Skip to main content
Top

2019 | OriginalPaper | Chapter

2. Acoustical Background

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The mathematical background for functions defined on the unit sphere was presented in Chap. 1. Spherical harmonics played an important role in presenting and manipulating these functions. In this chapter, functions on the sphere are defined through the formulations of fields in three dimensions. Although sound fields are of primary concern in this book, which is oriented towards microphone arrays, the material presented here can be applied to scalar fields in general. This chapter begins by presenting the acoustic wave equation in Cartesian and spherical coordinates, with possible solutions. Solutions to the wave equation in spherical coordinates are shown to involve spherical harmonics and spherical Bessel and Hankel functions. Having formulated the fundamental solutions, sound fields due to a plane wave and a point source are presented, including an analysis of the effect of a rigid sphere introduced into the sound field. The latter is useful for describing the sound field around a microphone array configured over a rigid sphere, for example. The chapter concludes with a formulation of the three-dimensional translation of sound fields.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Arfken, G., Weber, H.J.: Mathematical Methods for Physicists, 5th edn. Academic Press, San Diego (2001)MATH Arfken, G., Weber, H.J.: Mathematical Methods for Physicists, 5th edn. Academic Press, San Diego (2001)MATH
2.
go back to reference Ben Hagai, I., Pollow, M., Vorlander, M., Rafaely, B.: Acoustic centering of sources measured by surrounding spherical microphone arrays. J. Acoust. Soc. Am. 130(4), 2003–2015 (2011)CrossRef Ben Hagai, I., Pollow, M., Vorlander, M., Rafaely, B.: Acoustic centering of sources measured by surrounding spherical microphone arrays. J. Acoust. Soc. Am. 130(4), 2003–2015 (2011)CrossRef
3.
go back to reference Chew, W.C.: Waves and Fields in Inhomogeneous Media, 1st edn. Wiley-IEEE Press, New York (1999)CrossRef Chew, W.C.: Waves and Fields in Inhomogeneous Media, 1st edn. Wiley-IEEE Press, New York (1999)CrossRef
4.
go back to reference Fisher, E.: Near-field spherical microphone array processing with radial filtering. IEEE Trans. Audio Speech Lang. Process. 19(2), 256–265 (2011)MathSciNetCrossRef Fisher, E.: Near-field spherical microphone array processing with radial filtering. IEEE Trans. Audio Speech Lang. Process. 19(2), 256–265 (2011)MathSciNetCrossRef
5.
go back to reference Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999)MATH Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999)MATH
6.
go back to reference Kinsler, L.E., Frey, A.R., Coppens, A.B., Sanders, J.V.: Fundamentals of Acoustics, 4th edn. Wiley, New York (1999) Kinsler, L.E., Frey, A.R., Coppens, A.B., Sanders, J.V.: Fundamentals of Acoustics, 4th edn. Wiley, New York (1999)
7.
go back to reference Peleg, T., Rafaely, B.: Investigation of spherical loudspeaker arrays for local active control of sound. J. Acoust. Soc. Am. 130(4), 1926–1935 (2011)CrossRef Peleg, T., Rafaely, B.: Investigation of spherical loudspeaker arrays for local active control of sound. J. Acoust. Soc. Am. 130(4), 1926–1935 (2011)CrossRef
8.
go back to reference Williams, E.G.: Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography. Academic, New York (1999) Williams, E.G.: Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography. Academic, New York (1999)
Metadata
Title
Acoustical Background
Author
Boaz Rafaely
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-99561-8_2