Acoustics at Rensselaer Microphones and Loudspeakers Architectural Acoustics II April 3, 2008

Acoustics at Rensselaer 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

Acoustics at Rensselaer 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

Acoustics at Rensselaer 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 Velocity (m/s)

Acoustics at Rensselaer 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 (m 2 ) d = plate separation distance (m) Image from

Acoustics at Rensselaer Basic Microphone Types Dynamic (moving coil) Condenser (capacitor) Electret Ribbon Piezo-electric (crystal or ceramic)

Acoustics at Rensselaer 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, 2 nd image courtesy of Linda Gedemer V = B·l·u

Acoustics at Rensselaer 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

Acoustics at Rensselaer 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

Acoustics at Rensselaer 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, 2 nd image courtesy of Linda Gedemer

Acoustics at Rensselaer 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

Acoustics at Rensselaer Microphone Parameters 1/2-inch diameter B&K measurement microphone

Acoustics at Rensselaer Microphone Parameters Neumann U87 Ai Large Dual – diaphragm Microphone Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Frequency Response and Incidence Angle Long, Fig. 4.8, p. 121

Acoustics at Rensselaer Frequency Response and Incidence Angle Off-axis coloration Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Transient Response Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Other Microphone Types Shotgun Microphone Rossing, The Science of Sound, Figure 20.10, p. 398

Acoustics at Rensselaer Other Microphone Types Parabolic Microphone

Acoustics at Rensselaer Other Microphone Types Contact Microphones

Acoustics at Rensselaer Other Microphone Types Pressure Zone Microphone (PZM) Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Use of Boundary Mics Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Effects of Floor Reflections Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Soundfield Microphone 4 diaphragms in a tetrahedral pattern Essentially measures omni pressure (W) and X,Y, and Z-dimension pressure Used for 1 st -order spherical harmonic encoding of a sound field (1 st -order Ambisonics)

Acoustics at Rensselaer Microphones and Diffraction Blackstock, Fundamentals of Physical Acoustics, Figure 14.12, p cm 9.9 cm

Acoustics at Rensselaer 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)

Acoustics at Rensselaer 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

Acoustics at Rensselaer Directivity Patterns OmnidirectionalBidirectionalCardioid

Acoustics at Rensselaer Directivity Patterns HypercardioidSupercardioidAll Five Omni Supercardioid Hypercardioid Cardioid Bidirectional

Acoustics at Rensselaer Directivity in 3D OmnidirectionalBidirectionalCardioid Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Directivity in 3D Supercardioid Hypercardioid Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Directivity Patterns OmniBi- directional CardioidHyper- cardioid Supercardioid Pattern Polar Equation 1cosθ[1+ cosθ]/2[1+ 3·cosθ]/ ·cosθ Output at 90º (dB re 0º) 0-∞ Output at 180º (dB re 0º) 00-∞ Angle for which output is 0 NA90º180º110º126º

Acoustics at Rensselaer Combining Patterns: Dual Capsules Neumann U87Ai Georg Neumann GmbH Slide courtesy of Linda Gedemer

Acoustics at Rensselaer 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

Acoustics at Rensselaer Speaker Directivity Directivity Factor  I usually measured on axis Directivity Index Average intensity (I) if total power (W) is radiated uniformly over a spherical surface.

Acoustics at Rensselaer Speaker Directivity Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Speaker Parameters JBL Control 29 AV-1 Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Speaker Parameters JBL Control 29 AV-1 Slide courtesy of Linda Gedemer

Acoustics at Rensselaer Enclosures Direct radiator or Acoustic suspension Bass reflex with acoustic labyrinth Bass reflex with passive radiator Slide courtesy of Linda Gedemer

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

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

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

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

Acoustics at Rensselaer 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

Acoustics at Rensselaer Array Calculations Array of n elements (loudspeakers or microphones) … 1234n r1r1 r2r2 r3r3 r4r4 rnrn R p(R) = pressure at position R A = agglomeration of various constants r i = 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.

Acoustics at Rensselaer 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

Acoustics at Rensselaer Intensity vs. Log Magnitude IntensityLog Magnitude 8 elements at 10 cm spacing, 1 kHz, R at 10 m

Acoustics at Rensselaer Number of Elements

Acoustics at Rensselaer Phase (between elements) 0º0º 110º 60º 140º

Acoustics at Rensselaer Frequency 500 Hz 2 kHz 1 kHz 4 kHz

Acoustics at Rensselaer Spacing 5 cm 20 cm 10 cm 40 cm

Acoustics at Rensselaer Other Array Ideas Random spacing to address side lobes Constant beam width