 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021/7/iii/solution

For

Δ t = Δ x / c

y (x + Δ x, t + Δ t) = f (c t + c Δ t - x - Δ x) = f (c t - x) = y (x, t) .

Equivalently

y (x, t + Δ t) = y (x - c Δ t, t)

. Thus every value of the displacement is translated by the same distance

c Δ t

: the entire travelling wave profile keeps its shape. The wave speed is independent of the profile, as expected for this nondispersive wave equation.

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