[tonyarkles]

One of the things that engineering school really drove home for me was the idea that "all models are wrong, some models are useful". You're completely correct that this model is "wrong" because it doesn't account for relativity, but in a lot of cases (plucking a string, waves in water, sound, etc) the relatively component is so small as to be insignificant. We do this all the time across all disciplines: resistors are treated as purely resistive even though their leads have some amount of capacitance and inductance, steel beams are treated as isotropic even though they might have some kind of crystal-grain-induced directionality in strength, the classic F=mg model of gravity works just fine for lots of practical problems. All of these are "wrong" but they're still incredibly useful and give good-enough answers.

To the 1D/2D question, that's more a matter of semantics I think. A more accurate name for it would be the "Wave Equation for a wave propagating in one spatial dimension over time" but that doesn't quite roll of the tongue quite the same way :).