Question

Find the speed of sound in mercury, which has a bulk modulus of $2.8 \times 10^{10} \mathrm{Pa}\( and a density of \)1.36 \times\( \)10^{4} \mathrm{kg} / \mathrm{m}^{3}.$

Short answer

Answer: The speed of sound in mercury is approximately \(1443.29 \mathrm{m/s}\).

Step-by-step solution

Write down the given information

We are given the following information: Bulk modulus, \(B = 2.8 \times 10^{10} \mathrm{Pa}\) Density, \(ρ = 1.36 \times 10^{4} \mathrm{kg/m}^{3}\)

Use the formula for the speed of sound

We will use the formula for calculating the speed of sound in a material: \(v = \sqrt{\dfrac{B}{ρ}}\)

Substitute the values into the formula

Substitute the values of the bulk modulus and the density into the formula: \(v = \sqrt{\dfrac{2.8 \times 10^{10} \mathrm{Pa}}{1.36 \times 10^{4} \mathrm{kg/m}^{3}}}\)

Calculate the speed of sound

Now, perform the calculations to find the speed of sound in mercury: \(v = \sqrt{\dfrac{2.8 \times 10^{10}}{1.36 \times 10^{4}}} \mathrm{m/s}\) \(v \approx 1443.29 \mathrm{m/s}\) The speed of sound in mercury is approximately \(1443.29 \mathrm{m/s}\).