Dr. John VarrianoDr. Ted ClarkeJonathan Fili

Department of PhysicsChristian Brothers University

Electricity & Magnetism: Music to Our Ears

TAAPT Annual MeetingMarch 21, 2015

Austin-Peay State UniversityClarksville, TN

1. Electric “Guitar”

electromagnetic induction ac circuits standing waves musical scale

Physics

small coil with lots of turns (e.g. coil from a relay) small magnet (neodymium) steel wire wood, screws hook-up wire, connectors, soldering iron, solder amplifier, speaker, audio cables

Materials

Coil

relays

resistance 200-400

Example: NTE ELECTRONICS R46-5D12-12 POWER RELAYSPDT, PC BOARD Coil Voltage 12VDCContact Voltage 120VACContact current 12A

www.newark.com $3.89

Simple Design

coil/magnet

wire

washer & screw

bridgeconnectors

washer & screw

coilmagnet

wire

More Elaborate Design

wire

magnet

wire

magnet

bridgetuning peg finger board

Characterizing Coil

Measure resistance with meter.

R = 202

f = 500 Hz

Irms = 3.00 mA

Vrms = 4.00 V

Z = = 1333 Vrms

Irms

L 0.42 H

typical guitar pick-up coils R = 5-10 k, L = 1-9 H, C=1 nF

Determine inductance using impedance method.

222

22

)()1(

)(

RCLC

LRZ

VR

Lcoil

AIrms

Vrmsf C

22 )( LRZ

12-tone equal temperament

f12 = 2f0f0 f1 f2

octave

01 nff

)12/1(00

1212

2

2

n

ffnf

0)12/(2 ff m

m (1)

bridgenutL0

Lmdm

mm L

vf

Lvv

f

2

2 000

(2)

(3)

Combining (1), (2), (3) gives

)12/(0

)12/(0

2

11

2

mm

mm

Ld

LL

Fret Bars?

02

12 fnnff

0fnf mm

Coil Voltage Output (before amplification)

Coil Voltage Output

Microphone Voltage Output (Placed in Front of Speaker)

Fast Fourier Transforms

2. Theremin (Ætherphone)

capacitance ac circuits (RLC circuit resonance) frequency mixing (heterodyne principle)

Physics

Thereminwww.musiciansfriend.com

• Moog (already built ) $389-$499• Moog (kit) $339

amplifier, speaker, audio cables• Moog 15-watt amplifier/speaker ($99)

Materials

Theremin

http://en.wikipedia.org/wiki/Theremin

frequency “antenna”

volume “antenna”

Patented in 1928 by Lev Sergeyevich Termen (a.k.a. Leon Theremin in America)

played without physical contact hand and antenna act as plates of a capacitor distance between hand and antenna determines capacitance

http://www.thereminworld.com

Pitch Control uses 2 oscillators

one has fixed frequency other frequency determined by capacitance of antenna-hand distance difference of these two frequencies is audible frequency (heterodyne)

Why use 2 oscillators and heterodyne? Why not just 1 oscillator?

Capacitance is on order of picofarads so resonant frequency is in radio spectrum. Must mix two radio frequencies to get audible frequency.

Volume Control capacitance detunes oscillator which then attenuates signal

The theremin was used in movie soundtracks such as Miklós Rózsa's for Spellbound and The Lost Weekend and Bernard Herrmann's for The Day the Earth Stood Still, and as the theme tune for the TV show Midsomer Murders.

http://en.wikipedia.org/wiki/ThereminInteresting Trivia

http://www.northwestchicagofilmsociety.org/

http://www.youtube.com/watch?v=3ULhiVqeF5U