Solution
= Solution
Put $u=ct-x$ and assume $f$ has continuous second <derivatives>. The <chain rule> yields
$$
y_x=-f'(u),\quad y_{xx}=f''(u),\quad
y_t=cf'(u),\quad y_{tt}=c^2f''(u).
$$
Thus the <wave equation> is satisfied. A point of fixed <wave phase> $u=u_0$ has $x=ct-u_0$, so for $c>0$ this <travelling wave> moves in the $\boxed{\text{positive }x\text{ direction at speed }c}$.