If the Young’s modulus of elasticity for a steel rod is $2.9 \times 10^{11}$ Nm$^{-2}$ and density is $8…

If the Young’s modulus of elasticity for a steel rod is $2.9 \times 10^{11}$ Nm$^{-2}$ and density is $8 \times 10^3$ kg m$^{-3}$. Determine the velocity of longitudinal waves in the steel rod.

Solution

Sol. Given, Young's modulus, $Y = 2.9 \times 10^{11}$ Nm$^{-2}$ Density, $\rho = 8 \times 10^3$ kg m$^{-3}$ \therefore\ Velocity of longitudinal waves in steel, $v = \sqrt{\dfrac{Y}{\rho}} = \sqrt{\dfrac{2.9 \times 10^{11}}{8 \times 10^3}}$ $= 6.02 \times 10^3$ ms$^{-1}$ Answer: $6.02 \times 10^3$ ms$^{-1}$

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