acoustics at rensselaer microphones and loudspeakers architectural acoustics ii april 3, 2008
TRANSCRIPT
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Microphones and Loudspeakers
Architectural Acoustics II
April 3, 2008
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Final Exam Reminder
• 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
• Conversion of one form of energy into another• For microphones: acoustical → electrical• For loudspeakers: electrical → acoustical• Two basic categories of transducers
Sensors• Small• Low power• Don’t affect the environment they are sensing
Actuators• Large• High power• Meant to change the environment they are in
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Simple EE Review
• V = I·R (Ohm’s Law) 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
Rossing, The Science of Sound, Figure 18.2, p. 370
http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/images/c01347.jpg
Velocity (m/s)
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Simple EE Review
• Capacitors (formerly known as condensers) Q = C·V
• Q = charge (coulombs)
• C = capacitance (farads)
• V = voltage (volts)
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
• 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 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 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 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 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 sound-
pressure 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 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 MicrophoneSlide 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
Off-axis colorationSlide courtesy of Linda Gedemer
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Transient Response
Slide courtesy of Linda Gedemer
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Other Microphone TypesShotgun Microphone
http://aes.harmony-central.com/115AES/Content/Audio-Technica/PR/AT897.jpg
Rossing, The Science of Sound, Figure 20.10, p. 398
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Other Microphone Types
http://hyperphysics.phy-astr.gsu.edu/hbase/audio/mic3.html
Parabolic Microphone
http://homepage.ntlworld.com/christopher.owens2/Images/TelingaMount.jpg
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Other Microphone TypesContact Microphones
www.BarcusBerry.com
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Other Microphone Types
www.shure.com
Pressure Zone Microphone (PZM)
www.crownaudio.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
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Microphones and Diffraction
Blackstock, Fundamentals of Physical Acoustics, Figure 14.12, p. 487
0.2 cm
9.9 cm
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Directivity Patterns
• Single-diaphragm microphones are typically constructed to have one of a variety of directivity patterns 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
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Directivity PatternsOmnidirectional Bidirectional Cardioid
1P cosP2
cos1 P
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Directivity PatternsHypercardioid Supercardioid All Five
4
cos31 P cos63.37. P
Omni
Supercardioid
Hypercardioid
Cardioid
Bidirectional
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Directivity in 3DOmnidirectional Bidirectional Cardioid
1P cosP2
cos1 P
Slide courtesy of Linda Gedemer
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Directivity in 3DSupercardioidHypercardioid
4
cos31 P
cos63.37. PSlide courtesy of Linda Gedemer
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Directivity Patterns
Omni Bi-
directional
Cardioid Hyper-cardioid
Supercardioid
Pattern
Polar
Equation
1 cosθ [1+ cosθ]/2 [1+ 3·cosθ]/4
0.37+0.63·cosθ
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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Combining Patterns: Dual Capsules
Neumann U87Ai Georg Neumann GmbH
Slide courtesy of Linda Gedemer
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Basic Cone Loudspeaker Principles
Rossing, The Science of Sound, Figure 20.13, p. 402
• 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 Sensitivity Impedance Frequency response Directivity
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Speaker Directivity
• Directivity Factor
I usually measured on axis
• Directivity Index
AvgI
IQ
,, 24 r
WI Avg
Average intensity (I) if total power (W) is radiated uniformly over a spherical surface.
QDI 10log10
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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
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Enclosures
Direct radiator or Acousticsuspension
Bass reflex
Bass reflexwith acoustic labyrinth
Bass reflexwith passive radiator
Slide courtesy of Linda Gedemer
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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
• 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
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Array Calculations
n
i i
jkr
r
eARp
ii
1
Array of n elements (loudspeakers or microphones)
…1 2 3 4 n
r1 r2 r3 r4 rn
R
• 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.
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Far-Field Approximation
• 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
2sin
2sin
2
2
n
I
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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
8
4
16
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Phase (between elements)
0º
110º
60º
140º
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Frequency
500 Hz
2 kHz
1 kHz
4 kHz
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5 cm
20 cm
10 cm
40 cm
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Other Array Ideas
• Random spacing to address side lobes
• Constant beam width