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

(D) $6.32 \times 10^{3} \mathrm{~ms}^{-1}$

(A) $145.75 \times 10^{3} \mathrm{~ms}^{-1}$

(B) $3.65 \times 10^{3} \mathrm{~ms}^{-1}$

(C) $18.96 \times 10^{3} \mathrm{~ms}^{-1}$

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Waves & Sound

For a solid rod, the Young's modulus of elasticity is

3.2 \times 1 0^{11} Nm^{- 2}

and density is

8 \times 1 0^{3} kg m^{- 3}

. The velocity of longitudinal wave in the rod will be.

Answer: (D)

A longitudinal wave runs along a solid rod at

v = \frac{Y}{ρ}

, set by the stiffness and the inertia of the material. Substituting

Y = 3.2 \times 1 0^{11} N m^{- 2}

and

ρ = 8 \times 1 0^{3} kg m^{- 3}

gives

v = \frac{3.2 \times 1 0 ^{11}}{8 \times 1 0 ^{3}} = 4 \times 1 0^{7}

, which works out to about

6.32 \times 1 0^{3} m s^{- 1}

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Single correct option