Past exam of the mathematical methods II course of the University of Oxford / 2021 / 7 / iii / Solution

For $\Delta t=\Delta x/c$,Equivalently $\boxed{y(x,t+\Delta t)=y(x-c\Delta t,t)}$. Thus every value of the displacement is translated by the same distance $c\Delta t$: the entire travelling wave profile keeps its shape. The wave speed is independent of the profile, as expected for this nondispersive wave equation.