$=5 \times 10^{3} \mathrm{\,ms}^{-1}$

As the rod is clamped at the middle, therefore the middle point is a node. In the fundamental mode, the antinode is formed at each end as shown in figure.

Therefore, the distance two consecutive antinodes $=\mathrm{L}=1 \mathrm{\,m}$

But the distance between two consecutive antinodes is $\frac{\lambda}{2}$

$\therefore \frac{\lambda}{2}=1 \mathrm{\,m}$ or $\lambda=2 \mathrm{\,m}$

The frequency of the fundamental mode is

$v=\frac{v}{\lambda}=\frac{5 \times 10^{3} \mathrm{\,ms}^{-1}}{2 \mathrm{\,m}}=2.5 \times 10^{3} \mathrm{\,Hz}=2.5 \mathrm{\,KHz}$