Theory of Sound Field
Code  Completion  Credits  Range 

XP02TZP  ZK  4  2P 
 Garant předmětu:
 Ondřej Jiříček
 Lecturer:
 Milan Červenka, Ondřej Jiříček
 Tutor:
 Supervisor:
 Department of Physics
 Synopsis:

The aim of this course is deeper understanding the fundamentals of physical acoustics. The continuity equation, Euler and NavierStokes 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 KirchhoffHelmholtz 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.
 Requirements:

Foundations of physics, foundations of vector analysis, Founations of Fourier transform.
 Syllabus of lectures:

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 NavierStokes equation, viscosity, rotational and irrotational field, velocity potential.
5.Energy equation, equation of state.
6.Acoustic approximation of the fluiddynamics 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, freefield Green's function.
10.HelmholtzKirchhoff integral, application for a volume source, Sommerfeld radiation condition.
11.Rayleigh integral, farfield approximation, farfield of a circular piston, directivity.
12.Acoustic field at the axis of a circular piston, nearfield, transition to farfield, Rayleigh distance.
13.Fourier transform of transient sound field, circular aperture diffraction.
14.Fourier acoustics: description of sound radiation, evanescent wave, acoustical holography.
 Syllabus of tutorials:
 Study Objective:
 Study materials:

1.D. T. Blackstock, Fundamentals of Physical Acoustics, WileyInterscience, 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.
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/XP02TZP
 Timetable for winter semester 2023/2024:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 Doctoral studies, daily studies (compulsory elective course)
 Doctoral studies, combined studies (compulsory elective course)
 Doctoral studies, structured daily studies (compulsory elective course)
 Doctoral studies, structured combined studies (compulsory elective course)