Physics
Progressive Waves
Progressive waves are a type of wave that transfers energy from one point to another without transferring matter. They are characterized by the movement of energy through a medium, such as water or air, in a continuous and regular manner. Progressive waves can be transverse, where the oscillations are perpendicular to the direction of energy transfer, or longitudinal, where the oscillations are parallel to the direction of energy transfer.
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4 Key excerpts on "Progressive Waves"
eBook - PDF- Md Nazoor Khan, Simanchala Panigrahi(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
iii. There is a continuous phase difference between the particles of the medium when progressive wave advances. iv. The velocity of the progressive wave is uniform through out the medium. v. When a progressive wave propagates, each particle of the medium oscillates about their mean position with the same amplitude and time period. The velocity of the particle is different at different points. It is maximum at the mean position and zero at the extreme position. vi. The particle velocity is different from the wave velocity. vii. There is transmission of energy across every plane in the direction of propagation waves Oscillations and Waves 53 1.10 Stationary Waves A stationary wave is defined as a wave produced by the superposition of two identical Progressive Waves (i.e., Progressive Waves having the same wavelength, the same time period, the same frequency and the same speed) propagating through a medium in a line but in opposite directions. The new wave produced by this method is called a stationary wave because there is no transmission of energy across any plane. That means stationary waves do not carry energy. There are certain points in the medium at which particles of the medium are permanently at rest. These points are called nodes. There are certain points in the medium at which particles of the medium are oscillating with maximum amplitude. These points are called anti nodes. The stationary wave can not carry energy because the particles of the medium at the nodes are permanently at rest without having any energy. Stationary waves are also called standing waves. 1.10.1 Formation of stationary waves A stationary wave is formed when the incident wave and the corresponding wave reflected by a rigid wall are superimposed on each other. In Fig. 1.16, the displacement graphs of both incident and reflected waves are plotted. The incident wave is supposed to be travelling from left to right. The reflected wave (Fig. 1.17) is travelling from right to left.
eBook - PDF- Julian L. Davis(Author)
- 2021(Publication Date)
- Princeton University Press(Publisher)
C H A P T E R O N E Physics of Propagating Waves INTRODUCTION In this chapter we shall discuss the physics of propagating waves, starting with simple physical models and then giving an elementary combined physical and mathematical treatment of waves traveling in continuous media. A mathematical treatment is reserved for subsequent chapters. For our purposes a continuous medium is one in which there is a continuous distribution of matter in the sense that a differential volume of material (in the mathematical sense) has the same properties as the material in the large. This means that molecular and crystalline struc-tures are neglected. It is known that electromagnetic (EM) waves travel in a vacuum with the speed of light. (A vacuum is a continuous medium with zero density of matter.) A propagating medium involves oscillations of the material through which the wave travels, with a wave velocity characteristic of the material and the temperature. For example, sound waves travel with a wave velocity that depends on the temperature and the density of the medium (air or fluid). For EM waves traveling in a vacuum, we have an oscillating electric intensity vector and an oscillating magnetic intensity vector normal to the electric vector. DISCRETE WAVE-PROPAGATING SYSTEMS Although the main thrust of this book is a treatment of waves traveling in continuous media, it is useful to construct a physical model composed of a discrete set of oscillating masses coupled by springs. We shall neglect friction. The limit as the number of masses and springs becomes infinite in a finite region yields a continuous medium. The simplest oscillating system consists of a spring fixed at one end and coupled to a mass. The small-amplitude oscillations of the mass
eBook - PDF- Ariel Lipson, Stephen G. Lipson, Henry Lipson(Authors)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
2 Waves Optics is the study of wave propagation and its quantum implications, the latter now being generally called ‘photonics’. Traditionally, optics has centred around visible light waves, but the concepts that have developed over the years have been found increasingly useful when applied to many other types of wave, both inside and outside the electromagnetic spectrum. This chapter will first introduce the general concepts of classical wave propagation, and describe how waves are treated mathematically. However, since there are many examples of wave propagation that are difficult to analyze exactly, several concepts have evolved that allow wave propagation problems to be solved at a more intuitive level. The latter half of the chapter will be devoted to describing these methods, due to Huygens and Fermat, and will be illustrated by examples of their application to wave propagation in scenarios where analytical solutions are very hard to come by. One example, the propa-gation of light waves passing near a heavy massive body, called ‘gravitational lensing’ is shown in Fig. 2.1; the figure shows two images of distant sources distorted by such gravitational lenses, taken by the Hubble Space Telescope, com-pared with experimental laboratory simulations. Although analytical methods do exist for these situations, Huygens’ construction makes their solution much easier (§2.8). A wave is essentially a temporary disturbance in a medium in stable equi-librium. Following the disturbance, the medium returns to equilibrium, and the energy of the disturbance is dissipated in a dynamic manner. The behaviour can be described mathematically in terms of a wave equation , which is a differential equation relating the dynamics and statics of small displacements of the medium, and whose solution is a propagating disturbance. The first half of the chapter will be concerned with such equations and their solutions.
- Christopher Lavers(Author)
- 2017(Publication Date)
- Thomas Reed(Publisher)
Initially, particles are undisturbed (a), but then one is disturbed by a vertical motion (b) (figure 2.2). This first particle vibrates about the equilibrium position, as time progresses, out to a maximum extension (c). But this first particle is physically connected or joined to the second by molecular forces holding the material together and so a restoring force starts to act upon the first molecule, bringing it back from its position of maximum extension. Because of the molecular forces holding the material together, the second particle is forced to repeat the motion of the first but slightly later in time (d), and so on. Similar effects occur for all other particles in the chain. The disturbance thus travels through the medium until the disturbance has passed completely by the first particle, which once more returns to its undisturbed equilibrium position (i)- through a variety of loss or dampening mechanisms. The particles thus move in a direction at right angles (orthogonal, or at 90 degrees) to the wave propagation direction, and is said to be a transverse wave . This type of wave motion can be demonstrated by giving a taunt string a flick at right angles to the direction of the string. Types of Waves 25 25 Propagation Distance Displacement abo ve and belo w the undisturbed postion Time Increasing i h g e d c b a f Figure 2.4: Transverse wave generated along a string, showing individual molecular motion developing over time. As we have already seen, sound waves are longitudinal, while waves on a string are transverse. Many other forms of wave motion can be built up from these two fundamental modes. For example, the waves on the surface of the sea, which have a complicated form, may simply be considered as combinations of both longitudinal and transverse wave motion out of step, since if a particle moves forwards, then downwards, backwards and upwards, it will actually describe a rotational motion.
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