MIT 6 013 - Acoustic waves (23 pages)

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Acoustic waves



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Acoustic waves

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Lecture Notes


Pages:
23
School:
Massachusetts Institute of Technology
Course:
6 013 - Electromagnetics and Applications
Electromagnetics and Applications Documents

Unformatted text preview:

Chapter 13 Acoustics 13 1 Acoustic waves 13 1 1 Introduction Wave phenomena are ubiquitous so the wave concepts presented in this text are widely relevant Acoustic waves offer an excellent example because of their similarity to electromagnetic waves and because of their important applications Beside the obvious role of acoustics in microphones and loudspeakers surface acoustic wave SAW devices are used as radio frequency RF filters acoustic wave modulators diffract optical beams for real time spectral analysis of RF signals and mechanical crystal oscillators currently control the timing of most computers and clocks Because of the great similarity between acoustic and electromagnetic phenomena this chapter also reviews much of electromagnetics from a different perspective Section 13 1 2 begins with a simplified derivation of the two main differential equations that characterize linear acoustics This pair of equations can be combined to yield the acoustic wave equation Only longitudinal acoustic waves are considered here not transverse or shear waves These equations quickly yield the group and phase velocities of sound waves the acoustic impedance of media and an acoustic Poynting theorem Section 13 2 1 then develops the acoustic boundary conditions and the behavior of acoustic waves at planar interfaces including an acoustic Snell s law Brewster s angle the critical angle and evanescent waves Section 13 2 2 shows how acoustic plane waves can travel within pipes and be guided and manipulated much as plane waves can be manipulated within TEM transmission lines Acoustic waves can be totally reflected at firm boundaries and Section 13 2 3 explains how they can be trapped and guided in a variety of propagation modes closely resembling those in electromagnetic waveguides where they exhibit cutoff frequencies of propagation and evanescence below cutoff Section 13 2 4 then explains how these guides can be terminated at their ends with open or closed orifices thus forming



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