Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 5
Complex Time Signals
& Transfer Functions
Complex Time Signals
Several physical systems can be mathematically modeled
using differential equations.
The solu

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-26
TRANSMISSION BETWEEN TWO FLUIDS
AT OBLIQUE INCIDENCE
Introduction
In this lecture, we continue to explore propagation of sound
waves through two fluid media

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-19
CYLINDRICAL WAVES
Introduction
Just as we developed relation for spherical waves, we can also
develop relation for cylindrical waves. Three-dimensional
cyli

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 28
Waveguides & Transmission Lines
Waveguides and Transmission Lines
Waveguide is a structure, that guides waves. These waves may
be acoustical or electromagne

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-23
TRANSMISSION THROUGH TWO FLUID
MEDIA
Introduction
As a sound wave travelling in one medium, enters another
one, a fraction of its energy is transmitted thro

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE 21
SOUND PROPAGATION IN NON
HOMOGENOUS MEDIA
INTRODUCTION
In previous lecture, we had developed mathematical
formulations to understand propagation of acoustic

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-36
Radial Propagation Of Sound
Introduction
The applicability of 1-D wave equation for a Cartesian
reference frame is limited to sound propagation ducts, pipes

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-33
Sound Transmission Through A Thin
Rigid Partition
Introduction
On a large number of occasions, thin partitions are used to
provide acoustical insulation for

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-22
RAY PATHS
Ray Paths
The linear eikonal, i.e.
can be used to predict the
direction of the ray as it travels along a path. This holds valid if
the assumption

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-30
1-D Waves In Tubes
Open Tubes: Introduction
In previous two lectures, we developed relations for pressure
and velocity in closed tubes. In such cases, it wa

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-34
Transmission Through Thin
Partitions For Obliquely Incident
Waves
Introduction
Earlier, we had developed relation for transmission
coefficient T for acousti

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-37
Radial Propagation Of Sound
Solution For 1-D spherical Pressure
Wave
Eq. 36.7 represents propagation of a 1-D spherically
symmetric wave.
For a 1-D wave in

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-29
Transmission Line Equations
1-D Waves: Examples of a Closed Tube
Consider a tube which is rigidly closed at one end, while at its
other end, the air is exci

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-35
Transmission Through Three Media
Transmission Through Three Media
Several times, sound may pass through three different fluid
media at normal incidence. A c

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-32
KUNDTS APPARATUS
Introduction
Kundts apparatus is a device, originally invented by August
Kundt in 1866 to measure speed of sound. However, it may
also be u

SoundPropagation
Sound Propagation
throughMedia
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NachiketaTiwari
IndianInstituteofTechnologyKanpur
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Lecture40
Closure
Overview
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Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture-38
INTERFERENCE
Introduction
Earlier, we have developed relations for predicting pressure
and velocity for symmetric waves generated by monopoles.
Going forwa

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-31
1-D Waves In Tubes
Impedance In 1-D Tubes
Table 31.1
Characteristic
Impedance
Specific
Acoustic
Impedance
Infinitely Long
Tube
Z0=0c
Z0=0c
Finite Tube With
C

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-25
TRANSMISSION BETWEEN TWO FLUIDS
AT OBLIQUE INCIDENCE
Introduction
In this lecture, we continue to explore propagation of sound
waves through two fluid media

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 3
The Decibel Scale
The Decibel Scale
Decibel
Power
Pressure
Intensity
Adding and subtracting decibels
Coherent sources
Incoherent sources
Characterizing

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 4
The Decibel Scale
Adding Decibels
Three possible ways to add decibels
Adding dBs
40 dB + 40 dB = 80 dB
Adding powers
40 dB + 40 dB = 43 dB
Adding signal

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 6
Bode Plots
Bode Plots
Bode plots are graphical representations asymptotic
behavior of H(S), when S=j.
There are two types of Bode plots:
Magnitude
Phase p

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-12
WAVE PROPAGATION IN SOLIDS
In this lecture and also the next one, we will understand 1-D
wave propagation in solid media.
Examples of such waves may includ

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 14
Waves Propagation in Solids
Overview
Terminology: phasor, wave front, wave number,
phase velocity, and group speed
Wave propagation in:
Strings
Bars
Beams
Sh

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-11
1-D WAVE PROPAGATION IN LIQUIDS
For a perfect gas, we know that the p-v relationship during
acoustic propagation is adiabatic in nature and can be given
as:

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 2
Introduction
Overview - Terminology
Octave
Decade
Wave-number
Bandwidth
Tones
Noise
Octave & Decade
The human ear can sense sound corresponding to freq

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 7
Bode Plots
Bode Plots Depicting Phase
Bode plots for phase are asymptotic depictions of phase of
H(j). These plots have a low frequency asymptote and a high

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-15
3-D WAVE EQUATION
Introduction
In this lecture, we develop pressure wave equation applicable to
three-dimensional fluid medium. We will develop this equatio

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
LECTURE-16
3-D WAVE EQUATION
The Momentum Equation
Consider an imaginary small elemental volume dv of size
dx.dy.dz, which moves with the fluid it contains whose mass

Sound Propagation
through Media
Nachiketa Tiwari
Indian Institute of Technology Kanpur
Lecture 8
1-D Wave Equation
Introduction
As sound travels through air or other other fluids, it
generates pressure and velocity fluctuation in the medium.
These fluct