This document provides an overview of fundamental concepts in acoustics and audio fundamentals. It discusses the physics of sound, how sound is processed by the ear and brain, concepts of loudness and pitch, principles of sound measurement including decibels and meters, properties of sound waves like reflection and absorption, and applications in architectural acoustics. Key topics covered include the anatomy of the ear, function of the cochlea, psychoacoustics, principles of sound pressure, intensity and power levels, characteristics of VU and peak meters, and the inverse square law governing sound wave propagation.

1. Sound Fundamentals

2. Content
The Physics of Sound
Sound and the Ear
The Cochlea(Inner ear)
Mental Processes
Level and Loudness
Pitch
Frequency Response and Linearity
Audio Level Metering
Acoustic Intensity Level, Acoustic Power Level,
Acoustic Pressure Level

3. The Decibel in Acoustics
Inverse Square Law
The VU and the Volume Indicator Instrument
The Phon
Velocity of Sound
Reflection and Refraction
Absorption
Root Mean Square Measurements
Selection of sound absorbing materials
Architectural Acoustics
Content

4. The Physics of Sound
In a medium filled with fluid like air or water, any change of
distribution(Pressure) of the fluid or the velocity of fluid
causes vibrations
Normally, in a room filled with air, the air molecules are
colliding and rebounding with room walls
If a wall of the room is moved inside the room the rebounding
is faster and if the wall is moved outside the room the
rebounding is slower

5. The Physics of Sound
The sound waves are caused by vibrations in any
medium
Speed of sound is 344m/s(1234 Km/hour)
Like all other energies sound energy also follows the
E = mc2 relationship

6. Sound also can pass through solids.
As the medium gets denser, the velocity of sound gets
increased.
Unlike electronic signals, sound is a mechanical wave
For humans, hearing is normally limited to
frequencies between about 20 Hz and 20,000 Hz (20
kHz)
The Physics of Sound

7. Sound and the Ear
Ear is the organ in the body that senses the intensity
and frequencies present in the sound
Audio equipments can only be designed well with a
good knowledge of the human hearing mechanism
The hearing sense results from acoustic, mechanical,
hydraulic, nervous, and mental processes in the
ear/brain combination, leading to the term
psychoacoustics
Psychoacoustics is the branch of science studying
the psychological and physiological responses
associated with sound (including speech and music)

8. Sound and the Ear: Structure of the
ear

9. The organization of the ear is divided into 3 parts:
Outer , middle and inner ear
The outer ear works at low impedance, the inner ear
works at high impedance, and the middle ear is an
impedance matching device
The visible part of the outer ear is called the pinna,
which plays a subtle role in determining the direction
of arrival of sound at high frequencies
It is too small to have any effect at low frequencies
Incident sound enters the auditory canal or meatus
Sound and the Ear: Structure of the
ear

10. Sound vibrates the eardrum or tympanic membrane,
which seals the outer ear from the middle ear
The inner ear or cochlea works by sound traveling
though a fluid
Sound enters the cochlea via a membrane called the
oval window
If airborne sound were to be incident on the oval
window directly, the serious impedance mismatch
would cause most of the sound to be reflected
The middle ear remedies that mismatch by providing
a mechanical advantage
Sound and the Ear: Structure of the
ear

11. The tympanic membrane is linked to the oval window
by three bones known as ossicles, which act as a lever
system such that a large displacement of the tympanic
membrane results in a smaller displacement of the
oval window but with greater force
Sound and the Ear: Structure of the
middle ear

12. The malleus applies a tension to the tympanic
membrane, rendering it conical in shape
The incus acts on the stapes through a spherical joint
The middle ear is normally sealed, but ambient
pressure changes will cause static pressure on the
tympanic membrane, which is painful
The pressure is relieved by the Eustachian tube, which
opens involuntarily while swallowing
The Eustachian tubes open into the cavities of the
head and must normally be closed to avoid one’s own
speech appearing deafeningly loud
Sound and the Ear: Structure of the
middle ear

13. The middle ear reflex is an involuntary tightening of
the tensor tympani and stapedius muscles, which
heavily damp the ability of the tympanic membrane
and the stapes to transmit sound by about 12 dB at
frequencies below 1 kHz
The main function of this reflex is to reduce the
audibility of one’s own speech
However, loud sounds will also trigger this reflex,
which takes some 60 to 120 ms to occur, too late to
protect against transients such as gunfire
Sound and the Ear: Structure of the
middle ear

14. The cochlea is a tapering
spiral cavity within bony
walls, which is filled with
fluid
The widest part, near the
oval window, is called the
base and the distant end is
the apex
The Cochlea

15. The cochlea is divided
lengthwise into three
volumes by Reissner’s
membrane and the
basilar membrane
The scala vestibuli and
the scala tympani are
connected by a small
aperture at the apex of
the cochlea known as
the helicotrema
The Cochlea

16. The vibration of the basilar membrane is sensed by the
organ of Corti, which runs along the center of the
cochlea
The deflection of hair cells in the organ of Corti
triggers nerve firings and these signals are conducted
to the brain by the auditory nerve
The basilar membrane is not uniform, but tapers in
width and varies in thickness in the opposite sense to
the taper of the cochlea
The part of the basilar membrane that resonates as a
result of an applied sound is a function of the
frequency
The Cochlea

17. The distance from the apex where the maximum
resonance occurs is a logarithmic function of the
frequency
Essentially the basilar membrane is a mechanical
frequency analyzer
The Cochlea

18. Mental Processes
The nerve impulses are processed in specific areas of
the brain that appear to have evolved at different
times to provide different types of information.
The time domain response works quickly primarily
aiding the direction-sensing mechanism and is older
in evolutionary terms
The frequency domain response works more slowly,
aiding the determination of pitch and timbre and
evolved later, presumably as speech evolved.
In early times, the most important aspect of the
hearing mechanism was the ability to determine the
location of the sound source

19. Mental Processes
As shown in figure, the
brain can examine several
possible differences
between the signals
reaching the two ears.

20. At high frequencies the sound becomes directional
enough for the head to shade the distant ear, causing
what is called interaural intensity difference
Phase differences are only useful at low frequencies
and shading only works at high frequencies
A transient has a unique aperiodic waveform, which
suffers no ambiguity in the assessment of interaural
delay (IAD) between two versions
A one-degree change in sound location causes an IAD
of around 10 μs
The smallest detectable IAD is a 6 μ s. This should be
the criterion for spatial reproduction accuracy
Mental Processes

21. Transient noises produce a pressure step whose
source is accurately and instinctively located
Mental Processes

22. The time of arrival of the transient at the two ears will
be different and will locate the source laterally within a
processing delay of around a millisecond.
Following the event that generated the transient, the
air pressure equalizes
The time taken for this equalization varies and allows
the listener to establish the likely size of the sound
source
In an audio system that claims to offer any degree of
precision, every component must be able to reproduce
transients accurately
Mental Processes

23. Level and Loudness
The ear can detect a sound pressure variation of only
2x105
Pascals root mean square (rms) and so this
figure is used as the reference against which the
sound pressure level (SPL) is measured
The sensation of loudness is a logarithmic function of
SPL; consequently, a logarithmic unit, the decibel,
was adopted for audio measurement
The dynamic range of the ear exceeds 130 dB, but at
the extremes of this range, the ear either is straining
to hear or is in pain

24. The frequency response of the ear is not at all
uniform and it also changes with SPL
The subjective response to level is called loudness
and is measured in phons
The phon scale is defined to coincide with the SPL
scale at 1 kHz, but at other frequencies the phon scale
deviates because it displays the actual SPLs judged by
a human subject to be equally loud as a given level at 1
kHz
Level and Loudness

25. Level and Loudness

26. Loudness is a subjective reaction and is almost
impossible to measure
In addition to the level-dependent frequency
response problem, the listener uses the sound not for
its own sake but to draw some conclusion about the
source
For example, most people hearing a distant
motorcycle will describe it as being loud. Clearly, at
the source, it is loud, but the listener has compensated
for the distance
Level and Loudness

27. Pitch
Pitch is an auditory perceptual property that allows
the ordering of sounds on a frequency-related scale
 Pitches are compared as "higher" and "lower" in the
sense associated with musical melodies which require
"sound whose frequency is clear and stable enough to
be heard as not noise”
Pitch is a major auditory attribute of musical tones,
along with duration, loudness, and timbre
Pitch may be quantified as a frequency, but pitch is
not a purely objective physical property; it is a
subjective psycho acoustical attribute of sound

28. Frequency Response and
Linearity
It is a goal in high-quality sound reproduction that
the timbre of the original sound shall not be changed
by the reproduction process

29. Fundamental requirement for quality sound
reproduction is that the response to all frequencies
should be equal
Frequency response is easily tested using sine waves
of constant amplitude at various frequencies as an
input and noting the output level for each frequency
Another way in which timbre can be changed is by
nonlinearity
Frequency Response and
Linearity

30. All audio equipment
has a transfer function
between the input and
the output, which
form the two axes of a
graph
Unless the transfer
function is exactly
straight or linear , the
output waveform will
differ from the input
Frequency Response and
Linearity

31. A nonlinear transfer function will cause distortion,
which changes the distribution of harmonics and
changes timbre
Frequency Response and
Linearity

32. The decibel is a logarithmic measuring system and
has its origins in telephony where the loss in a cable is
a logarithmic function of the length
Human hearing also has a logarithmic response with
respect to sound
The Decibel

33. Audio Level Metering
There are two main reasons for having level meters in
audio equipment: to line up or adjust the gain of
equipment and to assess the amplitude of the
program material.
The simplest level meter is essentially an AC
voltmeter with a logarithmic response
As the ear is logarithmic, the deflection of the meter
is roughly proportional to the perceived volume,
hence the term used is volume unit (VU) meter

34. Logarithmic Response Curve

35. Real audio signals are rich in short transients, which
pass before the sluggish VU meter responds
Consequently, the VU meter is also called the
virtually useless meter in professional circles
Broadcasters developed the peak program meter
(PPM), which is also logarithmic, but which is
designed to respond to peaks as quickly as the ear
responds to distortion
If a peak is so short that the PPM fails to indicate its
true level, the resulting overload will also be so brief
that the ear will not hear it
Audio Level Metering

36. A further feature of the PPM is that the decay time of
the meter is very slow so that any peaks are visible for
much longer and the meter is easier to read because
the meter movement is less violent
In broadcasting, the use of level metering and line-up
procedures ensures that the level experienced by the
listener does not change significantly from program
to program
Consequently, in a transmission suite, the goal would
be to broadcast recordings at a level identical to that
which was determined during production
Audio Level Metering

37. The term “ level ” is always used for a power
expressed in decibels
Apparent power E I or E2
⁄ Z
The average real or absorbed power is (E2
⁄ Z )cos θ
The reactive power is ( E2
⁄ Z )sin θ
Power factor cos θ
The term dBm is used when the W2 = 0.001 w
The Decibel in Acoustics

38. In acoustics, the ratios encountered most commonly
are changes in pressure levels
For reference pressure level 0.00002 N/m2
is used.
If the pressure is measured in pascals
The Decibel in Acoustics

39. Acoustic Intensity Level, LI
The acoustic intensity LI (the acoustic power per unit
of area—usually in W/m2
or W/cm2
) is found by

40. Acoustic Power Level, LW
Acoustic Power Level, LW is found by

41. Acoustic Pressure Level, LP
Acoustic Pressure Level, LPis found as follows
Consider the acoustic intensity at the surface of the
sphere of is 1 W/m2
From this we can calculate the Prms
where Wa is the total acoustic power in watts and ρc
equals 406 RAYLS and is called the characteristic
acoustic resistance
ρ is the density of air in kilograms per cubic meter
(kg/m 3 ), c is the velocity of sound in meters per
second (m/s)

42. The sound specific impedance is the ratio between
the sound pressure and the particle velocity it
produces.
The specific impedance is one rayl if unit pressure
produces unit velocity.
Knowing the acoustic watts, Prms is easy to find
Thus the LP must be
Acoustic Pressure Level, LP

43. The LP , LI , and LW at 0.282 m are the same numerical
value if the source is omnidirectional

44. Inverse Square Law
If we double the radius of the sphere to 0.564 m, the
surface area of the sphere quadruples because the
radius is squared in the area equation (A = 4 πr2
)
Thus the intensity (power per unit area) will drop to
one-fourth its former value
Now an intensity change from 1 W to 0.25 W/m2
can
be written as a decibel change
The acoustic intensity has dropped 6 dB in any given
area This effect is commonly called the inverse square
law change in level
Gravity, light, and many other physical effects exhibit
this rate of change with varying distance from a

45. The VU and the Volume
Indicator Instrument
If all audio signals were sine waves, we could insert a
dBm meter into the circuit and get a reading that
would correlate with both electrical and acoustical
variations
Unfortunately, audio signals are complex waveforms
and their rms value is not 0.707 times peak but can
range from as small as 0.04 times peak to as high as
0.99 times peak
To solve this problem, broadcasting and telephone
engineers designed a special instrument for
measuring speech and music in communication
circuits

46. The VU and the Volume
Indicator Instrument
This instrument was called VU(Volume Unit)
The VU scales on meter gives correct readings only when
the measurement is being made across the impedance for
which it is calibrated (usually 150 or 600 Ω )
Readings taken across the design impedance are referred
to as true levels, whereas readings taken across other
impedances are called apparent levels
Apparent levels can be useful for relative frequency
response measurements
When the impedance is not 600 Ω , the correction factor
of 10 log (600/ new impedance ) can be added to the
formula containing the reference level

47. Correction formula
where, apparent level = instrument indication +
attenuator or sensitivity indicator
The instrument should be calibrated to read a true
level of zero VU when an input of a 1000-Hz steady-
state sine wave signal of 0 dBm (0.001 W) is
connected to it
The VU and the Volume
Indicator Instrument

48. Calculating number of decades
on a frequency span
To find the relationship of the number of decades
between the lowest and the highest frequencies, use
the following equations

49. The Phon
The phon is a unit of loudness level for pure tones
At 1000 Hz every decibel is the equivalent loudness of
a phon unit
1 phon is equal to 1 dBSPL at a frequency of 1 kHz
For two different sounds within a band they are
added in the same manner as decibel readings
where LP1 and LP2 are the individual sound levels in dB

50. Equal Loudness Contours

51. Velocity of Sound
For a given frequency, the relation of the wavelength
to the velocity of sound in the medium is
Where c is velocity of sound in m/s
In dealing with many acoustic interactions, the
wavelength involved is significant and the ability to
calculate it is important.
Therefore we need to be able to both calculate and
measure the velocity of sound quickly and accurately

52. The velocity of sound varies with temperature to a
degree sufficient to require our alertness to it
The velocity of sound under conditions likely to be
encountered in connection with architectural acoustic
considerations is dependent on three fundamental
factors
1) γ is the ratio of specific heats and is 1.402 for
diatomic molecules (air molecules)
2) PS is the equilibrium gas pressure in Newtons per
square meter (1.013 105
N/m2
)
3) ρ is the density of air in kilograms per cubic meter
(kg/m3
)
Velocity of Sound

53. Velocity of Sound
The formula for velocity of sound is as follows
The density of air varies with temperature, and an
examination of the basic equations reveals that,
indeed, temperature variations are the predominant
influence on the velocity of sound in air
The velocity of sound is temperature dependent. The
approximate formula for calculating velocity is

54. Velocity of Sound

55. Reflection and Refraction
Sound can be reflected by hitting an object larger
than one-quarter wavelength of the sound
When the object is one-quarter wavelength or slightly
smaller, it also causes diffraction of the sound
(bending around the object)
Refraction occurs when the sound passes from one
medium to another
The velocity of sound increases with increasing
temperature

56. Reflection and Refraction
According to above equation, velocity of sound is
inversely proportional to ρ density of air
ρ is inversely proportional to temperature and hence
velocity of sound is directly proportional to
temperature
Therefore sound emitted from a source located on
the frozen surface of a large lake on a sunny day will
encounter warmer temperatures

57. As the wave diverges upward, causing the upper part
of the wave to travel faster than the part of the wave
near the surface.
This causes a lens-like action to occur, which bends
the sound back down toward the surface of the lake
Reflection and Refraction

58. Wind blowing against a sound source on a frozen
causes temperature gradients near the ground surface
that result in the sound being refracted upward
Wind blowing in the same direction as the sound
produces temperature gradients along the ground
surface that tend to refract the sound downward
Reflections from large boundaries, when delayed in
time relative to the direct sound, can be highly
destructive of speech
Reflection and Refraction

59. Absorption
Absorption is the inverse of reflection
For a given material, the absorption coefficient ( a ) is
where EA is the absorbed acoustic energy, EI is the
total incident acoustic energy and (1-a) is the reflected
sound
If a material has an a of 0.25, it will absorb 25% of all
sound energy having the same frequency and it will
reflect 75% of the sound energy having that frequency

60. Root Mean Square
Measurements
According to Ohm’s law, the power dissipated in a
resistance is proportional to the square of the applied
voltage
This causes no difficulty with direct current (DC), but
with alternating signals such as audio it is harder to
calculate the power
Consequently, a unit of voltage for alternating signals
was devised
The average power delivered during a cycle must be
proportional to the mean of the square of the applied
voltage

61. Root Mean Square
Measurements
An AC signal of a given number of volts rms will
dissipate exactly the same amount of power in a given
resistor as the same number of volts DC
for a sine wave the rms voltage is obtained by
dividing the peak voltage Vpk by the square root of 2.
However, for a square wave the rms voltage and the
peak voltage are the same

62. Root Mean Square
Measurements

63. Selection of sound absorbing
materials
A material’s sound absorbing properties can be
described as a sound absorption coefficient in a
particular frequency range
Most good sound absorbers readily transmit sound
There are three basic categories of sound absorbers:
Porous materials commonly formed of matted or
spun fibers
Panel (membrane) absorbers having an impervious
surface mounted over an airspace
Resonators created by holes or slots connected to an
enclosed volume of trapped air

64. Porous absorbers: Common porous absorbers include
carpet, spray-applied cellulose, aerated plaster,
fibrous mineral wool and glass fiber, open-cell foam,
and cast porous ceiling tile
All of these materials allow air to flow into a cellular
structure where sound energy is converted to heat
Porous absorbers are the most commonly used sound
absorbing materials
Thickness plays an important role in sound
absorption by porous materials
Selection of sound absorbing
materials

65. Selection of sound absorbing
materials
Porous absorbers

66. Panel Absorbers: Typically, panel absorbers are non-
rigid, non-porous materials which are placed over an
airspace that vibrates in a flexural mode in response
to sound pressure exerted by adjacent air molecules
Common panel absorbers include thin wood paneling
over framing, lightweight impervious ceilings and
floors, glazing and other large surfaces capable of
resonating in response to sound
Panel absorbers are usually most efficient at
absorbing low frequencies
Selection of sound absorbing
materials

67. Selection of sound absorbing
materials
Panel Absorbers

68. Selection of sound absorbing
materials
Resonators: Resonators typically act to absorb sound
in a narrow frequency range
Resonators include some perforated materials and
materials that have openings
The resonant frequency is governed by the size of the
opening, the length of the neck and the volume of air
trapped in the chamber
The classic example of a resonator is the Helmholtz
resonator, which has the shape of a bottle

69. Selection of sound absorbing
materials
Resonator

70. Architectural acoustics
In any enclosed volume the sound transmission gets
complicated
First consider, an enclosed space that has an internal
volume ( V ), usually measured in cubic feet
Second, it has a total boundary surface area ( S ),
measured in square feet
The average absorption coefficient ( a ) for all the
surfaces together is found by
Where s1,2,...n are the individual boundary surface
areas in square feet

71. Architectural acoustics
a1,2,…n are the individual absorption coefficients of the
individual boundary surface areas, and S is the total
boundary surface area in square feet

72. Sound paths in a concert hall

73. Build-Up of the Reverberant
Sound Field
Shown in figure is the reflection pattern
The initial-signal-delay gap is followed by a
succession of sound reflections

74. Build-Up of the Reverberant
Sound Field
The reverberation time of the room is defined as the
time for reflections of a direct sound to decay by
60 dB below the level of the direct sound
The sound arriving at the listener has at least three
distinct divisions:
1. The direct sound level LD
2. The early reflections level LRE (under 50 ms after LD)
3. The reverberant sound level LR