Skip to main content
SpringerLink
Log in

Physical Fundamentals of Sound Fields

  • Chapter
  • First Online:
Analytic Methods of Sound Field Synthesis

Part of the book series: T-Labs Series in Telecommunication Services ((TLABS))

  • 1765 Accesses

Abstract

The present chapter outlines the mathematical and physical tools that are employed in the subsequent chapters. It is not written in a tutorial style but serves rather as a reference. The wave equation and its solutions in Cartesian as well as in spherical coordinates are introduced. Then, a number of useful representations of sound fields such as the wavenumber domain, spherical harmonics expansions, the angular spectrum representation, and alike are presented. The basis for the solutions to the problem of sound field synthesis is set by a discussion of useful integral relations such as the Rayleigh Integral and the Kirchhoff Helmholtz Integral.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abramowitz, M., & Stegun, I.A. (eds) (1999). Handbook of Mathematical Functions. New York: Dover Publications Inc.

    Google Scholar 

  • Ahrens, J., & Spors, S. (2009, June). Spatial encoding and decoding of focused virtual sound sources. In: Ambisonics Symposium.

    Google Scholar 

  • Ahrens, J., & Spors, S. (2010, March). An analytical approach to 3D sound field reproduction employing spherical distributions of non- omnidirectional loudspeakers. IEEE International Symposium, on Communications, Control and Signal Processing (ISCCSP) (pp. 1–5).

    Google Scholar 

  • Arfken, G., & Weber, H. (2005). Mathematical Methods for Physicists. San Diego: Elsevier Academic Press.

    MATH  Google Scholar 

  • Blackstock, D. T. (2000). Fundamentals of Physical Acoustics. Wiley and Sons, Inc: New York.

    Google Scholar 

  • Colton, D., & Kress, R. (1998). Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer.

    MATH  Google Scholar 

  • Condon, E. U., & Shortley, G. H. (1935). The Theory of Atomic Spectra. Cambridge: Cambridge University Press.

    Google Scholar 

  • Fazi, F., & Nelson, P. (2007). A theoretical study of sound field reconstruction techniques. In: 19th International Congress on Acoustics. (Sept.).

    Google Scholar 

  • Girod, B, Rabenstein, R, Stenger, A (2001). Signals and Systems. New York: Wiley.

    Google Scholar 

  • Gumerov, N. A., & Duraiswami, R. (2004). Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Amsterdam: Elsevier.

    Google Scholar 

  • Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete fourier transform. Proceedings of the IEEE, 66, 51–83.

    Article  Google Scholar 

  • Jessel, M. (1973). Acoustique Théorique: Propagation et Holophonie [Theoretical acoustics: Propagation and holophony]. New York: Wiley.

    Google Scholar 

  • Kennedy, R. A., Sadeghi, P., Abhayapala, T. D., & Jones, H. M. (2007). Intrinsic limits of dimensionality and richness in random multipath fields. IEEE Transactions on Signal Processing, 55(6), 2542–2556.

    Article  MathSciNet  Google Scholar 

  • Marathay, A. S., & Rock, D. F. (1980). Evanescent wave contribution to the diffracted amplitude for spherical geometry. Pramana, 14(4), 315–320.

    Article  Google Scholar 

  • Morse, P. M., & Feshbach, H. (1953). Methods of Theoretical Physics. Feshbach Publishing, LLC: Minneapolis.

    MATH  Google Scholar 

  • Nieto-Vesperinas, M. (2006). Scattering and Diffraction in Physical Optics. Singapore: World Scientific Publishing.

    MATH  Google Scholar 

  • Rabenstein, R., Steffen, P., & Spors, S. (1980). Representation of twodimensional wave fields by multidimensional signals. EURASIP Signal Processing Magazine, 14(4), 315–320.

    Google Scholar 

  • Wefers, F. (2008, March). OpenDAFF: Ein freies quell-offenes Software-Paket für richtungsabhängige Audiodaten [OpenDAFF: An open-source software package for direction-dependent audio data]. Proceedings of 34th DAGA (pp. 1059–1060). text in German.

    Google Scholar 

  • Weisstein, E. W. (2002). CRC Concise Encyclopedia of Mathematics. London: Chapman and Hall/CRC.

    Book  Google Scholar 

  • Williams, EG (1999). Fourier Acoustics: Sound Radiation and Nearfield Acoustic Holography. London: Academic.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deutsche Telekom Laboratories, Technische Universität Berlin, Ernst-Reuter-Platz 7, 10587, Berlin, Germany

    Jens Ahrens

Authors
  1. Jens Ahrens
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ahrens, J. (2012). Physical Fundamentals of Sound Fields. In: Analytic Methods of Sound Field Synthesis. T-Labs Series in Telecommunication Services. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25743-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25743-8_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25742-1

  • Online ISBN: 978-3-642-25743-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation