Physics
Wave Speed
Wave speed refers to the rate at which a wave travels through a medium. It is determined by the frequency and wavelength of the wave, and is typically measured in meters per second. The formula for calculating wave speed is given by the product of the wavelength and frequency of the wave.
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11 Key excerpts on "Wave Speed"
eBook - PDF- John Kimball(Author)
- 2015(Publication Date)
- CRC Press(Publisher)
The wavelength is the distance between wave peaks. The frequency is the number of times a wave oscillates up and down each second. The amplitude is the height of the wave. The speed of a wave is the distance one of the wave peaks moves in 1 second. It is related to wavelength and frequency by an impor-tant equation. ( Wave Speed ) = ( Wavelength ) × ( Frequency ) For example, if the frequency is 6 hertz (cycles per second), then six waves pass a fixed point each second. If the wavelength is 8 meters, then the six wave peaks will have moved 6 × 8 meters in 1 second, and the speed is 48 meters/second. The speed of a light wave (in vacuum) is a constant regardless of its frequency or its amplitude. Audible sound Wave Speed is almost constant. The constant speed means plane wave shapes do not change in time. Water Wave Speeds do depend on the wavelength, which Amplitude Distance along wave Figure 5.2 The sine wave shape. For water waves, the amplitude is the height. For sound, it is atomic displacement or pressure. For electromagnetic waves, it is the electric field. Figure 5.1 Water waves spreading from a central point. 149 WAVES means the wave shapes evolve. This is one reason water waves are more complicated. Waves contain energy and transmit energy at the Wave Speed (assuming a constant speed). The energy in each cubic meter of wave is proportional to the square of its amplitude. Multiplying the energy in each cubic meter times the Wave Speed gives the “energy flux,” or the number of joules hitting 1 square meter of surface each second. The most important energy flux is from sunlight. The sun’s 1370 watts/ square meter keep us from freezing in the dark. 5.2.2 Sound in Solids The basic mechanism of sound propagation in solids is shown in Figure 5.3. This is a greatly magnified segment of a crystal lattice showing only three of the atoms (spheres) and the atomic forces (springs) that make up the periodic crystal structure.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
Velocity = v The time for one car to pass is the period T Wavelength = λ Figure 16.6 A train moving at a constant speed serves as an analogy for a traveling wave. 16.3 | The Speed of a Wave on a String 425 the wavelength l and the period T. Since the frequency of a wave is f 5 1/T, the expression for the speed is v 5 l T 5 f l (16.1) The terminology just discussed and the fundamental relations f 5 1/T and v 5 fl apply to longitudinal as well as to transverse waves. Example 1 shows how the wave- length of a wave is determined by the Wave Speed and the frequency established by the source. Check Your Understanding (The answer is given at the end of the book.) 3. A sound wave (a periodic longitudinal wave) from a loudspeaker travels from air into water. The frequency of the wave does not change, because the loudspeaker producing the sound determines the frequency. The speed of sound in air is 343 m/s, whereas the speed in fresh water is 1482 m/s. When the sound wave enters the water, does its wavelength increase, decrease, or remain the same? 16.3 | The Speed of a Wave on a String The properties of the material* or medium through which a wave travels determine the speed of the wave. For example, Figure 16.7 shows a transverse wave on a string and draws attention to four string particles that have been drawn as colored dots. As the wave moves to the right, each particle is displaced, one after the other, from its undisturbed position. In the drawing, particles 1 and 2 have already been displaced upward, while particles 3 and 4 are not yet affected by the wave. Particle 3 will be next to move because the section of string immediately to its left (i.e., particle 2) will pull it upward. Figure 16.7 leads us to conclude that the speed with which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force exerted by its adjacent neighbors.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times faster in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), than in air at 20 degrees Celsius. In solids, sound waves propagate as two different types. A longitudinal wave is associated with compression and decompression in the direction of travel, which is the same process as all sound waves in gases and liquids. A transverse wave, often called shear wave, is due to elastic deformation of the medium perpendicular to the direction of wave travel, The direction of deformation is called the polarization of the wave. In general, transverse waves occur as a pair of orthogonal polarizations. These different waves (compression waves and the different polarizations of shear waves) may have ________________________ WORLD TECHNOLOGIES ________________________ different speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake, where sharp compression waves arrive first, and rocking transverse waves seconds later. The speed of an elastic wave in any medium is determined by the medium's compressibility and density. The speed of shear waves, which can occur only in solids, is determined by the solid material's stiffness, compressibility and density. Basic concept U.S. Navy F/A-18 breaking the sound barrier. The white halo consists of condensed water droplets formed by the sudden drop in air pressure behind the shock cone around the aircraft. The transmission of sound can be illustrated by using a toy model consisting of an array of balls interconnected by springs. For real material the balls represent molecules and the springs represent the bonds between them.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times faster in water (1,484 m/s), and n early 15 times as fast in iron (5,120 m/s), than in air at 20 degrees Celsius. In solids, sound waves propagate as two different types. A longitudinal wave is asso-ciated with compression and decompression in the direction of travel, which is the same process as all sound waves in gases and liquids. A transverse wave, often called shear wave, is due to elastic deformation of the medium perpendicular to the direction of wave travel, The direction of deformation is called the polarization of the wave. In general, transverse waves occur as a pair of orthogonal polarizations. These different waves (compression waves and the different polarizations of shear waves) may have different ________________________ WORLD TECHNOLOGIES ________________________ speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake, where sharp compression waves arrive first, and rocking transverse waves seconds later. The speed of an elastic wave in any medium is determined by the medium's compressibility and density. The speed of shear waves, which can occur only in solids, is determined by the solid material's stiffness, compressibility and density. Basic concept U.S. Navy F/A-18 breaking the sound barrier. The white halo consists of condensed water droplets formed by the sudden drop in air pressure behind the shock cone around the aircraft. The transmission of sound can be illustrated by using a toy model consisting of an array of balls interconnected by springs. For real material the balls represent molecules and the springs represent the bonds between them.
eBook - PDF- Srinivasan Gopalakrishnan(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
In wave propagation problems, two parameters are very important, namely, the wavenumber and the speeds of the propagation. This chapter provides a general methodology to compute these quantities for a material system. There are many types of waves that can be generated in structure. Wavenum- ber expression reveals the type of waves that are generated. Hence, in wave propagation problems, two relations are very important, namely, spectrum relations, which is a plot of the wavenumber with the frequency, and dis- persion relations, which is a plot of wave velocity with the frequency. These relations reveal the characteristics of different waves that are generated in a given material system. This chapter is organized as follows. First, the concept of phase and group speeds and their behavior in different mediums are explained. The expressions for evaluating them are derived. Next, some of the commonly used wave prop- agation terminologies are explained. This is followed by a subsection, wherein the spectral analysis of motion is explained for a general one-dimensional second-order material system. If the governing equation of the material system is derived using higher-order theories, computation of wavenumbers becomes extremely difficult. In such situations, we need to obtain them numerically. In the last part of this chapter, this issue is addressed, wherein general methods of numerically computing wavenumbers and their corresponding wave ampli- tudes is given. Introduction to Wave Propagation 109 5.1 CONCEPT OF WAVENUMBER, GROUP SPEEDS, AND PHASE SPEEDS A wave propagating in a medium can be represented as u(x, t) = e i(kx-ωt). (5.1) Eqn. (5.1) is an alternate way of representing a wave, which is given in Chapter 1 (Eqn. (1.1). In the above equation, k is the wavenumber, which specifies the behavior of the wave. The exponent in Eqn. (5.1) i(kx - ωt) is called the phase of the wave.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
For different gases, the speed of sound is inversely dependent on square root of the mean molecular weight of the gas, and affected to a lesser extent by the number of ways in which the molecules of the gas can store heat from compression, since sound in gases is a type of compression. Although, in the case of gases only, the speed of sound may be expressed in terms of a ratio of both density and pressure, these quantities are not fully independent of each other, and canceling their common contributions from physical conditions, leads to a velocity expression using the independent variables of temperature, composition, and heat capacity noted above. In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times faster in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), than in air at 20 degrees Celsius. In solids, sound waves propagate as two different types. A longitudinal wave is associated with compression and decompression in the direction of travel, which is the same process as all sound waves in gases and liquids. A transverse wave, often called shear wave, is due to elastic deformation of the medium perpendicular to the direction of wave travel; the direction of shear-deformation is called the polarization of this type of wave. In general, transverse waves occur as a pair of orthogonal polarizations. These different waves (compression waves and the different polarizations of shear waves) may have different speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake, where sharp compression waves arrive first, and rocking transverse waves seconds later. The speed of an elastic wave in any medium is determined by the medium's compressibility and density.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
For different gases, the speed of sound is inversely dependent on square root of the mean molecular weight of the gas, and affected to a lesser extent by the number of ways in which the molecules of the gas can store heat from compression, since sound in gases is a type of compression. Although, in the case of gases only, the speed of sound may be expressed in terms of a ratio of both density and pressure, these quantities are not fully independent of each other, and canceling their common contributions from physical conditions, leads to a velocity expression using the independent variables of temperature, composition, and heat capacity noted above. In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times faster in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), than in air at 20 degrees Celsius. In solids, sound waves propagate as two different types. A longitudinal wave is associated with compression and decompression in the direction of travel, which is the same process as all sound waves in gases and liquids. A transverse wave, often called shear wave, is due to elastic deformation of the medium perpendicular to the direction of wave travel; the direction of shear-deformation is called the polarization of this type of wave. In general, transverse waves occur as a pair of orthogonal polarizations. These different waves (compression waves and the different polarizations of shear waves) may have different speeds at the same frequency. Therefore, they arrive at an observer at different times, an extreme example being an earthquake, where sharp compression waves arrive first, and rocking transverse waves seconds later. The speed of an elastic wave in any medium is determined by the medium's com-pressibility and density.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
A higher linear density corresponds to a slower Wave Speed. Plan The distance traveled, which is equal to the product of speed and time, is the same in each case (wet and dry). Let t 0.36 s 1 = and t 0.41 s 2 = be the times corresponding to the clothesline being dry and wet, respectively. Let µ be the dry linear density and 3.4 g m µ ∆ = be the increase in linear density. Equate the product of speed and time for each case using Equation 16.2.2. Solve According to Equation 16.2.2, the Wave Speed is v Fµ = . Equating the products of speed and time for each case, we have t F t F 1 2 µ µ µ = + ∆ Solve (a) From Equation 16.2.2, we have v F 46.2 N 2.81 10 kg m 128.22 m s 128 m s 3 µ = = × = → − (b) The time taken to travel the length of the string is equal to the length of the string divided by the speed of the wave: time length of string speed of wave = 0.328 m 128.22 m s 2.56 10 s 3 = = × − Interpret Converting the speed from part (a) to units of kilometers per hour, we have 128.22 m s 1 km 10 m 3600 s 1 h 462 km h 3 = This speed exceeds the top speed of the fastest production automobile. I N T E R A C T I V E F E A T U R E Sound Waves | 443 Sound Waves Sound waves travel through solids, liquids, and gases, and are the longitudinal vibrations of the constituent particles of the medium. Animated Figure 16.3.1 illustrates the production of a sound wave by the periodic disturbance of a gas that is confined to a tube. As the speaker Squaring both sides, we have t F t F 1 2 2 2 µ µ µ = + ∆ Dividing both sides by F and multiplying both sides by µ µ µ ( ) + ∆ , we have t t t 1 2 1 2 2 2 µ µ µ + ∆ = To solve for µ, we subtract t 1 2 µ from both sides, factor out µ on the right side, and then divide both sides by t t 2 2 1 2 − .
- Srinivasan Gopalakrishnan(Author)
- 2022(Publication Date)
- CRC Press(Publisher)
Dispersion Relations, which is a plot of wave velocity with the frequency. These relations reveal the characteristics of different waves that are generated in a given material system.3.1CONCEPT OF WAVENUMBER, GROUP SPEEDS AND PHASE SPEEDS
A wave propagating in a medium can be represented asu ( x , t ) =(3.1)ei ( k x − ω t )Eqn. (3.1) is an alternate way of representing wave, which is given in Chapter 1 (Eqn. (1.1)). In the above equation k is the wavenumber, which specifies the behavior of the wave. The exponent in Eqn. (3.1)i ( k x − ω t )is called the phase of the wave. If the wave moves with constant phase, then we have(3.2)= 0 , ord ( i ( k x − ω t )d t=d xd tC p=ω kIn the above equation, Cprepresents the speed of the wave that moves with constant phase and hence it is called Phase speed. From the point of view of sending information, these waves are not useful. They are the same throughout the time and the space. Some quantities must therefore be modulated, such as frequency or amplitude, in order to convey information. The resulting wave may be a perturbation that acts over a short distance, which is called a wave packet
eBook - ePub- Srinivasan Gopalakrishnan(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
Chapter 4 . The most common integral transform used for transformation of variables to the frequency domain is the FFT, although more recently the wavelet transform and Laplace transform are also becoming popular. All of these transforms have a discrete representation and hence these are amenable to numerical implementation, which makes their use very attractive for wave propagation analysis. By transforming the problem into the frequency domain, the complexity of the governing partial differential equation is reduced by removing the time variable from the formulation, thus making the solution of the resulting ODE (in the 1D case) much simpler than the original PDE. In wave propagation problems, two parameters are very important, namely, the wavenumber and the speeds of the propagation. This chapter provides a general methodology to compute these quantities for a material system. There are many types of waves that can be generated in structure. Wavenumber expression reveals the type of waves that are generated. Hence, in wave propagation problems, two relations are very important, namely, spectrum relations, which is a plot of the wavenumber with the frequency, and dispersion relations, which is a plot of wave velocity with the frequency. These relations reveal the characteristics of different waves that are generated in a given material system.This chapter is organized as follows. First, the concept of phase and group speeds and their behavior in different mediums are explained. The expressions for evaluating them are derived. Next, some of the commonly used wave propagation terminologies are explained. This is followed by a subsection, wherein the spectral analysis of motion is explained for a general one-dimensional second-order material system. If the governing equation of the material system is derived using higher-order theories, computation of wavenumbers becomes extremely difficult. In such situations, we need to obtain them numerically. In the last part of this chapter, this issue is addressed, wherein general methods of numerically computing wavenumbers and their corresponding wave amplitudes is given.
A wave propagating in a medium can be represented as5.1 CONCEPT OF WAVENUMBER, GROUP SPEEDS, AND PHASE SPEEDSu ( x , t ) =e.i ( k x − ω t )( 5.1 )Eqn. (5.1) is an alternate way of representing a wave, which is given in Chapter 1 (Eqn. (1.1) . In the above equation, k is the wavenumber, which specifies the behavior of the wave. The exponent in Eqn. (5.1) i(kx – ωt
- (Author)
- 2001(Publication Date)
- Academic Press(Publisher)
7. SPEED OF SOUND AS A THERMODYNAMIC PROPERTY OF FLUIDS Daniel G. Friend Physical and Chemical Properties Division Chemical Science and Technology Laboratory National Institute of Standards and Technology Boulder, Colorado Abstract In this Chapter, we review the principles of sound propagation in fluid systems. From a study of the hydrodynamic equations, sound propagation is shown to be a wave phenomenon. The speed of sound then can be derived at any state point from a knowledge of the thermodynamic surface of the fluid of interest. Several model equations of state are reviewed, and it is shown how the speed of sound can be obtained for a variety of systems. We then focus on several fluids of particular interest, and show the behavior of the sound speed over a wide range of the temperature and pressure variables. Tabulated values of the speed of sound are given for argon, nitrogen, water, and air based on the current standard reference thermodynamic surfaces. 7.1 Introduction In this Chapter, we discuss the propagation of sound in fluids and provide information about the thermodynamic speed of sound over substantial ranges of the state variables for a variety of fluids. In the context of this chapter, we consider sound to arise from a small periodic and isentropic (constant entropy) perturbation of the local equilibrium in a fluid, which, as we shall see, gives rise to a standard wave equation. The systems under consideration include both pure fluids and mixtures in the liquid, vapor, and supercritical states. Thus the range in temperature is from the melting line to very high temperatures (a dissociation limit), and the range in pressure is from very low values (below which the continuum approximation would not be valid) to the solidification locus (at least in principle).
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