For a solid rod, the Young's modulus of elasticity is $$3.2 \times 10^{11}$$ N m$$^{-2}$$ and density is $$8 \times 10^3$$ kg m$$^{-3}$$. The velocity of longitudinal wave in the rod will be

We need to find the velocity of a longitudinal wave in a solid rod.

Formula for velocity of longitudinal wave in a solid: $$v = \sqrt{\frac{Y}{\rho}}$$

where $$Y$$ is Young's modulus and $$\rho$$ is the density.

Substitute the values: $$v = \sqrt{\frac{3.2 \times 10^{11}}{8 \times 10^3}}$$

$$= \sqrt{4 \times 10^7}$$

$$= 2 \times 10^{3.5} = 2 \times 3162.3 \approx 6324.6 \text{ m s}^{-1}$$

$$\approx 6.32 \times 10^3 \text{ m s}^{-1}$$

The correct answer is Option D: $$6.32 \times 10^3$$ m s$$^{-1}$$.