Answer to Question #184973 in Civil and Environmental Engineering for John Prats

Question

Longitudinal waves are set up in an aluminum rod. Calculate the velocity of the wave if the modulus of elasticity of aluminum is 6.9×10^11 dynes per sq. cm. and a density of the aluminum is 2.69 gram per cu. cm.

Answer 1

1 dyn/cm² to N/m² = 0.1 N/m²

6.9×10$^{11}$ dynes per sq. cm= $6.9 \times 10^{10} N/m^2$

density of aluminum = 2.69 g/cm$^3$ = 2690 $Kg/m^3$

Velocity of a wave in solid medium $\nu= \sqrt{\frac{Young's modulus}{density of material}}$

$\nu= \sqrt{\frac{Y}{\rho}}= \sqrt{\frac{6.9 \times 10^{10}}{2690}} = 5064 m/s$