Aco

usti

cs a

t Ren

ssel

aer

Microphones and Loudspeakers

Architectural Acoustics II

April 3, 2008

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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)

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Basic Microphone Types

• Dynamic (moving coil)

• Condenser (capacitor)

• Electret

• Ribbon

• Piezo-electric (crystal or ceramic)

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Microphone Parameters

1/2-inch diameter B&K measurement microphone

Aco

usti

cs a

t Ren

ssel

aer

Microphone Parameters

Neumann U87 Ai Large Dual – diaphragm MicrophoneSlide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Frequency Response and Incidence Angle

Long, Fig. 4.8, p. 121

Aco

usti

cs a

t Ren

ssel

aer

Frequency Response and Incidence Angle

Off-axis colorationSlide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Transient Response

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Other Microphone Types

http://hyperphysics.phy-astr.gsu.edu/hbase/audio/mic3.html

Parabolic Microphone

http://homepage.ntlworld.com/christopher.owens2/Images/TelingaMount.jpg

Aco

usti

cs a

t Ren

ssel

aer

Other Microphone TypesContact Microphones

www.BarcusBerry.com

Aco

usti

cs a

t Ren

ssel

aer

Other Microphone Types

www.shure.com

Pressure Zone Microphone (PZM)

www.crownaudio.com

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Use of Boundary Mics

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Effects of Floor Reflections

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Microphones and Diffraction

Blackstock, Fundamentals of Physical Acoustics, Figure 14.12, p. 487

0.2 cm

9.9 cm

Aco

usti

cs a

t Ren

ssel

aer

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)

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Directivity PatternsOmnidirectional Bidirectional Cardioid

1P cosP2

cos1 P

Aco

usti

cs a

t Ren

ssel

aer

Directivity PatternsHypercardioid Supercardioid All Five

4

cos31 P cos63.37. P

Omni

Supercardioid

Hypercardioid

Cardioid

Bidirectional

Aco

usti

cs a

t Ren

ssel

aer

Directivity in 3DOmnidirectional Bidirectional Cardioid

1P cosP2

cos1 P

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Directivity in 3DSupercardioidHypercardioid

4

cos31 P

cos63.37. PSlide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Combining Patterns: Dual Capsules

Neumann U87Ai Georg Neumann GmbH

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Speaker Directivity

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Speaker Parameters

JBL Control 29 AV-1 Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Speaker Parameters

JBL Control 29 AV-1

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Enclosures

Direct radiator or Acousticsuspension

Bass reflex

Bass reflexwith acoustic labyrinth

Bass reflexwith passive radiator

Slide courtesy of Linda Gedemer

Aco

usti

cs a

t Ren

ssel

aer

Cabinets and Diffraction

Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.

Aco

usti

cs a

t Ren

ssel

aer

Cabinets and Diffraction

Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.

Aco

usti

cs a

t Ren

ssel

aer

Cabinets and Diffraction

Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.

Aco

usti

cs a

t Ren

ssel

aer

Cabinets and Diffraction

Svensson and Wendlandt, “The influence of a loudspeaker cabinet’s shape on the radiated power”, Baltic Acoustic 2000.

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

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.

Aco

usti

cs a

t Ren

ssel

aer

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

Aco

usti

cs a

t Ren

ssel

aer

Intensity vs. Log Magnitude

Intensity Log Magnitude

8 elements at 10 cm spacing, 1 kHz, R at 10 m

Aco

usti

cs a

t Ren

ssel

aer

Number of Elements

2

8

4

16

Aco

usti

cs a

t Ren

ssel

aer

Phase (between elements)

0º

110º

60º

140º

Aco

usti

cs a

t Ren

ssel

aer

Frequency

500 Hz

2 kHz

1 kHz

4 kHz

Aco

usti

cs a

t Ren

ssel

aerSpacing

5 cm

20 cm

10 cm

40 cm

Aco

usti

cs a

t Ren

ssel

aer

Other Array Ideas

• Random spacing to address side lobes

• Constant beam width