Transcript Fundamentals of Acoustics - Rensselaer Polytechnic Institute

Acoustics at Rensselaer
Microphones and Loudspeakers
Architectural Acoustics II
April 3, 2008
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Final Exam Reminder
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Wednesday December 10
3:00 – 6:00
Greene 120 (this building, first floor)
Handwritten notes on 2 sides of 8.5” x 11”
paper are allowed, along with a calculator
• No laptops
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Transduction
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Conversion of one form of energy into another
For microphones: acoustical → electrical
For loudspeakers: electrical → acoustical
Two basic categories of transducers
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Sensors
• Small
• Low power
• Don’t affect the environment they are sensing

Actuators
• Large
• High power
• Meant to change the environment they are in
Simple EE Review
• V = I·R (Ohm’s Law)
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
V = voltage (volts)
I = current (amperes)
R = resistance (ohms)
• V = B·l·u (Electromagnetic induction)

V = voltage
 B = magnetic field (Teslas)
 l = length of wire (m)
 u = wire or magnet
Velocity (m/s)
Rossing, The Science of Sound, Figure 18.2, p. 370
http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01347.jpg
Simple EE Review
• Capacitors (formerly known as condensers)
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
Q = C·V
• Q = charge (coulombs)
• C = capacitance (farads)
• V = voltage (volts)
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C  A/d
• A = area of the capacitor plate (m2)
• d = plate separation distance (m)
Image from http://upload.wikimedia.org/wikipedia/en/b/b5/Capacitor.png
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Basic Microphone Types
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Dynamic (moving coil)
Condenser (capacitor)
Electret
Ribbon
Piezo-electric (crystal or ceramic)
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Dynamic Microphone
• Sound pressure on the diaphragm
causes the voice coil to move in a
magnetic field
• The induced voltage mimics the
sound pressure
• Comments
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Diaphragm and coil must be light
Low output impedance – good with
long cables
Rugged
Long, Fig. 4.1, p. 116, 2nd image courtesy of Linda Gedemer
V = B·l·u
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Condenser Microphone
• Diaphragm and back plate
form a capacitor
• Incident sound waves move
the diaphragm, change the
separation distance, change
the capacitance, create
current
• Comments
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Requires a DC polarizing
voltage
High sensitivity
Flat frequency response
Fragile
High output impedance,
nearby pre-amp is necessary
Q = C·V
C  A/d
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Electret Microphone
• Same basic operation principle
as the condenser mic
• Polarizing voltage is built into
the diaphragm
• Comments
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High sensitivity
Flat frequency response
Fragile
High output impedance, nearby
pre-amp is necessary
Long, Fig. 4.1, p. 116
Q = C·V
C  A/d
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Ribbon Microphone
• Conductive ribbon diaphragm
moving in a magnetic field
generates an electric signal
• Comments
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Lightweight ribbon responds to
particle velocity rather than
pressure
Both sides are exposed resulting in
a bidirectional response
Sensitive to moving air
Easily damaged by high soundpressure levels
Long, Fig. 4.1, p. 116, 2nd image courtesy of Linda Gedemer
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Piezo-Electric Microphone
(a.k.a. Crystal or Ceramic Microphone)
• Diaphragm mechanically coupled to
a piezoelectric material
• Piezo (lead zirconate titanate (PZT),
barium titanate, rochelle salt)
generates electricity when strained
• Comments
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No polarization voltage
Generally rugged
See Finch, Introduction to Acoustics,
Chapter 7, “Piezoelectric Transducers”
for details
Long, Fig. 4.1, p. 116
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Microphone Parameters
1/2-inch diameter B&K measurement microphone
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Microphone Parameters
Neumann U87 Ai Large Dual – diaphragm Microphone
Slide courtesy of Linda Gedemer
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Frequency Response and
Incidence Angle
Long, Fig. 4.8, p. 121
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Frequency Response and
Incidence Angle
Slide courtesy of Linda Gedemer
Off-axis coloration
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Transient Response
Slide courtesy of Linda Gedemer
Other Microphone Types
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Shotgun Microphone
Rossing, The Science of Sound, Figure 20.10, p. 398
http://aes.harmony-central.com/115AES/Content/Audio-Technica/PR/AT897.jpg
Other Microphone Types
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Parabolic Microphone
http://homepage.ntlworld.com/christopher.owens2/Images/TelingaMount.jpg
http://hyperphysics.phy-astr.gsu.edu/hbase/audio/mic3.html
Other Microphone Types
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Contact Microphones
www.BarcusBerry.com
Other Microphone Types
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Pressure Zone Microphone (PZM)
www.crownaudio.com
www.shure.com
Slide courtesy of Linda Gedemer
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Use of Boundary Mics
Slide courtesy of Linda Gedemer
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Effects of Floor Reflections
Slide courtesy of Linda Gedemer
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Soundfield Microphone
• 4 diaphragms in a
tetrahedral pattern
• Essentially measures omni
pressure (W) and X,Y, and
Z-dimension pressure
• Used for 1st-order
spherical harmonic
encoding of a sound field
(1st-order Ambisonics)
http://www.soundfield.com/soundfield/soundfield.php
Microphones and Diffraction
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9.9 cm
0.2 cm
Blackstock, Fundamentals of Physical Acoustics, Figure 14.12, p. 487
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Directivity Patterns
• Single-diaphragm microphones are typically
constructed to have one of a variety of
directivity patterns
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Omni directional
Bidirectional
Cardioid
Hypercardioid
Supercardioid
General mathematical form A + B·cos(θ)
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Directivity and Ports
 In a directional (ported) microphone, sound reflected from surfaces behind the diaphragm is
permitted to be incident on the rear side of the diaphragm.
 Sound reaching the rear of the diaphragm travels slightly farther than the sound at the front,
and it is slightly out of phase. The greater this phase difference, the greater the pressure
difference and the greater the diaphragm movement. As the sound source moves off of the
diaphragm axis, this phase difference decreases due to decreasing path length difference. This is
what gives a directional microphone its directivity.
Shure Pro Audio Technical Library
Directivity Patterns
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Omnidirectional
P 1
Bidirectional
Cardioid
P  cos 
1  cos 
P
2
Directivity Patterns
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Hypercardioid
1  3  cos 
P
4
Supercardioid
P  .37  .63  cos 
All Five
Omni
Bidirectional
Cardioid
Hypercardioid
Supercardioid
Directivity in 3D
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Omnidirectional
P 1
Slide courtesy of Linda Gedemer
Bidirectional
Cardioid
P  cos 
1  cos 
P
2
Directivity in 3D
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Hypercardioid
Supercardioid
1  3  cos 
P
4
P  .37  .63  cos 
Slide courtesy of Linda Gedemer
Directivity Patterns
Omni
Bidirectional
Cardioid
Hypercardioid
Supercardioid
Polar
Equation
1
cosθ
[1+ cosθ]/2
[1+
3·cosθ]/4
0.37+0.63·cos
θ
Output at 90º
(dB re 0º)
0
-∞
-6
-12
-8.6
Output at 180º
(dB re 0º)
0
0
-∞
-6
-11.7
Angle for
which output
is 0
NA
90º
180º
110º
126º
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Pattern
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Combining Patterns: Dual Capsules
Neumann U87Ai Georg Neumann GmbH
Slide courtesy of Linda Gedemer
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Basic Cone Loudspeaker Principles
• Paper (or other light-weight
material) cone attached to a
coil suspended in a
magnetic field
• Audio signal (voltage) is
applied to the wire, causing
it to move
• Mechanism is enclosed to
prevent dipole radiation
• Typical characteristics
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Sensitivity
 Impedance
 Frequency response
 Directivity
Rossing, The Science of Sound, Figure 20.13, p. 402
Speaker Directivity
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• Directivity Factor
I  ,  
Q ,   
I Avg
I Avg
W

4r 2
Average intensity (I) if total power (W) is
radiated uniformly over a spherical surface.
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I usually measured on axis
• Directivity Index
DI  10 log10 Q
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Speaker Directivity
Slide courtesy of Linda Gedemer
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Speaker Parameters
JBL Control 29 AV-1
Slide courtesy of Linda Gedemer
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Speaker Parameters
JBL Control 29 AV-1
Slide courtesy of Linda Gedemer
Enclosures
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Direct
radiator or
Acoustic
suspension
Bass reflex
with passive
radiator
Slide courtesy of Linda Gedemer
Bass reflex
Bass reflex
with acoustic
labyrinth
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Cabinets and Diffraction
Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.
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Cabinets and Diffraction
Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.
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Cabinets and Diffraction
Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.
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Cabinets and Diffraction
Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.
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Array Behavior
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Proper calculations
Far-field approximations
Change in behavior with number of elements
Change in behavior with phasing
Change in behavior with spacing
Change in behavior with frequency
Array Calculations
e  jkri  i
p R   A  
ri
i 1
n
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R
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r1 r2 r3 r4
1
2
3
4
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rn
…
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n
Array of n elements
(loudspeakers or microphones)
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p(R) = pressure at position R
A = agglomeration of various
constants
ri = distance from element i to
position R
e-jkr - δ = Green’s function for a
point element
k = wavenumber
δ = phase
Sweep R in an arc centered at the center of the array to create a polar directivity plot.
This expression does not account for the directivity of individual elements in the
array! All are assumed to be point sources or omnidirectional microphones.
Far-Field Approximation
 n 
sin 

2 

I
2  
sin  
2
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2
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I = intensity of the array
n = number of array elements
β = kd·cos(θ) – δ
k = wave number
d = distance between array elements
θ = angular position relative to the center of the array
δ = constant phase difference between elements
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Intensity vs. Log Magnitude
Intensity
Log Magnitude
8 elements at 10 cm spacing, 1 kHz, R at 10 m
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Number of Elements
2
4
8
16
Phase (between elements)
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0º
110º
60º
140º
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Frequency
500 Hz
1 kHz
2 kHz
4 kHz
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Spacing
5 cm
10 cm
20 cm
40 cm
Other Array Ideas
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• Random spacing to address side lobes
• Constant beam width