A Kundt's tube apparatus features a copper rod of length 1.0 m...

The distance between the heaps of powder in a Kundt's tube corresponds to the distance between two consecutive nodes in the air column, which is $\dfrac{\lambda_a}{2}$.

$\dfrac{\lambda_a}{2} = 5.0 \text{ cm} \Rightarrow \lambda_a = 10.0 \text{ cm} = 0.1 \text{ m}$

The frequency of the sound wave is given by:

$f = \dfrac{v_a}{\lambda_a} = \dfrac{340}{0.1} = 3400 \text{ Hz}$

The copper rod of length $1.0 \text{ m}$ is clamped at $25 \text{ cm}$ from one end. The clamped point acts as a node and the free ends act as antinodes. The distance from the node to the nearest antinode is $\dfrac{\lambda_c}{4}$.

$\dfrac{\lambda_c}{4} = 25 \text{ cm} \Rightarrow \lambda_c = 100 \text{ cm} = 1.0 \text{ m}$

The speed of sound in the copper rod is:

$v_c = f \lambda_c = 3400 \times 1.0 = 3400 \text{ m/s}$