Speed of sound: The density of aluminum is 2.7 × 10³ kg/m³. The speed of longitudinal waves in an aluminum rod is measured to be 5.1 × 10³ m/s. What is the value of Young's modulus for this aluminum?

Question

Quizplus · Accepted Answer

Young's modulus (E) can be calculated using the formula $E = \rho v^2$, where $\rho$ is the density of the material and $v$ is the speed of sound in the material. Substituting the given values, $\rho = 2.7 \times 10^3 \, \text{kg/m}^3$ and $v = 5.1 \times 10^3 \, \text{m/s}$, we get $E = 2.7 \times 10^3 \times (5.1 \times 10^3)^2 = 7.0 \times 10^{10} \, \text{N/m}^2$.

Speed of Sound: the Density of Aluminum Is 2