Subject description - XP02TZP

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XP02TZP Theory of Sound Field
Roles:S Extent of teaching:2P
Department:13102 Language of teaching:
Guarantors:Jiříček O. Completion:ZK
Lecturers:Červenka M., Jiříček O. Credits:4
Tutors:  Semester:Z

Web page:


The aim of this course is deeper understanding the fundamentals of physical acoustics. The continuity equation, Euler and Navier-Stokes equations and the energy equation are derived from the prime laws of fluid dynamics. These equations are utilized for derivation of a linear wave equation under the acoustical approximation; its special solutions are discussed. General solutions of the wave equation and Helmholtz equation are formulated using the integrals of Kirchhoff-Helmholtz and Rayleigh. Using these integrals, some problems of acoustic radiation and diffraction are studied. Problem of the acoustic field description is further developed using the methods of Fourier acoustics.

Course outlines:

1. Recapitulation: differential operators, Gauss law, 1D wave equation, method of characteristics, d'Alembert solution of wave equation.
2. 3D wave equation, planar, spherical and cylindrical wave.
3. Acoustic particle, Lagrange and Euler description of fluid motion, material derivative, continuity equation.
4. Euler and Navier-Stokes equation, viscosity, rotational and irrotational field, velocity potential.
5. Energy equation, equation of state.
6. Acoustic approximation of the fluid-dynamics equations, wave equation for acoustic pressure and velocity potential.
7. Acoustic intensity, acoustic energy density, planar wave, specific acoustic impedance, representation using phasors.
8. Acoustic field generated by a pulsating sphere, radiated power, simple and volume source.
9. Homogeneous and inhomogeneous Helmholtz equation, free-field Green's function.
10. Helmholtz-Kirchhoff integral, application for a volume source, Sommerfeld radiation condition.
11. Rayleigh integral, far-field approximation, far-field of a circular piston, directivity.
12. Acoustic field at the axis of a circular piston, near-field, transition to far-field, Rayleigh distance.
13. Fourier transform of transient sound field, circular aperture diffraction.
14. Fourier acoustics: description of sound radiation, evanescent wave, acoustical holography.

Exercises outline:


1. D. T. Blackstock, Fundamentals of Physical Acoustics, Wiley-Interscience, 2000.
2. P. M. Morse, K. Uno Ingard, Theoretical Acoustics, Princeton University Press, 1987.
3. E. G. Williams, Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography, Academic Press, 1999.
4. J. W. Goodman, Introduction to Fourier Optics, Roberts and Company Publishers, 2004.
5. D. J. Griffiths, Introduction to Electrodynamics, Addison Wesley, 1999.


Foundations of physics, foundations of vector analysis, Founations of Fourier transform.


acoustics, sound field, wave equation, Helmholtz equation, Rayleigh integral.

Subject is included into these academic programs:

Program Branch Role Recommended semester
DOKP Common courses S
DOKK Common courses S

Page updated 16.6.2024 17:52:04, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)