The Young's modulus for aluminum is 7.02 × 10¹⁰ N/m². If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m³). A) 11.3 × 10³ B) 7.80 × 10³ C) 2.70 × 10³ D) 29.3 × 10³ E) 1.40 × 10³

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Quizplus · Accepted Answer

The density ($\rho$) can be found using the formula for the speed of sound in a solid, $v = \sqrt{\frac{Y}{\rho}}$, where $v$ is the speed of sound and $Y$ is Young's modulus. Rearranging for $\rho$, we get $\rho = \frac{Y}{v^2}$. Substituting $Y = 7.02 \times 10^{10} \, \text{N/m}^2$ and $v = 5.10 \times 10^3 \, \text{m/s}$, we find $\rho = 2.70 \times 10^3 \, \text{kg/m}^3$.

The Young's Modulus for Aluminum Is 7