Theory of Sound Field

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 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.

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 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.

Syllabus of tutorials:

Study Objective:

Study materials:

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.

Note:

Further information:

https://moodle.fel.cvut.cz/courses/XP02TZP

Time-table for winter semester 2024/2025:

	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	roomT2:B2-48 Červenka M. 14:30–16:00 (lecture parallel1) Dejvice Konzultační
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table 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)