Helmhurts

A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn’t. Well, spurred on by a shocking amount of spare time, I’ve given it a go here.

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It turns out that the Helmholtz equation can also be applied to the modelling of the forced vibrations of the square plate, where the choice of conditions above equates to applying a force at the centre of the plate and clamping the edges. The rice/sand/etc settles at the nodes of the plate, i.e. the positions which stay stationary in the oscillation.