The speed of longitudinal waves in a long brass rod is $3,260 \mathrm{~m} / \mathrm{s}$. If the density of brass is $8,470 \mathrm{~kg} / \mathrm{m}^{3}$, then what is the elastic modulus of brass?
A) $9.00 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
B) $8.70 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
C) $9.80 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
D) $8.10 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
E) $8.50 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

Question

The speed of longitudinal waves in a long brass rod is $3,260 \mathrm{~m} / \mathrm{s}$. If the density of brass is $8,470 \mathrm{~kg} / \mathrm{m}^{3}$, then what is the elastic modulus of brass?
A) $9.00 \times 10^{10}  \mathrm{~N} / \mathrm{m}^{2}$
B) $8.70 \times 10^{10}  \mathrm{~N} / \mathrm{m}^{2}$
C) $9.80 \times 10^{10}  \mathrm{~N} / \mathrm{m}^{2}$
D) $8.10 \times 10^{10}  \mathrm{~N} / \mathrm{m}^{2}$
E) $8.50 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

Quizplus · Accepted Answer

The speed of longitudinal waves in a material is given by $v = \sqrt{\frac{E}{\rho}}$, where $v$ is the speed of the wave, $E$ is the elastic modulus of the material, and $\rho$ is the density of the material. Rearranging for $E$, we get $E = v^2 \rho$. Substituting the given values, $E = (3260 \, \text{m/s})^2 \times 8470 \, \text{kg/m}^3 = 9.00 \times 10^{10} \, \text{N/m}^2$.

The Speed of Longitudinal Waves in a Long Brass Rod 3,260 m/s3,260 \mathrm{~m} / \mathrm{s}3,260 m/s

The Speed of Longitudinal Waves in a Long Brass Rod $3,260 \mathrm{~m} / \mathrm{s}$