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Fundamentals of Acoustics

Prof. Venkata R. Sonti · IISc Bangalore

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About

The course teaches the partial differential equation that describes the behavior of sound, i.e., the wave equation. The course starts initially with lumped vibrations, then 1-D waves on strings and rods and then finally to 1-D and 3-D acoustic wave equations. The 1-D equation is solved using the assumed wave solution. The 3-D wave equation is solved using the Kirchhoff Helmholtz Integral Equation and the Green function. Several examples are solved in rectangular, cylindrical and spherical coordinate systems. Both interior and exterior problems are addressed.

Intended audience: M.Sc. and PhD students

Prerequisites: A course in vibrations of lumped systems.

Lectures

Week 1 Introduction to vibrations and waves

  1. The vibrating spring-mass-damper system YouTube
  2. Power calculations in a vibrating spring-mass-damper system YouTube
  3. Wave propagation on a string YouTube
  4. Examples of waves on strings: finite and semi-infinite cases. YouTube
  5. General solution to 1-D wave equation: physical insights. YouTube

Week 2 Waves propagation on strings and rods: 1-D wave equation

  1. Wave solution: real notation vs complex notation. YouTube
  2. The vibrating string with a general mechanical impedance. YouTube
  3. The forced finite string with an end mass. YouTube
  4. The one-D wave solution: physical insights. YouTube
  5. Longitudinal wave propagation in a rod. YouTube

Week 3 The Acoustic Wave Equation

  1. Forced semi-infinite and finite rods. YouTube
  2. The derivation of the acoustic wave equation. YouTube
  3. The derivation of the acoustic wave equation contd. YouTube
  4. The derivation of the acoustic wave equation contd. YouTube
  5. The derivation of the acoustic wave equation contd. YouTube

Week 4 Solutions to 1-D acoustic wave equation

  1. Sound propagation in piston driven semi-infinite and finite ducts. YouTube
  2. Acoustics inside a piston driven finite duct with a general end impedance. YouTube
  3. Time averaged power in a 1-D acoustic wave YouTube
  4. The Free Space Green Function in acoustics YouTube
  5. The Free Space Green Function contd. YouTube

Week 5 The Kirchhoff Helmholtz Integral Equation (KHIE)

  1. Various Green Functions and their uses YouTube
  2. Derivation of the interior Kirchhoff Helmholtz Integral Equation YouTube
  3. Derivation of the exterior Kirchhoff Helmholtz Integral Equation YouTube
  4. Acoustic wave equation in spherical coordinates. YouTube
  5. Legendre polynomials, spherical harmonics, orthogonality relations. YouTube

Week 6 Neumann and Dirichlet Green functions in spherical coordinates

  1. Spherical harmonics, Legendre polynomials and their orthogonality relations contd. YouTube
  2. Interior Neumann Green function. YouTube
  3. Exterior Neumann and Dirichlet Green functions. YouTube
  4. Pulsating sphere using the exterior Neumann Green function YouTube
  5. Equivalence of Neumann Green function and separation of variables solution. YouTube

Week 7 Exterior sound fields

  1. Sound from a pulsating sphere using boundary matching technique. YouTube
  2. Sound from a pulsating sphere using boundary matching technique contd. YouTube
  3. Sound radiation from a spherical cap on a rigid sphere using the Neumann Green function. YouTube
  4. Scattering of a plane acoustic wave from a rigid sphere YouTube
  5. Example to show that the surface in the KHIE is notional (not actual) YouTube

Week 8 Sound radiation from an oscillating piston placed in a rigid baffle

  1. The Rayleigh Integral YouTube
  2. Sound field of an oscillating piston in a rigid baffle YouTube
  3. Sound field of an oscillating piston in a rigid baffle contd. YouTube
  4. Physics of the sound field of an oscillating piston in a rigid baffle. YouTube
  5. Physics of the sound field of an oscillating piston in a rigid baffle contd. YouTube

Week 9 Interior sound fields

  1. Physics of the sound field of the oscillating piston (cap) on a rigid sphere. YouTube
  2. The Sommerfeld radiation condition YouTube
  3. Sound field inside a rigid walled box due to initial conditions. YouTube
  4. Sound field inside a rigid walled box due to a harmonic source YouTube
  5. Sound field inside a rigid walled hollow cylinder due to initial conditions YouTube

Week 10 Acoustic response inside a cylindrical enclosure and measures of sound

  1. Modeshape visualization inside a rigid walled cylinder YouTube
  2. Sound field inside a rigid walled hollow cylinder due to initial conditions contd. YouTube
  3. Green function inside a rigid walled cylinder. YouTube
  4. Measures of sound YouTube
  5. Measures of sound contd. YouTube

Week 11 Measures of sound including frequency analysis and integral transforms

  1. Average mean square value of different frequency sinusoids YouTube
  2. Frequency analysis of sounds in terms of third octave bands YouTube
  3. Transient solution of the wave equation using Fourier series YouTube
  4. Total solution of the harmonically forced wave equation with initial conditions using Fourier series YouTube
  5. Total solution of the forced wave equation with initial conditions using Laplace transform and Fourier series YouTube

Week 12 Miscellaneous topics: branched systems, Helmholtz resonator, radiation impedance, special techniques for wave…

  1. Branched systems, Helmholtz resonator YouTube
  2. The radiation impedance and acoustic power YouTube
  3. Acoustic potential, combined systems, special techniques for solving the acoustic wave equation YouTube
  4. Why do we take the real value of the solution in acoustic wave problems YouTube
  5. Course summary part 1 YouTube
  6. Course summary part 2. YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Mechanical Engineering
Teacher
Prof. Venkata R. Sonti
Level
Graduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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