Investigating Electromagnetic and Acoustic Properties of Loudspeakers Using Phase Sensitive Equipment Katie Butler DePaul University Advisor: Steve Errede

Why investigate loudspeakers? Most important link in the audio chain Last piece of equipment audio signal passes through Many variables in loudspeakers; permanent magnet, size and weight, material of cone, size and type of enclosure, etc. TheToneChamber.com

How speakers work Voice coil (electromagnet) is positioned in constant magnetic field from permanent magnet Current across voice coil constantly changes, changing the magnetic field polarity and strength causing the voice coil and diaphragm to move Cross-section of typical loudspeaker

Loudspeaker analogous circuit Using electrical components to model the mechanical components of the loudspeaker, further work must be done to accurately calculate these using data collected

Low distortion power amplifier No audio amplifiers readily available in lab Need to amplify signal from function generator to power loudspeaker Building amp using widely available LM3875 chip amp Constant voltage source, typical for powering speakers Component going into amplifier

Amplifier pictures

Data acquisition technique for measuring electromagnetic properties of loudspeaker Based on UIUC Physics 498POM PC-Based Pickup Impedance Measuring System

Complex pressure p and particle velocity u measurements Acoustic measurements will be taken at the same time as electromagnetic measurements

Impedance and Power Electrical Impedance (Ohms, e ) Electrical Power (W) Radiation Impedance (Pa-s/m ac ) Acoustic Intensity (W/m 2 )

Phase sensitive equipment SR830 Dual-Channel DSP lock-in amplifiers

The Speaker Italian Jensen C12N Ceramic magnet 12, 8 50 watt rated power Designed to emulate American made Jensens from the 1960s

Apparatus Took measurements 3 ways: in free air, on baffle board, in speaker cabinet Microphones are on movable arms controlled by computer program Current and voltage cables attached underneath Foam sound absorbers used under speaker to prevent reflections Setup with speaker on baffle board

Speaker Cabinet Designed and built by Steve Errede, based on Marshall 1965B 4 10 straight speaker cabinet Sound absorptive material placed in cabinet behind speaker

Frequency Sweep Data Complex acoustic impedance; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data Complex sound intensity; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data Complex electrical impedance; speaker in free air (blue), on baffle board (green), in cabinet (red)

Frequency Sweep Data Complex electrical power; speaker in free air (blue), on baffle board (green), in cabinet (red)

Voltage versus particle velocity Magnitude of voltage (left) and magnitude of particle velocity (right), the electromagnetic resonance (120.5 Hz) appears as a resonance in particle velocity at 0.40 centimeters above the speaker

Acoustic pressure of speaker in free air versus mounted on baffle board Acoustic pressure across surface at 0.40 centimeters above speaker in free air (left) and speaker mounted on 24 square baffle board (right), driven at 120 Hz

Particle velocity of speaker in free air versus mounted on baffle board Particle velocity across surface at 0.40 centimeters above speaker in free air (left) and speaker mounted on 24 square baffle board (right), driven at 120 Hz

Sound intensity across surface of speaker driven at various frequencies Magnitude of sound intensity across surface of speaker in enclosure Driven at Hz (left), Hz (center), and 10,000 Hz (right)

30 Hz – 20,000 Hz Acoustic intensity (top) and EM power (bottom) versus frequency for speaker in enclosure at a height of 0.40 centimeters.

Sound Intensity Level(s) RHS plot: Sound Intensity Level SIL= 10log 10 (I/I o ) (blue), Sound Pressure Level SPL=20log 10 (p/p o ) (green), Sound Particle Velocity Level SUL = 20log 10 (u/u o ) (red) versus frequency for speaker in enclosure at a height of 0.40 centimeters. LHS plot: The differences dSLip = SPL-SIL (blue), dSLiu = SIL-SIU (green) and dSLpu = SPL-SUL (red) versus frequency for speaker in enclosure at a height of 0.40 centimeters.

Acknowledgments Special thanks to Professor Steve Errede for his commitment to our projects. Also thank you to Gregoire Tronel for sharing the lab space and equipment. Thank you to the REU program for this research opportunity, which is supported by the National Science Foundation Grant PHY