Phys12 - Unit 12 Physical Properties of Waves I 12.1 12.2...

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1 Unit 12 Physical Properties of Waves I 12.1 Types of waves 12.2 Useful quantities in describing waves 12.3 Waves on a string 12.4 Sound waves 12.5 The frequency of a sound wave 12.6 Sound intensity 12.7 Human perception of sound 12.8 The Doppler effect 12.9 Superposition and interference 12.10 Standing waves 12.11 Beats 12.1 Types of waves A disturbance that propagates from one place to another is referred to as a wave. Waves propagate with well-defined speeds determined by the properties of the material through which they travel. For example, sound waves have different speeds in different materials. The following table lists a sampling of sound speed in various materials. Material Speed (m/s) Aluminum 6420 Steel 5960 Copper 5010 Plastic 2680 Fresh water (20 o C) 1480 Air (20 o C) 343 Waves carry energy and propagate it when the waves travel. There are two typical waves, namely, the transverse waves and the longitudinal waves.
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2 Transverse waves: The displacement of individual particles is perpendicular to the direction of propagation of the wave, e.g. holding one end of a string with another end fixed on the wall. When you swing your hands vertically, the waves propagate horizontally along the string and the particles of string moves up and down. Longitudinal waves: The displacement of individual particles is in the same direction as the direction of propagation of the waves, e.g. sound waves. The particles of air move back and forth such that a series of compression and rarefaction are observed. Note that the particle does not travel with the wave, but vibrating about its equilibrium position.
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3 12.2 Useful quantities in describing waves Wavelength: The distance over which a wave repeats, e.g. the distance between successive crests and the distance between successive troughs. Wavelength is quite often labeled as λ . The SI unit is, of course, meter, m. Angular wave number: The angular wave number is defined as π 2 = k . The SI unit is radian per meter. Angular frequency: It is the measure of how many radians the waves change in one second. It is labeled as ω . Frequency: The number of oscillation per unit time, f, where f 2 = . Period: The time for one oscillation, it is labeled as T , where 2 1 = = f T . Velocity: The distance that the wave travels per unit time is referred to as the velocity.
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4 The wave equation is: ) sin( ) , ( t kx y t x y m ω = , in general we have ) sin( ) , ( φ + = t kx y t x y m , where is the phase angle. A useful relation in waves: k f v λ = = . 12.3 Waves on a string The speed of a wave is determined by the properties of the medium through which it propagates. For a string of length L , there are two factors that vary the speed of a wave: (i) the tension in the string F , and (ii) the mass of the string. For the second factor, we should say it more precisely that the speed of a wave varies with the density of the string (mass per length) µ . The definition of is m/L . The unit is kg/m.
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This note was uploaded on 09/06/2010 for the course BSC PHY1417 taught by Professor Prof during the Spring '08 term at HKU.

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Phys12 - Unit 12 Physical Properties of Waves I 12.1 12.2...

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