The Young's modulus of aluminum is $6.90 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$. If the density of aluminum is $2,700 \mathrm{~kg} / \mathrm{m}^{3}$, then what is the speed of longitudinal waves along a thin aluminum rod?

Question

Quizplus · Accepted Answer

The speed of longitudinal waves in a material is given by $v = \sqrt{\frac{Y}{\rho}}$, where $Y$ is Young's modulus and $\rho$ is the density. Substituting $Y = 6.90 \times 10^{10} \, \mathrm{N/m^2}$ and $\rho = 2700 \, \mathrm{kg/m^3}$, we get $v = \sqrt{\frac{6.90 \times 10^{10}}{2700}} \approx 5060 \, \mathrm{m/s}$.

The Young's Modulus of Aluminum Is 6.90×1010 N/m26.90 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}6.90×1010 N/m2

The Young's Modulus of Aluminum Is $6.90 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$