Electroacoustics

1. Electroacoustics 550.516
Lecture 1

2. Class Information
 Course Description and Syllabus
 Questionnaire – please fill out and e-mail to
me
 List of Software
 Project Description

3. Texts for the Class
REQUIRED
MATERIALS
Loudspeaker Handbook Second Edition by John Eargle
The Microphone Book Second or Third Edition by John Eargle
BIBLIOGRAPHY Loudspeaker and Headphone Handbook by Borwick
High Performance Loudspeakers by Colloms
Introduction to Electroacoustics & Audio Amplifier Design by Leach
Electroacoustics by Mendel Kleiner
Loudspeaker Design Cookbook by Dickason
Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers
and Rooms by Floyd Toole

4. Materials Available in
Blackboard
 A Brief History of Electroacoustics
 Basic Principles of Sound
 Fundamentals of Acoustics
 Syllabus

5. Why Should One Care About
Electro-acoustics?
• Recording acoustic events.
• Microphones
• Sensors
• Amplification of acoustic events.
• Microphones
• Sensors
• Loudspeakers
• Playback or monitoring of electronic signals such as musical
recordings, electronic instruments, etc..
• Loudspeakers
• Headphones
• Use of electro-acoustical devices for sound manipulation.
• Loudspeakers
• Buzzers & Shakers
• Microphones
• Sensors
• Noise and vibration control

6. Recording, for example.
 As an artist, audio engineer, etc., what is
the goal?
 The conveyance of ideas or acoustical events.
 These particular ideas or events are ultimately
perceived by the brain of the listener, which is a
combination of chemical and electrical cues.
 We can't transmit from brain to brain directly, yet.
Telepathy, nerve induction, Vulcan mind meld, etc.
have not been developed so far.

7. Transmission, Storage, and
Retrieval/Reproduction
 Since we can't transmit from brain to brain,
we must use different forms of transmission.
 These forms require many different forms of
energy.
 Changing from one form of energy to
another is transduction.
 A device which transforms one type of
energy to another is a transducer.

8. Human Transduction
• For example,
the human
auditory system
uses
transducers.
• Acoustical to
mechanical to
electrical and
chemical.

9. Storage and Retrieval
 All we need for transmission of live acoustical
events is the event itself and a human to
perceive it. A live orchestra, for example.
 What if we want to store and retrieve it?
 There are no means of storing acoustical
energy for arbitrary lengths of time.
 We must use other energy forms.
 One of the first such systems was wax tubes
 Acoustic → mechanical → acoustic
 Relatively low fidelity
 200Hz-4kHz
 Low S/N., etc.
 Note the horn used for increasing the acoustic
efficiency.

10. More Transduction
 We want better fidelity than the wax cylinder. → Phonograph,
magnetic tape, optical disc, silicon, etc..
 Let's look at the recording chain for making a compact disc.
 Acoustic event →
 Microphone(s) [acoustical to mechanical to electrical/magnetic] →
 Recording device, signal manipulation [electrical] →
 Laser [electrical to optical to mechanical] →
 Disc [mechanical]

11. Retrieval
• Laser  optical to electrical
• Amplifiers, etc.  electrical
• Loudspeakers, headphones, etc. 
electrical to mechanical to acoustical

12. Musical Instruments
• Most musical instruments we think of
convert mechanical energy into acoustic
energy.
• Brass/woodwinds – air from the lungs into
standing waves in the instrument.
• Percussion – mechanical force from the
striking implement creates vibration in the
instrument.
• Some instruments, such as synthesizers,
do not make any sound until they are
coupled to a loudspeaker system.

13. Door to Door
• If we consider the entire chain of
transduction from the movement of the
performer to the brain of the listener
there are an astounding number of
transduction events!
• Transduction is inherently difficult, lossy
and usually introduces distortion.
• Distortion is usually, but not always,
undesirable and we typically want to
minimize it.

14. Distortion
• Alteration of the original signal.
• Linear
• Frequency spectrum (e.g. EQ)
• Reflections
• Gain
• Non-linear – usually adds new frequencies.
• Clipping
• Intermodulation, etc.
• Compression
• Usually what people mean when the say
distortion.

15. Critical
• The distortion created during transduction is often
much greater than that produced anywhere else in
the production-reproduction chain.
• Typical amplifier: >0.1% THD
• Coding-decoding: >0.0001% THD
• Loudspeakers: as much as 1-3% in mid-band, can be
much greater at low frequencies.
• Frequency response
• +/-0.5dB over a wide bandwidth not uncommon for most
electronics.
• Microphones or loudspeakers with +/-1dB over the
audible spectrum are rare. +/-10dB or more not
uncommon for either.
• Therefore, much attention must be paid to the
transducers in a system if one cares about fidelity.

16. Desirable Distortion in
Electroacoustics
 Part of The Instrument
 Speaker in an electric or bass guitar rig
 Instrument pickups
 As an effect
 Frequency shaping
 Adding distortion
 As a warning
 Too loud
 Reaching physical limits

17. Electro-Acoustics
 Microphones, loudspeakers and
headphones are electro-acoustic
devices.
 They transform acoustic energy to
mechanical energy to electrical energy
and vice versa.
 As such, they form an indispensable part
of the audio production-reproduction
system.

18. Topics of Study for the
Course
 The History of Electroacoustics
 Transducer Theory
 Moving coil system
 Electrical analogies
 Acoustical properties
 Construction & materials
 Magnetics
 Non-linearities
 Electrostatic and planar magnetic transducers

19. Topics of Study for the
Course
 Loudspeaker Systems
 Low frequency systems
 Crossovers
 Signal processing
 Arrays
 Horns
 Planar and line source loudspeakers

20. Topics of Study for the
Course
• Electrical interface
• Cabling and other losses
• Impedance matching
• Amplifiers
• Signal processing
• Power considerations

21. Topics of Study for the
Course
• Acoustical interface
• Room interactions
 Headphones
 Construction and materials
 Acoustic properties
 Special measurement techniques

22. Topics of Study for the
Course
 Microphones
 Construction
 Theory
 Polar patterns
• Electrical interface
• Measurement
• Other Electro-acoustical Devices
• Musical instrument pick-ups
• Piezo-electric devices
• Exotic transducers

23. Pre-requisites
• Basic electrical engineering: resistors,
capacitors, basic circuits, etc.
• Basic physics: waves, f=ma, etc.
• Basic acoustics
• If you lack understanding in any of these
areas, you’ll have some catching up to
do.

24. Electroacoustics History
 Read “A Brief History of Electroacoustics”
 1800: Volta invents the electrical battery.
 1819: Oersted discovers magnetic field
surrounding wire carrying current.

25. Electroacoustics History pg.2
 1827: Ohm discovers relationship
between voltage, current and
resistance.
 1831: Faraday discovers concept of
mutual induction.

26. Electroacoustics History pg.
3
 1837: Telegraph developed
 1860-1877: Telephone developed
 1874: Siemens designs
electromechanical relay.

27. Electroacoustics History pg.
4
 1876: Phonograph developed
 1877: Carbon button microphone
developed
 1880: Prescott and Curie discover
piezoelectric effect

28. Electroacoustics History pg.
5
 1889: dynamic cone driver
developed by Oliver Lodge based
on Siemens relay

29. Electroacoustics History pg.
6
 1900-1925: spread of electricity
availability
 1904: development of vacuum tube
rectifier
 1906: development of vacuum tube
triode

30. Electroacoustics History pg.
7
 1917 - Development of the condenser
microphone
RCA Model 3A Condenser Mic

31. Loudspeaker Systems
History
 1910's-1930's: horn based systems. Single ended
triode based amps (~1W).
 1930's-1950's: Increased use in film, compression
drivers, high power amps, multichannel sound,
coaxial loudspeakers, LP records.
 1950-1975: acoustic suspension (sealed)
enclosures, radial horns, Thiele-Small parameters,
horn improvements, more power.
 1975-present: more power, DSP, powerful
measurement capability, modeling, active control,
etc.

32. Loudspeaker Systems
Trajectory
 Loudspeakers have been around since
1889 (Lodge). Haven’t we figured them
out yet?
 Loudspeakers and microphones are very
complex devices, despite their apparent
simplicity.
 Advancements
 Measurement
 Materials Science
 Computer Aided Design and Modelling
 Amplifier Design and Signal Processing

33. Fundamentals of Acoustics
 Read Fundamentals of Acoustics
 Read Basic Principals of Sound

34. What Is Sound?
• An acoustic or mechanical wave in an
elastic medium.
• Elastic mediums: air, water, concrete,
steel, etc.
• For sinusoidal waves:
𝑥 𝑡 = 𝑅𝑒 𝑥0𝑒𝑗𝜔𝑡
= 𝑥0 cos 𝜔𝑡 + 𝜑
Where: 𝑥0 = 𝑐𝑜𝑚𝑝𝑙𝑒𝑥 𝑝ℎ𝑎𝑠𝑜𝑟, 𝑥0 = 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒,
𝜔 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 2𝜋𝑓, 𝜑 = 𝑝ℎ𝑎𝑠𝑒

35. What is sound? pg. 2
 Period = T = 1/f in seconds (s)
 How long it takes one cycle of sound to
propagate.
 Wavelength = λ in meters (m)
 The distance the wave travels in one cycle.
 Speed of sound = c (m/s)
 The velocity of sound in the medium.
 Velocity of the wave itself, not the particles of
the medium.

36. Sound In Air
• In air, the speed of sound, 𝑐 ≅ 345 𝑚
𝑆
• We assume an adiabatic process (heat is not
transferred).
𝑐 =
𝛾𝑃0
𝜌0
• 𝛾 = 1.4, The ratio of specific heat of air at constant pressure to the
specific heat at constant volume
• 𝑃0 = 1.013 × 105𝑃𝑎, static air pressure
• 𝜌0 = 1.18 𝑘𝑔 𝑚3, density of air
• Changes with temperature, altitude, humidity
• 𝑐 = 331.4 + 0.607℃ 𝑚 𝑆 at sea level.

37. Human Hearing
• Frequency range: roughly 20-20kHz
• Can be sensed above and below with sufficient
amplitude.
• Changes with age, exposure to loud sounds,
illness, drugs, etc.
• Humans sense changes in frequency not
linearly, but more logarithmically, so we
generally use logarithmic scales.
• One decade: f2 = 10f1, one octave: f2 = 2f1
•
1
𝑥
𝑜𝑐𝑡𝑎𝑣𝑒𝑠 =
𝑓2
𝑓1
= 2
1
𝑥

38. Human Hearing pg. 2
• Dynamic range: roughly 130dBSPL.
• 𝑆𝑃𝐿 = 20 log
𝑃𝑟𝑚𝑠
𝑃𝑟𝑒𝑓
dB
• Pref is the quietest audible sound (at 1kHz).
• 𝑃𝑟𝑒𝑓 = 2 × 10−5𝑃𝑎 = 20𝜇𝑃𝑎 = 0𝑑𝐵𝑆𝑃𝐿
• Threshold of pain ≈ 130dBSPL re 20μPa
• 130𝑑𝐵 = 63.25𝑃𝑎,
63.25
0.00002
= 3,162,277.66
• 1Pa = 94dBSPL re 20μPa, a common
reference point

39. Human Hearing, pg 3
• 1 atmosphere = 101325 Pa
• So, the loudest possible non-rectified
sound is 101325 Pa = 194dBSPL
• Above this level, louder pressure waves
are possible, but the negative going
portion cannot drop below vacuum.
• Saturn V rocket = 204dBSPL
• Krakatoa volcano eruption = 170dBSPL at
100 mi. distant!

40. Equi-loudness
 The human hearing
mechanism does not
respond to SPL at all
frequencies equally.
 In the reading, the older
Fletcher-Munson curves
are referenced.

41. Equi-loudness and Bass
Reproduction
• Note that the equi-loudness curves are compressed at
low frequencies.
• To increase from 40 to 60 phons at 1kHz requires a
20dBSPL increase.
• At 20Hz, it only takes 10dBSPL to increase from 40 to
60 phones.
• This basically (bass-ically, ha!) says that a 0.5dB SPL
change is 1 phon louder.
• Another way of looking at it is that we are more
sensitive to SPL changes in the low frequencies, even
though they need to be louder to begin with. Keep this
in mind when analyzing a loudspeaker’s low frequency
performance.

42. Definitions
• Sound Pressure – deviation in the static
local air pressure.
• Particle Velocity – speed of a particle of
air in a sound wave. Not the speed of
the wave.
• Particle Displacement – distance from
equilibrium of a particle of air in a sound
wave.

43. Acoustic Power and
Intensity
• Acoustic Watts (W) = J/S
• J = joules, work/energy
• S = seconds, time
• Intensity = W/m2, energy flow per unit
area

44. Plane Wave
• Amplitude is constant normal to the
direction of travel.
• Pressure is in phase with particle
velocity.
• Not physically realizable in free air.
• Functionally used in plane wave tubes.

45. Plane Wave Equations
 Pressure in the positive X-direction :
𝑝𝑥+ = 𝐴𝑒𝑗(𝜔𝑡−𝑘𝑥)
 A = amplitude
 ω = frequency = 2πf
 t = time
 k = wave number =
2𝜋
𝜆
=
2𝜋𝑓
𝑐

46. Plane Wave Equations
• Particle velocity: 𝑢 =
−1
𝑗𝜔𝜌0
𝑑𝑝
𝑑𝑥
• 𝑢 =
𝐴
𝜌0𝑐
𝑒𝑗(𝜔𝑡−𝑘𝑥)
=
𝑝
𝜌0𝑐
• Particle displacement: 𝜉 = 𝑡
𝑢 𝑑𝑡 ζ =
𝐴
𝜌0𝑐𝑗𝜔
𝑒𝑗(𝜔𝑡−𝑘𝑥)
=
𝑝
𝑗𝜔𝜌0𝑐
• Velocity and pressure are in phase.
• Particle displacement lags by 90
degrees.

47. Simple Point Source
• Sound emanates from infinitely small
point.
• Produces spherical waves.
• Also not realizable, but sources do
approach this ideal.

48. Point source equations
 Pressure: p =
𝐴
𝑟
𝑒𝑗(𝜔𝑡−𝑘𝑟)
 r = distance from source (radius)
 Note that distance is now a factor in the
amplitude!

49. Point Source Equations
 Particle velocity: 𝑢 = 1 −
𝑗
𝑘𝑟
𝐴
𝜌0𝑐𝑟
𝑒𝑗(𝜔𝑡−𝑘𝑟) =
𝑝
𝜌0𝑐
1 −
𝑗
𝑘𝑟
 Particle displacement ζ =
𝑝
𝜌0𝑐
1
𝑗𝜔
−
𝑐
𝜔2𝑟
 Note velocity becomes like a plane wave at
large r.
 At small r, the relationship between pressure
and velocity approaches 90 degrees.
 These differences between plane and spherical
waves becomes particularly important to
microphone behavior.

50. Inverse Square Law for
Spherical Waves
 𝐼 =
𝑊
4𝜋𝑟2 , 𝑤ℎ𝑒𝑟𝑒 𝐼 = 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦, 𝑊 =
𝑝𝑜𝑤𝑒𝑟 𝑎𝑛𝑑 𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠
 𝑝 = 𝐼𝜌0𝑐, 𝑤ℎ𝑒𝑟𝑒 𝜌0𝑐 =
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑎𝑐𝑜𝑢𝑠𝑡𝑖𝑐𝑎𝑙 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎𝑖𝑟
 𝑙𝑒𝑡 𝐼𝑟 =
𝑊
4𝜋𝑟2 , 𝑡ℎ𝑒𝑛 𝐼2𝑟 =
𝑊
4𝜋 2𝑟 2
 𝑝𝑟 =
𝑊𝜌0𝑐
4𝜋𝑟2 , 𝑎𝑛𝑑 𝑝2𝑟 =
𝑊𝜌0𝑐
4𝜋 2𝑟 2

51. Inverse Square Law for
Spherical Waves
 𝑝2𝑟 =
1
2
𝑊𝜌0𝑐
4𝜋𝑟2 =
1
2
𝑝𝑟
 𝑑𝐵 = 20 log
𝑝2𝑟
𝑝𝑟
= 20log 0.5 = −6.02
 SPL halves for each doubling of
distance. For any two distances from a
source, the difference in SPL is:
 𝑑𝐵 = 20 log
𝑑1
𝑑2

52. Inverse Square Law for
Spherical Waves

53. Volume Velocity (U)
• V= volume displaced
• Sd= surface area of source
• x = displacement
• U = volume velocity
• u = velocity
• 𝑉 = 𝑆𝑑𝑥, 𝑈 = 𝑆𝑑
𝑑𝑥
𝑑𝑡
= 𝑆𝑑𝑢
• Volume velocity is important to
loudspeaker behavior.

54. Acoustic Impedance
• Acoustic impedance is the pressure
divided by the particle velocity times the
surface area:
• 𝑍 =
𝑝
𝑢𝑆
• It is frequency dependent.
• In general, it indicates how much sound
pressure is generated by a given
amount of particle vibration at that
frequency.

55. Radiation Space
 𝑝 𝑟 ≅ 𝑗𝜔𝜌0𝑈
𝑒−𝑗𝑘𝑟
4𝜋𝑟
, 𝑤ℎ𝑒𝑟𝑒 𝑘 =
𝜔
𝑐
• k is also known as the wave
number.
• This equation is for a source
radiating into full space or 4π
steradians.
• A steradian can be defined as
the solid angle subtended at the
center of a unit sphere by a unit
area on its surface. - Wikipedia

56. Radiation Space pg. 2
• If we move the source to a boundary, it acts like
a source having twice the volume velocity,
hence twice SPL (+6dB). (see pg. 23 of Leach
for addition of source and its reflection)
• We refer to this as 2π space or half space.
• A junction of two walls = π space or quarter
space (+12dB).
• A corner =1/2 π space or eighth space (+18dB).

57. Diffraction (cabinet) of
Sound
• Diffraction is caused by a change in
acoustic impedance.
• This is most readily seen at a
loudspeaker’s cabinet edge.
• The front baffle of a loudspeaker will
provide a 2π loading for higher
frequencies. When waves reach the
edge, the space they radiate into
becomes large, thereby changing the
acoustic impedance.

58. Diffraction, pg2
• A change in impedance always causes a
reflection.
• That reflection will cause interference
patterns in the free-field.
• As the wavelength gets larger, the baffle
becomes smaller in relation and the wave
“sees” 4π radiation, so no diffraction
occurs.

59. Diffraction, pg3
 The most obvious effect of this change in
impedance is the “baffle step”. At low
freqeuncies the speaker will be 6dB less than at
high frequencies.
 The corner frequency of this effect depends on
the size of the baffle.
 The other main effect is the comb filter behavior
caused by the reflections at high freqeuncies.
 See Diffraction presentation

60. For Next Time
• Reading from this week:
• A Brief History of Electroacoustics
• Basic Principles of Sound
• Fundamentals of Acoustics
• Next week: Loudspeaker and
Transducer Fundamentals
• Read chapter 1-3 of Loudspeaker
Handbook.
• Return the questionnaire.