K String Turing machine Given any $k$-string Turing machine $M$ operating within time $f(n)$, we can construct a single-string Turing machine $M$ operating within time $O(f(n)^2)$ such that for any input $x$, $M(x)=M(x)$

How can we prove that converse is false?
Just take $k=1$ and use the time hierarchy theorem.