For supplement problem 2 K-4, we are asked to
1)interpret physically the solution of w = f(x+ct)
2)say what f(x) represents and
3)state the relation of f(x+ct) to f(x)
For (1) is it fair to say that f(x+ct) represents a wave travelling in the negative x direction? My answer for (2) is that is represents a 'snapshot' of the wave at t = 0 and for (3), f(x+ct) is a translation of f(x) in the negative x direction by magnitude ct. Are there any other interpretations?
OCW Scholar - Multivariable Calculus
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i don't have access to the supplement you mention but i would certainly agree broadly with your descriptions
you can get the travelling wave equation from a Galilean transformation:
so you can also look at the differences that are highlighted by describing frames of reference. so y = f(x) is what the guy sitting riding the wave sees, y = f(x - vt) is what the observor at rest (lying on the beach drinking beer!) sees.