= Solution
The explicit <travelling wave> speed increases with $q$:
$$
c'(q)=\frac{q}{2\sqrt2(q+2)^{3/2}}>0,\qquad c(q)\to2\ (q\downarrow0),\quad c(q)\sim\sqrt{q/2}\ (q\to\infty).
$$
Its two tails change differently. Near the leading empty state, $U\sim a^{-2/q}e^{-kz}$ with $k=\sqrt{2/(q+2)}$ decreasing as $q$ grows: that tail lengthens. Near the filled state, $1-U\sim(2a/q)e^{bz}$, with $b=q/\sqrt{2(q+2)}$ increasing: that tail becomes steeper. Thus the change is not a uniform sharpening of the whole profile. For example the half-height slope is $-\tfrac{k}{2}(1-2^{-q/2})$.
For meaningful comparison, the figure aligns all fronts at $U(0)=1/2$ by choosing $a=2^{q/2}-1$. It displays the speed increase and the unequal changes of the two tails. Since $f'(0)=1$ for every $q$, the minimum admissible speed remains two; the explicit family has $c(q)>2$ for $q>0$. The invariant-triangle proof above extends with boundary <derivative> $U^{q+1}\geq0$.
\Image[/past-exam-of-the-topics-in-applied-mathematics-course-of-the-university-of-oxford/2011-travelling-fronts.png]
{title=Half-height-aligned generalized Fisher fronts and the speed of the explicit front family}
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