Question

For a solid rod, the Young's modulus of elasticity is $32 \times 10^{11} Nm ^{-2}$ and density is $8 \times 10^3 kg m ^{-3}$ The velocity of longitudinal wave in the rod will be

• A. $3.65 \times 10^3 ms ^{-1}$
• B. $18.96 \times 10^3 ms ^{-1}$
• C. $145.75 \times 10^3 ms ^{-1}$
• D. $6.32 \times 10^3 ms ^{-1}$

Hint:

The velocity of longitudinal waves in a solid is determined by the Young's modulus and density of the material.

Answer 1

The Correct Option is D

The velocity of longitudinal wave in the rod will be :
\(v = \sqrt{\frac{3.2\times10^{11}}{8 \times 10^3}}\)
= \(6.32 \times 10^3\;m/s\)
The Correct Option is (D) \(6.32×10^3\;ms^{−1}\)

Answer 2

The velocity \( v \) of longitudinal waves in a solid rod is given by the formula: \[ v = \sqrt{\frac{Y}{\rho}} \] where \( Y \) is the Young's modulus and \( \rho \) is the density. Substitute the given values \( Y = 3.2 \times 10^{11} \, \text{Nm}^{-2} \) and \( \rho = 8 \times 10^3 \, \text{kg m}^{-3} \): \[ v = \sqrt{\frac{3.2 \times 10^{11}}{8 \times 10^3}} = \sqrt{4 \times 10^7} = 6.32 \times 10^3 \, \text{ms}^{-1} \]