The bulk modulus of mercury is $2.85 \times 1010 \mathrm{~N} / \mathrm{m}^{2}$. If the density of mercury is $1.36 \times 104 \mathrm{~kg} / \mathrm{m}^{3}$, then what is the speed of sound in mercury?
A) $6.91 \times 10^{-4} \mathrm{~m} / \mathrm{s}$
B) $1.45 \times 10^{3} \mathrm{~m} / \mathrm{s}$
C) $4.77 \times 10^{-7} \mathrm{~m} / \mathrm{s}$
D) $2.10 \times 10^{6} \mathrm{~m} / \mathrm{s}$
E) $2.44 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Question

Quizplus · Accepted Answer

The speed of sound in a material can be calculated using the formula $v = \sqrt{\frac{B}{\rho}}$, where $v$ is the speed of sound, $B$ is the bulk modulus, and $\rho$ is the density of the material. Substituting the given values, $B = 2.85 \times 10^{10} \, \text{N/m}^2$ and $\rho = 1.36 \times 10^4 \, \text{kg/m}^3$, we get $v = \sqrt{\frac{2.85 \times 10^{10}}{1.36 \times 10^4}} \approx 1.45 \times 10^3 \, \text{m/s}$.

The Bulk Modulus of Mercury Is 2.85×1010 N/m22.85 \times 1010 \mathrm{~N} / \mathrm{m}^{2}2.85×1010 N/m2

The Bulk Modulus of Mercury Is $2.85 \times 1010 \mathrm{~N} / \mathrm{m}^{2}$