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Unformatted text preview: 8.1 Wave Phenomenon: Acoustics All wave motion provides a mechanism for the transfer of energy from one point to another without the physical transport of matter between those points. Specifically, mechanical wave motion is an energy-carrying disturbance (wave pulse) produced by the repeated periodic motion of the elastic medium . A sound wave is an example of a mechanical wave insofar as it is not capable of transmitting its energy through a vacuum. The repeating and periodic disturbance which moves through a medium from one location to another is referred to as a wave . By virtue of the speed (kinetic energy) and changing position (elastic potential energy) of the particles, energy is transmitted by the waveform . The assumption is made that the source of the wave pulse is periodic in that the source moves in a fixed path returning to each position and respective velocity after a definite time interval . In the absence of friction, this behavior is simple harmonic motion [SHM]. Transverse Waves In transverse wave pulses, the motion of the particles is perpendicular to the direction of wave propagation . Such a traveling wave in a mechanical system is the result of the disturbances in the position of the particles of the system from their normal positions, which moves or propagates through the system. Consider a wave pulse traveling in one dimension as in a string. The wave pulse maintains its same shape as it travels assuming negligible frictional forces and that the height or amplitude of the pulse does not appreciably affect the tension of the string. Although energy is transported through an elastic system, the total net displacement of each particle is zero. The waveform produced in a string whose free end is repeatedly moved vertically by a source exhibits simple harmonic motion. The vertical position (y) of the string at the source is given by the equation y=Asin(t " kx) . If the source moves in a sinusoidal fashion, then at any fixed value of time (t), the vertical position (y) of a particle is a sinusoidal function of its horizontal displacement (x). The speed (v) of any repetitive wave train through any medium equals the product of its frequency (f) and its wavelength (). v = f f = 1/T The wavelength of a wave pulse is the distance between any two successive points in phase . Particles in phase have the same vertical displacement and direction of horizontal motion such that the difference in their phase angles is either zero or some multiple of 360 o . The frequency of the wave, measured in hertz, equals the number of wavefronts passing a given point per given time interval or the reciprocal of the period (T). The points of maximum positive and negative vertical displacement from the equilibrium position or origin in a transverse wave are termed the crest and the trough . These points respectively possess maximum positive and negative elastic potential energy. At the point of inflection, the velocity of the wave velocity and thus its kinetic energy is a maximum...
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