Solution
= Solution
For $\Delta t=\Delta x/c$,
$$
y(x+\Delta x,t+\Delta t)=f\bigl(ct+c\Delta t-x-\Delta x\bigr)=f(ct-x)=y(x,t).
$$
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>.