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Chapter 12: Problem 190

The speed of sound is used in many applications. Make a list of the speed of sound at \(P_{0}, T_{0}\) for gases, liquids, and solids. Find at least three different substances for each phase. List a number of applications where knowledge of the speed of sound can be used to estimate other quantities of interest.

Short Answer

Expert verified
The speed of sound varies across different substances and is crucial in fields like meteorology, medical imaging, and oceanography.

Step by step solution

01

List Speeds of Sound in Gases

For gases at standard atmospheric pressure and temperature: 1. Air: The speed of sound is approximately 343 meters per second (m/s). 2. Helium: In helium, the speed of sound is about 965 m/s. 3. Carbon Dioxide (CO2): The speed of sound is around 259 m/s.
02

List Speeds of Sound in Liquids

For liquids at standard conditions: 1. Water: The speed of sound in water is approximately 1,480 m/s. 2. Seawater: The speed of sound in seawater is about 1,530 m/s. 3. Ethanol: The speed of sound in ethanol is around 1,200 m/s.
03

List Speeds of Sound in Solids

For solids, which typically conduct sound faster than gases and liquids: 1. Steel: The speed of sound in steel is approximately 5,900 m/s. 2. Glass: The speed of sound in glass is about 3,900 m/s. 3. Aluminum: The speed of sound in aluminum is around 6,320 m/s.
04

Applications of Speed of Sound

Knowledge of the speed of sound is vital in various fields: 1. Meteorology: Used to measure atmospheric properties by analyzing sound propagation. 2. Medical Imaging: Utilized in ultrasounds to create images of internal body structures. 3. Oceanography: Important for sonar technology to estimate depth and underwater object distances.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gases and the Speed of Sound
The speed of sound in gases significantly varies based on factors like temperature and molecular composition.
At standard atmospheric pressure, different gases allow sound to travel at varying velocities:
  • Air: The speed of sound is about 343 meters per second (m/s) in air.
  • Helium: Helium allows sound to travel much faster, at approximately 965 m/s.
  • Carbon Dioxide (CO2): Sound moves slower in CO2, around 259 m/s.
This variance is primarily due to the mass and structure of the molecules of these gases.
Lighter gases like helium have less molecular mass, resulting in faster sound propagation.
Liquids and Sound Velocity
Liquids generally transmit sound faster than gases because their molecules are closer together.
However, sound speeds can differ based on the liquid's density and composition:
  • Water: Sound travels at approximately 1,480 m/s.
  • Seawater: Due to its unique composition, sound travels a bit faster in seawater at about 1,530 m/s.
  • Ethanol: In ethanol, the speed of sound is around 1,200 m/s.
These speeds are vital for applications such as sonar and acoustic measurements in oceanography, largely because sound travels well in water.
Solids and Sound Propagation
Sound travels through solids more effectively than in gases and liquids due to the tightly packed molecules.
As a result, sound can travel faster and with less attenuation:
  • Steel: Sound velocity is approximately 5,900 m/s, making it an excellent medium for structural integrity tests.
  • Glass: With a speed of about 3,900 m/s, glass can effectively transmit sound.
  • Aluminum: Features a speed of sound around 6,320 m/s, favored in many engineering applications.
This property of solids is harnessed in fields such as non-destructive testing and construction, where accurate sound measurements can reveal material flaws.
Applications of Sound Speed
The speed of sound data finds usage in various practical applications across different fields.
  • Meteorology: Used to estimate atmospheric properties and forecast weather by analyzing sound propagation.
  • Medical Imaging: In ultrasound technology, sound speed knowledge helps create images of the body's internal structures, crucial for diagnostics.
  • Oceanography: Essential for sonar technology, it aids in depth estimation and the detection of underwater objects.
By understanding sound speed in various media, these applications enhance precision and provide critical insights into their respective fields.
Measurement Techniques for Speed of Sound
To measure the speed of sound, various techniques are employed depending on the medium:
  • Time of Flight: Involves sending a sound wave pulse through a medium and measuring the time it takes to return.
  • Phase Comparison: Uses phase shifts in sound waves passing through the medium to calculate speed.
  • Acoustic Resonance: Determines speed by assessing resonant frequencies in a medium, especially useful in gases.
These methods, among others, provide accuracy and reliability in measuring sound speeds, facilitating advancements in research and technology. Depending on the context, one technique may be favored over others for its suitability and precision.

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Most popular questions from this chapter

A cylinder fitted with a piston contains liquid methanol at \(70 \mathrm{~F}, 15 \mathrm{lbf} / \mathrm{in} .^{2}\) and volume \(1 \mathrm{ft}^{3}\). The piston is moved, compressing the methanol to \(3000 \mathrm{lbf} / \mathrm{in} .^{2}\) at constant temperature. Calculate the work required for this process. The isothermal compressibility of liquid methanol at \(70 \mathrm{~F}\) is \(8.3 \times 10^{-6} \mathrm{in}^{2} / \mathrm{lbf}\)

A piston/cylinder contains \(10 \mathrm{lbm}\) butane gas at \(900 \mathrm{R}, 750 \mathrm{lbf} / \mathrm{in} .^{2}\). The butane expands in a reversible polytropic process to \(820 \mathrm{R}, 450\) lbf/in. \(^{2}\). Determine the polytropic exponent and the work done during the process.

In a Carnot heat engine, the heat addition changes the working fluid from saturated liquid to saturated vapor at \(T, P .\) The heat rejection process occurs at lower temperature and pressure \((T-\Delta T)\) \((P-\Delta P) .\) The cycle takes place in a piston cylinder arrangement where the work is boundary work. Apply both the first and second laws with simple approximations for the integral equal to work. Then show that the relation between \(\Delta P\) and \(\Delta T\) results in the Clapeyron equation in the limit \(\Delta T \rightarrow d T\)

A certain refrigerant vapor enters a steady-flow, constant-pressure condenser at \(150 \mathrm{kPa}, 70^{\circ} \mathrm{C}\), at a rate of \(1.5 \mathrm{~kg} / \mathrm{s}\), and it exits as saturated liquid. Calculate the rate of heat transfer from the condenser. It may be assumed that the vapor is an ideal gas and also that at saturation, \(v_{f} \ll v_{g} .\) The following is known: $$\ln P_{g}=8.15-1000 / T \quad C_{p 0}=0.7 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}$$ with pressure in \(\mathrm{kPa}\) and temperature in \(\mathrm{K}\). The molecular mass is 100 .

A 2 -kg mixture of \(50 \%\) argon and \(50 \%\) nitrogen by mole is in a tank at \(2 \mathrm{MPa}, 180 \mathrm{~K}\). How large is the volume using a model of (a) ideal gas and (b) van der Waals' EOS with \(a, b\) for a mixture?
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