prior knowledge. Being able to translate a lumped acoustic system into an equivalent electric circuit is a useful thing to be able to do

But if your students don't already have the expertise to look at a circuit and see what it does, doing so won't provide the insight into the original acoustic system that you might have hoped.

You don't need very much vector calculus to go quite a long way in acoustics, but if you assume it's there and it isn't then there'll be trouble.

One day I'll try to write an acoustics textbook that bears some of these points in mind