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Chapter 12: Problem 7

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

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

Step by step solution

01

Write down the given information

We are given the following information: Bulk modulus, \(B = 2.8 \times 10^{10} \mathrm{Pa}\) Density, \(ρ = 1.36 \times 10^{4} \mathrm{kg/m}^{3}\)
02

Use the formula for the speed of sound

We will use the formula for calculating the speed of sound in a material: \(v = \sqrt{\dfrac{B}{ρ}}\)
03

Substitute the values into the formula

Substitute the values of the bulk modulus and the density into the formula: \(v = \sqrt{\dfrac{2.8 \times 10^{10} \mathrm{Pa}}{1.36 \times 10^{4} \mathrm{kg/m}^{3}}}\)
04

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 \(1443.29 \mathrm{m/s}\).

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Most popular questions from this chapter

Doppler ultrasound is used to measure the speed of blood flow (see Problem 42). The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is \(0.10 \mathrm{m} / \mathrm{s},\) the ultrasound frequency used is \(5.0 \mathrm{MHz},\) and the speed of sound in blood is \(1570 \mathrm{m} / \mathrm{s},\) what is the beat frequency?
A musician plays a string on a guitar that has a fundamental frequency of \(330.0 \mathrm{Hz}\). The string is \(65.5 \mathrm{cm}\) long and has a mass of \(0.300 \mathrm{g} .\) (a) What is the tension in the string? (b) At what speed do the waves travel on the string? (c) While the guitar string is still being plucked, another musician plays a slide whistle that is closed at one end and open at the other. He starts at a very high frequency and slowly lowers the frequency until beats, with a frequency of \(5 \mathrm{Hz}\), are heard with the guitar. What is the fundamental frequency of the slide whistle with the slide in this position? (d) How long is the open tube in the slide whistle for this frequency?
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