PHY2048_chapter16 - Chapter 16 Waves I In this chapter we...

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Chapter 16 Waves I In this chapter we will start the discussion on wave phenomena. We will study the following topics: Types of waves Amplitude, phase, frequency, period, propagation speed of a wave Mechanical waves propagating along a stretched string Wave equation Principle of superposition of waves Wave interference Standing waves, resonance (16 – 1)
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A wave is defined as a disturbance that is self-sustained and propagates in space with a constant speed Waves can be classified in the following three categories: 1. Mechanical waves. These involve motions that are governed by Newton’s laws and can exist only within a material medium such as air, water, rock, etc. Common examples are: sound waves, seismic waves, etc. 2. Electromagnetic waves. These waves involve propagating disturbances in the electric and magnetic field governed by Maxwell’s equations. They do not require a material medium in which to propagate but they travel through vacuum. Common examples are: radio waves of all types, visible, infra-red, and ultra- violet light, x-rays, gamma rays. All electromagnetic waves propagate in vacuum with the same speed c = 300,000 km/s 3. Matter waves. All microscopic particles such as electrons, protons, neutrons, atoms etc have a wave associated with them governed by Schroedinger’s equation. (16 – 2)
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Waves can be divided into the following two categories depending on the orientation of the disturbance with respect to the wave propagation velocity . If the disturba v Transverse and Longitudinal waves r nce associated with a particular wave is perpendicular to the wave propagation velocity, this wave is called " ". An example is given in the upper figure which depicts a mechanical wave that transverse propagates along a string. The movement of each particle on the string is along the -axis; the wave itself propagates along the -axis. y x A wave in which the associated disturbance is parallel to the wave propagation velocity is known as a " ". An example of such a wave is given in the lower figure. It is produced by a p lonitudinal wave iston oscillating in a tube filled with air. The resulting wave involves movement of the air molecules along the axis of the tube which is also the direction of the wave propagation velocity . v r (16 – 3)
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Consider the transverse wave propagating along the string as shown in the figure. The position of any point on the string can be described by a function ( , ). Further along the chapter we shall s y h x t = ( 29 ee that function has to have a specific form to describe a wave. Once such suitable function is: ( , ) sin - Such m h y x t y kx t ϖ = a wave which is described by a sine (or a cosine) function is known as " ". The various terms that appear in the expression for a harmonic waveare identified in the lower figure Function ( y x harmonic wave ( 29 , ) depends on and . There are two ways to visualize it. The first is to "freeze" time (i.e. set ). This is like taking a snapshot of the wave at . , The second is to set .
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