By Earl G. Williams
Meant a either a textbook and a reference, Fourier Acoustics develops the speculation of sound radiation uniquely from the perspective of Fourier research. This robust viewpoint of sound radiation presents the reader with a complete and useful knowing in order to let her or him to diagnose and remedy sound and vibration difficulties within the twenty first Century. due to this attitude, Fourier Acoustics is ready to current completely and easily, for the 1st time in e-book shape, the idea of nearfield acoustical holography, an incredible strategy which has revolutionised the size of sound. depending little on fabric open air the publication, Fourier Acoustics can be important as a graduate point textual content in addition to a reference for researchers in academia and undefined. Key positive factors * The physics of wave propogation and sound vibration in homogeneous media *Acoustics, similar to radiation of sound, and radiation from vibrating surfaces *Inverse difficulties, akin to the speculation of nearfield acoustical holography *Mathematics of specialised capabilities, akin to round harmonics
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Extra resources for Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
41). kxo and kyo are the given wavenumbers of the modal pattern of the plate, and k~o is a function of them representing the variation of the pressure in the direction normal to the plate. 8 Wavenumber Space" k-space Vibrations due to wave phenomena and resulting radiation can be represented in kspace. Often this presentation is extremely powerful in displaying the physics underlying the phenomena. 6 and discussed in the captions. To illustrate further we continue with the infinite plate example of the last section.
Math. , 9, p. 2001. 36 CHAPTER 2. P L A \ T E WAVES which reduces to an identity. We will discuss Eq. 67) in more detail after we derive Rayleigh's first integral formula, which is better known than his second and is extensively used in the study of radiation from finite plates. Again we use the angular spectrum approach for the derivation. This formula relates the velocity on the surface to the pressure radiated and thus we look for the angular spectrum representation which relates normal velocity to pressure.
_@sin 0 sin 0). 100) The following figure, Fig. 13, provides a linear plot of the Fourier transform of the square piston using a three-dimensional plot. The value at the center is unity (I~I:/L 2 is plotted) and the levels are greatest along the coordinate axes. decaying rapidly from the center. Along the diagonals the decay is most rapid. 13: Surface plot of sinc(kxL/2) sinc(kyL/2). It is often desirable to plot the farfield on a dB scale, to show more dynamic range in the plot. 14 is a contour plot of Eq.