n the Chapter on energy, we studied in some detail the behaviour of a single particle. We found that the concepts of kinetic and potential energy usefully describe the motion of a particle. A particle is point-like in the sense that at any instant it occupies a single point. The natural generalization from a single particle is to a continuous body. Continuous bodies are of two kinds, namely rigid and fluid. A rigid body, even though it is extended over space, is essentially like a point particle, since all of its points move together. Fluid bodies are liquid and gaseous. Extended bodies are that are spread over space are called a medium. Fluid bodies such as the atmosphere, oceans and so on have new features not present in particles. Fluid bodies have two kinds of motion that are commonly observed. Namely, one in which there is a net transport of matter such as in the flow of river water and the other being periodic motion such as the motion of a life buoy, which never strays very far from its position of equilibrium. Elastic bodies lie somewhere between rigid and fluid media. In the case of say the flow of a river the entire medium is in motion, and there is a net physical transport of the particles of water from the source of the river to the sea. The study of the motion of the material forming a medium, water in the case of a river, is studied in the discipline of fluid mechanics. In addition to net material movement, a medium has a simpler form of motion. Anyone who has been to a beach has seen ocean waves traveling on the surface of the ocean. Such oscillatory motion of the medium is generically called waves. Wave motion pervades nature; waves on an ocean or in a bathtub are familiar to all. What is equally familiar but may not be recognized as originating in waves, is the whole phenomenon of sound, which is the response of the ear to pressure waves in air. There are more complex forms of waves such as earthquakes, radio and television waves, thermal waves, and non-classical waves that appear in quantum mechanics called probability waves, and so on. What distinguishes wave motion from the behavior of a particle is that a wave is spread out over space, and it tends to consist of periodic oscillations of some underlying medium, be it the water of the ocean or the air around us. For example, a life buoy on the ocean's surface will bob up and down about its equilibrium position as the wave passes through it. Similarly, sound propagates by the air particles oscillating about their equilibrium position. When we hear a sound, the energy in the sound wave is deposited on our ear drums, causing the sensation of sound. The concept of energy is essential for understanding wave motion, as it is for so many other central phenomena of physics. All waves have in common the fact that they are disturbances of a continuous media - for example air or water - in which energy and momentum are transferred from one part of space to another without the net physical transference of matter. The example of waves shows us how subtle and pervasive are the various forms of energy. Waves are classified as transverse and longitudinal, depending on the kind of vibration or oscillation that the underlying media in undergoing. The simplest possible wave is one that repeats its shape, and allows us to study only a finite portion of an otherwise infinitely spread out medium. Such a wave is called a simple wave, and its fixed pattern repeats itself throughout the medium. Most waves we see in daily life are far from simple, and look irregular and non-periodic. There is a branch of mathematics, called Fourier Analysis, that shows how any arbitrary and complicated wave can be resolved into a sum of simple waves. Hence, instead of considering complicated oscillatory motion for the entire medium, we need to study only simple wave which consists of only a finite pattern that repeats itself. An example of simple wave-motion is what one generates by, say, dropping a piece of stone into water. What we observe are ripples, which are waves, created in water. We make the idealization that the pattern of the ripples propagates forever; this idealization is similar to the one made in ignoring friction in Newtonian mechanics, and is very useful in understanding the essential properties of real waves. Hence, the idealized simple wave has a fundamental pattern, say the height and length of a single ripple, that is repeated throughout the medium.

Joey.