Physics
Transverse Wave
A transverse wave is a type of wave in which the disturbance or oscillation is perpendicular to the direction of wave propagation. This means that the particles of the medium through which the wave is travelling move up and down or side to side, rather than back and forth in the same direction as the wave. Examples of transverse waves include light waves and electromagnetic waves.
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11 Key excerpts on "Transverse Wave"
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
16.12 Calculate the transverse acceleration a(t) of a string element as a Transverse Wave moves through its location. 16.13 Given a graph of displacement, transverse veloc- ity, or transverse acceleration, determine the phase constant ϕ. 380 Key Ideas ● Mechanical waves can exist only in material media and are governed by Newton’s laws. Transverse mechani- cal waves, like those on a stretched string, are waves in which the particles of the medium oscillate perpendicu- lar to the wave’s direction of travel. Waves in which the particles of the medium oscillate parallel to the wave’s direction of travel are longitudinal waves. ● A sinusoidal wave moving in the positive direction of an x axis has the mathematical form y(x, t) = y m sin(kx − ωt), where y m is the amplitude (magnitude of the maximum displacement) of the wave, k is the angular wave number, ω is the angular frequency, and kx − ωt is the phase. The wavelength λ is related to k by k = 2π λ . ● The period T and frequency f of the wave are related to ω by ω 2π = f = 1 T . ● The wave speed v (the speed of the wave along the string) is related to these other parameters by v = ω k = λ T = λf. ● Any function of the form y(x, t) = h(kx ± ωt) can represent a traveling wave with a wave speed as given above and a wave shape given by the mathemati- cal form of h. The plus sign denotes a wave traveling in the negative direction of the x axis, and the minus sign a wave traveling in the positive direction. 381 16-1 Transverse WaveS What Is Physics? One of the primary subjects of physics is waves. To see how important waves are in the modern world, just consider the music industry. Every piece of music you hear, from some retro-punk band playing in a campus dive to the most elo- quent concerto playing on the web, depends on performers producing waves and your detecting those waves.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
KEY IDEAS • Mechanical waves can exist only in material media and are governed by Newton’s laws. Transverse mechanical waves, like those on a stretched string, are waves in which the particles of the medium oscillate perpendicular to the wave’s direction of travel. Waves in which the particles of the medium oscillate parallel to the wave’s direction of travel are longitudinal waves. • A sinusoidal wave moving in the positive direction of an x axis has the mathematical form y (x, t) = y m sin(kx − t), where y m is the amplitude (magnitude of the maximum displacement) of the wave, k is the angular wave number, is the angular frequency, and kx − t is the phase. The wavelength is related to k by k = 2 . Pdf_Folio:313 • The period T and frequency f of the wave are related to by = 2f = 2 T . • The wave speed v (the speed of the wave along the string) is related to these other parameters by v = k = T = f. • Any function of the form y (x, t) = h (kx ± t) can represent a travelling wave with a wave speed as given above and a wave shape given by the mathematical form of h. The plus sign denotes a wave travelling in the negative direction of the x axis, and the minus sign a wave travelling in the positive direction. Why study physics? The Australian whipcracking championships, at the Sydney Royal Easter Show, demonstrate how a whip is designed to take advantage of the relationship between the speed of the wave travelling along a whip and the mass per unit length of the whip. Seismic waves in New Zealand give rise to longitudinal waves (compressional, primary or P-waves) and Transverse Waves (shear wave, secondary or S-waves), which enable the location of the earthquake’s epicentre to be determined. 1 This chapter focuses on waves travelling along a stretched string, such as on a guitar. The next chapter focuses on sound waves, such as those produced by a guitar string being played.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propagation, such as optics, seismology, telecommunications and radar science. The polarization of light can be measured with a polarimeter. Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and ________________________ WORLD TECHNOLOGIES ________________________ wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, impose the transversality requirement that the electric and magnetic field be perpe-ndicular to the direction of propagation and to each other. Conventionally, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two components have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathematically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 2 Polarization (Waves) Polarization (also polarisation ) is a property of certain types of waves that describes the orientation of their oscillations. Electromagnetic waves, such as light, and gravitational waves exhibit polarization; acoustic waves (sound waves) in a gas or liquid do not have polarization because the direction of vibration and direction of propagation are the same. By convention, the polarization of light is described by specifying the orientation of the wave's electric field at a point in space over one period of the oscillation. When light travels in free space, in most cases it propagates as a Transverse Wave—the polarization is perpendicular to the wave's direction of travel. In this case, the electric field may be oriented in a single direction (linear polarization), or it may rotate as the wave travels (circular or elliptical polarization). In the latter cases, the oscillations can rotate either towards the right or towards the left in the direction of travel. Depending on which rotation is present in a given wave it is called the wave's chirality or handedness. In general the polarization of an electromagnetic (EM) wave is a complex issue. For instance in a waveguide such as an optical fiber, or for radially polarized beams in free space, the description of the wave's polarization is more complicated, as the fields can have longitudinal as well as transverse components. Such EM waves are either TM or hybrid modes. For longitudinal waves such as sound waves in fluids, the direction of oscillation is by definition along the direction of travel, so there is no polarization. In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propa-gation, such as optics, seismology, telecommunications and radar science. The polar-ization of light can be measured with a polarimeter. Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and ________________________ WORLD TECHNOLOGIES ________________________ wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, im-pose the transversality requirement that the electric and magnetic field be perpendicular to the direction of propagation and to each other. Conventionally, when considering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two com-ponents have exactly the same frequency. However, these components have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathematically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
In a solid medium, however, sound waves can be transverse. In this case, the polarization is associated with the direction of the shear stress in the plane perpendicular to the propagation direction. This is important in seismology. Polarization is significant in areas of science and technology dealing with wave propagation, such as optics, seismology, telecommunications and radar science. The polarization of light can be measured with a polarimeter. ________________________ WORLD TECHNOLOGIES ________________________ Theory Basics: plane waves The simplest manifestation of polarization to visualize is that of a plane wave, which is a good approximation of most light waves (a plane wave is a wave with infinitely long and wide wavefronts). For plane waves Maxwell's equations, specifically Gauss's laws, impose the transversality requirement that the electric and magnetic field be per-pendicular to the direction of propagation and to each other. Conventionally, when con-sidering polarization, the electric field vector is described and the magnetic field is ignored since it is perpendicular to the electric field and proportional to it. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). For a simple harmonic wave, where the amplitude of the electric vector varies in a sinusoidal manner in time, the two components have exactly the same frequency. However, these com-ponents have two other defining characteristics that can differ. First, the two components may not have the same amplitude. Second, the two components may not have the same phase, that is they may not reach their maxima and minima at the same time. Mathe-matically, the electric field of a plane wave can be written as, or alternatively, where A x and A y are the amplitudes of the x and y directions and φ is the relative phase between the two components.
eBook - PDFPhysical Optics
Principles and Practices
- Abdul Al-Azzawi(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
The acceleration is proportional to the displacement and in the opposite direction. The proportionality between acceleration and displacement occurs in many types of vibrating objects, such as clock pendu-lums, children’s swings, and rotating arms. 1.3 TYPES OF WAVES There are two basic types of wave motion for mechanical waves: longitudinal and transverse. The following sections demonstrate these types of waves and illustrate the difference between the motion of the wave and the motion of the particles in the medium through which the wave is travelling. 1.3.1 T RANSVERSE W AVES In a Transverse Wave, the particle displacement is perpendicular to the direction of wave propa-gation. Figure 1.5 shows a one-dimensional transverse plane wave propagating from left to right by a spring. The particles do not move along with the wave; they simply oscillate up and down about their individual equilibrium positions as the wave propagates. As shown in this figure, the spring is attached to a wall. To generate a wave, pull on the free end with your hand, producing a tension in the spring, and then move your hand up and down. This action generates a wave pulse that will travel along the spring towards the wall. When the hand moves up and down with simple harmonic motion, the wave on the spring will have the shape of a sine or cosine wave. The motion of these waves is known as a simple harmonic motion. More details on the sine and cosine waves will be presented in the following sections. 1.3.2 L ONGITUDINAL W AVES A longitudinal wave is easer to see when a spring has a large diameter. The spring is tied to a wall, as shown in Figure 1.6. Compress the spring several coils closer together at one end. Such a distortion is called compression. If these compressed coils are released, they attempt to spread out to their equilibrium positions, compressing the coils immediately to the right.
eBook - PDF- Robert Resnick, David Halliday, Kenneth S. Krane(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
427 SOUND WAVES I n Chapter 18 we studied transverse mechanical waves, in particular the vibrations of a stretched string. Now we turn our attention to longitudinal mechani- cal waves, in particular sound waves. What we call sound is a longitudinal mechanical vibration with fre- quencies from about 20 Hz to about 20,000 Hz, which is the typical range of human hearing. Longitudinal waves of higher frequency, which are called ultrasonic waves, are used in locating underwater objects and in medical imaging. Longitudinal (and transverse) mechanical waves of lower frequency, called infrasonic, occur as seismic waves in earthquakes. In this chapter we discuss the properties of sound waves, their propagation, and their production by vi- brating systems. 19-1 PROPERTIES OF SOUND WAVES Like the Transverse Wave on the string, sound is a mechani- cal wave, meaning that the disturbance propagates due to the mechanical (elastic) forces between particles in the medium. Mechanical waves can travel through any material medium (solid, liquid, or gas). In solids, mechanical waves can be longitudinal or transverse, but in fluids (which can- not support shearing forces) the waves are only longitudi- nal, which means that the particles of the medium oscillate along the same direction that the wave is traveling. When we discuss sound waves, we normally mean lon- gitudinal waves in the frequency range 20 Hz to 20,000 Hz, the normal range of human hearing. However, the branch of physics and engineering that deals with the study of sound waves, called acoustics, generally includes the study of me- chanical waves of all frequencies, with transverse as well as longitudinal vibrations in the case of solids. In this chapter we consider mainly sound waves in air, which are strictly longitudinal. Although a small source of sound in an open area emits waves that are three-dimensional, we will simplify the prob- lem by considering one-dimensional waves.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
3. Matter waves. Although these waves are commonly used in modern technol- ogy, they are probably very unfamiliar to you. These waves are associated with electrons, protons, and other fundamental particles, and even atoms and molecules. Because we commonly think of these particles as constituting matter, such waves are called matter waves. 4. Gravitational waves. In 1916, Albert Einstein predicted that when any mass accelerates, it sends out gravitational waves that are oscillations of space itself (more precisely, spacetime). In normal circumstances, the oscillations are so small as to be undetectable. The first direct detection of the waves came in 2015 when a detector based on the design of Rainer Weiss of MIT recorded the waves due to the merger of two distant black holes. The oscillations were much less than the radius of a proton. Much of what we discuss in this chapter applies to waves of all kinds. However, for specific examples we shall refer to mechanical waves. Transverse and Longitudinal Waves A wave sent along a stretched, taut string is the simplest mechanical wave. If you give one end of a stretched string a single up-and-down jerk, a wave in the form of a single pulse travels along the string. This pulse and its motion can occur because the string is under tension. When you pull your end of the string upward, it begins to pull upward on the adjacent section of the string via tension between the two sections. As the adjacent section moves upward, it begins to pull the next section upward, and so on. Meanwhile, you have pulled down on your end of the string. As each section moves upward in turn, it begins to be pulled back downward by neighboring sections that are already on the way down. The net result is that a distortion in the string’s shape (a pulse, as in Fig. 16.1.1a) moves along the string at some velocity v → . If you move your hand up and down in continuous simple harmonic motion, a continuous wave travels along the string at velocity v → .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
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 ass-ociated 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 ________________________ WORLD TECHNOLOGIES ________________________ 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 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. 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. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to their springs, and so on.
eBook - PDFPhysics at a Glance
Full Physics Content of the New GCSE
- Tim Mills(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
28 Questions 1. Identify the measurements a, b and c in the following diagrams: 2. Write a sentence to define each of the following terms: a. Wavelength. b. Frequency. c. Amplitude. 2. Give one similarity and one difference between a longitudinal and Transverse Wave and give an example of each. 3. For each of particles a, b, and c in the diagram decide if the particle is moving up, moving down, or is momentarily stationary. A wave is a periodic disturbance of a medium. TRANSFER OF ENERGY WAVES Describing Waves All waves transfer energy from one place to another, without transferring any matter. Speed = distance travelled by a wave crest or compression in one second. The direction of wave motion is defined as the direction energy is transferred. Frequency is the number of waves per second produced by the source that pass through a given point in the medium. Measured in waves per second or Hertz, Hz. The particles of the medium oscillate about fixed positions along the same line as the wave energy travels. Wave direction Particles of the medium oscillate about fixed positions at right angles to the direction of wave travel. Wavelength ( λ ) – distance between the same point on two adjacent disturbances. Measured in metres. Amplitude – distance between a crest or trough and the undisturbed position . Trough All particles moving down Examples longitudinal: • Sound Particles spread out – rarefaction Particles close – compression Shows direction of energy transfer Examples transverse: • Surface water waves • Light • Plucked guitar string Wavefront Ray at right angles to wavefront Particles oscillating up and down Wave direction Crest (peak) All particles moving up λ λ λ The medium is the material that is disturbed as the wave passes through it. W A V E S T w o t y p e s T r a n s v e r s e w a v e s L o n g i t u d i n a l w a v e s Particles oscillating side to side Compression Rarefaction a b Position along wave c a b c Wave direction
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