Learn · Fundamentals of Acoustics
Lecture 55 of 61Week 11 Measures of sound including frequency analysis and integral transforms
Total solution of the forced wave equation with initial conditions using Laplace transform and Fourier series
Prof. Venkata R. Sonti · IISc Bangalore
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- Fundamentals of Acoustics, IISc Bangalore (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- The vibrating spring-mass-damper system
- Power calculations in a vibrating spring-mass-damper system
- Wave propagation on a string
- Examples of waves on strings: finite and semi-infinite cases.
- General solution to 1-D wave equation: physical insights.
- Wave solution: real notation vs complex notation.
- The vibrating string with a general mechanical impedance.
- The forced finite string with an end mass.
- The one-D wave solution: physical insights.
- Longitudinal wave propagation in a rod.
- Forced semi-infinite and finite rods.
- The derivation of the acoustic wave equation.
- The derivation of the acoustic wave equation contd.
- The derivation of the acoustic wave equation contd.
- The derivation of the acoustic wave equation contd.
- Sound propagation in piston driven semi-infinite and finite ducts.
- Acoustics inside a piston driven finite duct with a general end impedance.
- Time averaged power in a 1-D acoustic wave
- The Free Space Green Function in acoustics
- The Free Space Green Function contd.
- Various Green Functions and their uses
- Derivation of the interior Kirchhoff Helmholtz Integral Equation
- Derivation of the exterior Kirchhoff Helmholtz Integral Equation
- Acoustic wave equation in spherical coordinates.
- Legendre polynomials, spherical harmonics, orthogonality relations.
- Spherical harmonics, Legendre polynomials and their orthogonality relations contd.
- Interior Neumann Green function.
- Exterior Neumann and Dirichlet Green functions.
- Pulsating sphere using the exterior Neumann Green function
- Equivalence of Neumann Green function and separation of variables solution.
- Sound from a pulsating sphere using boundary matching technique.
- Sound from a pulsating sphere using boundary matching technique contd.
- Sound radiation from a spherical cap on a rigid sphere using the Neumann Green function.
- Scattering of a plane acoustic wave from a rigid sphere
- Example to show that the surface in the KHIE is notional (not actual)
- The Rayleigh Integral
- Sound field of an oscillating piston in a rigid baffle
- Sound field of an oscillating piston in a rigid baffle contd.
- Physics of the sound field of an oscillating piston in a rigid baffle.
- Physics of the sound field of an oscillating piston in a rigid baffle contd.
- Physics of the sound field of the oscillating piston (cap) on a rigid sphere.
- The Sommerfeld radiation condition
- Sound field inside a rigid walled box due to initial conditions.
- Sound field inside a rigid walled box due to a harmonic source
- Sound field inside a rigid walled hollow cylinder due to initial conditions
- Modeshape visualization inside a rigid walled cylinder
- Sound field inside a rigid walled hollow cylinder due to initial conditions contd.
- Green function inside a rigid walled cylinder.
- Measures of sound
- Measures of sound contd.
- Average mean square value of different frequency sinusoids
- Frequency analysis of sounds in terms of third octave bands
- Transient solution of the wave equation using Fourier series
- Total solution of the harmonically forced wave equation with initial conditions using Fourier series
- Total solution of the forced wave equation with initial conditions using Laplace transform and Fourier series
- Branched systems, Helmholtz resonator
- The radiation impedance and acoustic power
- Acoustic potential, combined systems, special techniques for solving the acoustic wave equation
- Why do we take the real value of the solution in acoustic wave problems
- Course summary part 1
- Course summary part 2.