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21 Pages

### Phys332_Wk4

Course: PHYS 332, Fall 2004
School: Old Dominion
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Word Count: 680

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of Physics Music Lecture 4: Analysis and Synthesis of Tones Berg &amp; Stork, Chapter 4 Fourier Analysis Pure Tones Noise Frequency and Intensity scales Frequency: Each Octave is a factor of two change in Frequency (Pythagorous) Musical Octave sounds in unison 3 dB (deci-Bel) is a factor of 2 change in Intensity: 3.01=10.*log(2) Intensity: 21 Sept 2004 C.E. Hyde-Wright, PHYS332 2 Joseph Fourier...

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of Physics Music Lecture 4: Analysis and Synthesis of Tones Berg & Stork, Chapter 4 Fourier Analysis Pure Tones Noise Frequency and Intensity scales Frequency: Each Octave is a factor of two change in Frequency (Pythagorous) Musical Octave sounds in unison 3 dB (deci-Bel) is a factor of 2 change in Intensity: 3.01=10.*log(2) Intensity: 21 Sept 2004 C.E. Hyde-Wright, PHYS332 2 Joseph Fourier (17681830) (1807) Any periodic wave of frequency f can be constructed as a superposition of standard (particularly sine & cosine) waves of frequency f, 2f, 3f, 4f, Any non-periodic wave can be constructed as a superposition of standard waves of all frequencies. C.E. Hyde-Wright, PHYS332 3 21 Sept 2004 Wavelets W av e A new formalism for describing signals that are simultaneously localized in frequency and time See also Spectral View mode of CoolEdit. 21 Sept 2004 2 1.5 1 0.5 Am plitude 0 0 -0.5 2 4 6 8 10 12 -1 -1.5 -2 -2.5 Tim e C.E. Hyde-Wright, PHYS332 4 Digital Sampling CD sampling is 44100 Samples/sec Highest possible frequency is 22050 Hz Nyquist condition: sampling at 44100 /sec gives same output for 22050 Hz, 66150 Hz e.g. 4096 frequency samples, Frequency resolution is 22050 Hz / 4096 = 5.4 Hz Lowest possible frequency discernible = 1/T A bassoon can not be played as fast as a piccolo C.E. Hyde-Wright, PHYS332 5 CoolEdit2000 Fast Fourier Transform (FFT) Sound fragment of length T: 21 Sept 2004 Fourier Synthesis: Mathematical functions Square wave (frequency f) B&S Fig 4-5: Frequencies f, 3f, 5f, Amplitudes 1, 1/3, 1/5, Frequencies f, 2f, 3f, 4f, Amplitudes 1, , 1/3, , 1/5, Frequencies f, 2f, 3f, 4f, 5f, Amplitudes 1, 1, 1, 1, 1, C.E. Hyde-Wright, PHYS332 6 Sawtooth (ramp) B&S Fig 4-6: Repetitive Pulse B&S Fig. 4-7: 21 Sept 2004 Triangle Wave Sum of Three Harmonics 1.5 1 Wave Amplitude 0.5 0 0 -0.5 3.14 6.28 N=1 N=3 N=5 Sum -1 -1.5 Time 21 Sept 2004 C.E. Hyde-Wright, PHYS332 7 Square Wave (Synthesized) 21 Sept 2004 C.E. Hyde-Wright, PHYS332 8 Soprano Recorder, C above Middle C 21 Sept 2004 C.E. Hyde-Wright, PHYS332 9 PanPipes = Noisy Triangle Wave 21 Sept 2004 C.E. Hyde-Wright, PHYS332 10 Chalumeau.wav Fundamental at 155.7 Hz = D# (I was trying to build D) 3x155.7 Hz = 467 Hz (A#) 5x155.7 Hz = 778.5 Hz (G) 7x155.7 Hz = 1090 Hz 9x155.7 Hz = 1401 Hz Observed frequencies: 467 Hz, 768 Hz, 1041 1284 Hz, Hz C.E. Hyde-Wright, PHYS332 11 Expect odd harmonics at 21 Sept 2004 Non Periodic Sound Sources Real music (vs. synthesized sound) Vibrato, tremolo, attack, decay, etc. Inharmonicities Air Flow (flute) Instrument noises (keys, valves) Articulation transients Sung Consonants Percussion C.E. Hyde-Wright, PHYS332 12 Noise 21 Sept 2004 White Noise & Pink Noise (see Noise.wav) White Noise: Equal (random) intensity at all frequencies Pink Noise: Equal acoustic power in each octave. Intensity diminishes 3dB with each octave. Integrated acoustic energy = intensity times bandwidth. Each octave is twice as large in frequency range as octave below. 21 Sept 2004 C.E. Hyde-Wright, PHYS332 13 Sample of White & Pink Noise 21 Sept 2004 C.E. Hyde-Wright, PHYS332 14 Frequency Spectra: White and Pink (1/f) Noise White Noise Pink Noise 21 Sept 2004 C.E. Hyde-Wright, PHYS332 15 White Noise, Normal Distribution White noise has a well defined mean and standard deviation. S.d. = square root of variance Variance = mean of the square of the deviations from the mean Precision of measurement of mean improves with 1 over square root of number of samples. Public opinion polls have a precision of 3% with just 1000 people questioned: 0.03 = 1/square root (1000) 21 Sept 2004 C.E. Hyde-Wright, PHYS332 16 Pink Noise, 1/f-Noise Pink Noise does not have a well defined mean or variance. If weather follows a Pink Noise distribution, then there is no such thing as climate. 100-yr flood is a flood expected once in 100 years, and 10 x worse than the average flood in any 10 year period. C.E. Hyde-Wright, PHYS332 17 21 Sept 2004 Frequency Spectrum of Symphonic Music (Pink Noise?) A. Dvorak, Concerto for Cello & Orchestra 1st 2:10 21 Sept 2004 C.E. Hyde-Wright, PHYS332 18 Timbre / Tone Quality Attack / Decay Transients Spectrum of driving force Reed, Lips, Bowing, Hammer, Plucking Clarinet has some even harmonics (slightly conical bore) Harmonic response of each instrument Sounding box/board of String instruments Formants (especially human voice) Finite string size stretches Piano octaves. Wind harmonics not necessarily pure integers C.E. Hyde-Wright, PHYS332 19 Inharmonicities: 21 Sept 2004 Resonances in open and closed tubes 21 Sept 2004 C.E. Hyde-Wright, PHYS332 20 Musical Instrument 21 Sept 2004 C.E. Hyde-Wright, PHYS332 21
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Old Dominion - PHYS - 332
Physics of Music, Lecture 5: Human Perception of SoundProf. Charles Hyde-WrightReference materialsThe Physics of Sound, R.E. Berg, D.G. Stork The Science of Sound, T.D. RossingLaboratory Projects in sound perception &amp; discrimination Just
Old Dominion - PHYS - 332
Physics of Music: Lecture 6 The Human Vocal TractFormants &amp; Harmonics Vowels &amp; Consonants Prof. C. E. Hyde-Wright Oct 1, 2002Anatomy of the vocal tractThe [adult] vocal tract is a tube 17-18 cm long, closed at the vocal folds, open (or closed)
Old Dominion - PHYS - 332
Physics of Music: Lecture 7October 8, 2002Sound Recording and Reproduction Berg &amp; Stork, Chapter 7 Prof. C.E. Hyde-WrightAnalogThe sound amplitude is recorded by a continuously varying signal: Shape of groove cut in wax/plastic on 78/45/
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Pumpkin Drop Theory35 30Distance, Velocity, wavelengths25 20 15 10 5 0 -5 -10 -15 0 0.25 0.5 0.75 1 1.25Time (s) Height Velocity Direct Distance Echo Distance Diff/lambda V-Doppler1.51.7522.252.5y istance istance bda ler20Wavele
Old Dominion - PHYS - 332
Physics of Music Lecture 8Room Acoustics Prof. Charles E. Hyde-Wright Berg &amp; Stork Chapter 8Reverberation Sound bounces off the walls. The listener hears both direct sound and (multiply) reflected sound. With each bounce, the intensity I0 d
Old Dominion - PHYS - 332
Physics of Music Lecture 10Tuning and TemperamentBerg &amp; Stork, Chapter 9 Prof. Charles Hyde-Wright Old Dominion UniversityTuning Concert A = 440 Hz Historic pitch: Large variations in custom with period and location. Gradual historical ten
Old Dominion - PHYSICS - 332
Physics 332W Prof. C.E. Hyde-Wright Name SignatureHomework 2IDNovember 16, 2004 Due November 30, 2004Frequency times Wavelength = Wave Velocity: f=v Wave Velocity for waves on a string = square root of Tension divided by the mass per unit leng
Old Dominion - PHYSICS - 332
Physics 332W Prof. C.E. Hyde-Wright Name SignatureHomework 2IDNovember 16, 2004 Due November 30, 2004Frequency times Wavelength = Wave Velocity: f=v Wave Velocity for waves on a string = square root of Tension divided by the mass per unit leng
Old Dominion - PHYS - 332
Physics of Music Lecture 12 Brass InstrumentsProf. Charles Hyde-Wright Old Dominion University November 12, 2002 Berg &amp; Stork, Chapter 11Brass InstrumentsVery ancient: Animal horns Shells Hollowed out tree branch (didgeridoo)Some Rena
Old Dominion - PHYS - 332
Violin AcousticsPhysics 332 Prof. HydeWrightBowing,Stick-Slip FrictionBow motionBow at position L/n suppresses mode n=1,2, or, Bow pulls on string until tension is too great. String completes one oscillation until string is again moving
Old Dominion - PHYS - 332
Study Guide Physics 332WProf. C.E. Hyde-Wright Autumn 2002You are not expected to memorize the formulae given here. If you are given the formula, you are expected to be able to use it. For example: how does one value change if a parameter is double
Old Dominion - AO - 2007
Old Dominion - AO - 07
Old Dominion University Fall 2007 OfficialFall 2007 Demographi GENDER America cs Femal Unkno ne GENDER Female Male Unknown ETHNICITY American Indian Asian Black Hispanic Other White Missing CITIZENSHI P US Citizen NonImmigrant Permanent Resident Mi
Old Dominion - AO - 98
Old Dominion University Fall 1998Fall 1998 Demographics Gender Ethnicity Native Male Female American Black NRA Asian Hispanic White Other Total Gender Male Female Ethnicity Native American Black NRA Asian Hispanic White Other Citizenship Citizen Non
Old Dominion - PHYS - 604
Homework 2 (Part 1), Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Tuesday Sept 27, 2005)Some useful integrals:x sin x dx = x cos x + sin x x2 sin x dx = x2 cos x + 2x sin x 2 cos x(1) (2)Homework 2 (part 1), Problems2.1. A point c
Old Dominion - PHYS - 604
PHYSICS 604, Homework 5Due: Tuesday November 8, 20055.1. Dene the dierential operator (Boldface symbols are (3-) vectors): Lf (r) = r for any function f (x, y, z). In component form:3f (r)Li f (r) =j,k=1 123ijk rjk f (r)= 1 andijk
Old Dominion - PHYS - 604
PHYSICS 604, Homework 6Due: Tuesday November 15, 20056.1. A charge Q is at the center of a dielectric sphere of radius R and permittivity . (a) Find the electric eld, as a function of radius r &lt; R (inside the sphere). (b) Find the electric eld, as
Old Dominion - PHYS - 604
PHYSICS 604, Homework 7Due Tuesday, Nov 29, 20051. A capacitor is made out of two parallel plates of surface area A. The gap, of width d is lled with a homogeneous isotropic linear dielectric of permittivity &gt; 0 (in Gauss units, (Gauss) = (M KS)/
Old Dominion - PHYS - 604
r0 z I z B1 (0, 0, z) = z 3 r0 0 I 2r0 [(z z )2 + r2 ]3/2 0 r0 I z0 /2 z0 z Bz z0 (x,y,z)=02 Bz z0 z 2=0
Old Dominion - PHYS - 604
a b z H = H0 x B = x2 + y 2 tan1 (y/x) (x + y y )/ x (y x + x)/. y = = = M (, , z) = 2 M (, , z) = 1 + z M (, , z) +
Old Dominion - PHYS - 111
Physics 111Monday, September 29, 2003Prof. Hyde-Wright 7:10pm 8:15 pmTest 1 (100pts) Show your workUse Dimensional Analysis!Name Signature1. (32) A projectile is launched horizontally with an initial speed v0 from a height y0. Neglect aero
Old Dominion - PHYS - 111
Physics 111Monday, November 10, 2003Prof. Hyde-WrightShow your workName Honor Code SignatureTest 2 (100pts) 7:10pm 8:20 pm Use Dimensional Analysis!I.D.Net Force = Mass times Acceleration FNet = ma Normal Force means force perpendicular
Old Dominion - PHYS - 111
Welcome to Physics 111NProfessor Charles E. Hyde-Wright Autumn 2003http:www.physics.odu.edu http:www.physics.odu.edu/~hyde/Teaching/Fall03/Phys111.htmPreliminary list of topics Walker, Chapters 1-18 Description of motion: Kinematics Position (i
Old Dominion - PHYS - 111
Chapter 2 One-Dimensional KinematicsOne dimensional kinematics refers to motion along a straight line. Even though we live in a 3-dimension world, motion can often be abstracted to a single dimension. We can also describe motion along a curved pat
Old Dominion - PHYS - 111
Walker, Chapter 3Vectors &amp; Trigonometry Prof. Charles E. Hyde-Wright Physics 111 Fall 2003Vectors and Scalars A Scalar is a physical quantity with magnitude (and units). Examples: Temperature, Pressure, Distance, Speed A Vector is a physical q
Old Dominion - PHYS - 111
Applications of Newtons Laws Walker, Chapter 6Phys 111 Prof. Charles E. Hyde-Wright Fall 2005Manipulating Fractionsaa a c ac = 1= = bb b c bc Example : Simplify denominator : a ca ac ac = = = b / c c b / c b (c / c ) b Example : Introduce commo
Old Dominion - PHYS - 111
Chapter 7: Energy(I) Work and Kinetic EnergyPhys 111 Fall 2005 Prof. Charles E. Hyde-WrightEnergy How are we here? Nuclear energy in the sun, is converted into kinetic energy of the nuclei and electrons in the sun, Is converted into light,
Old Dominion - PHYS - 111
Chapter 1-8Review SlidesLab P07 Kinetic Friction Our model of kinetic (sliding) friction says Friction force on mass m = Coefficient of kinetic friction (k) times the normal (perpendicular) force acting on the mass from the surface. Friction fo
Old Dominion - PHYS - 111
Chapter 12: Universal Gravitation The earth exerts a gravitational force mg on a mass m. By the action-reaction law, the mass m exerts a force mg on the earth. By symmetry, since the force mg is proportional to the mass m, the value of g must also
Old Dominion - PHYS - 111
Chapter 16: Temperature and HeatTemperature is a fundamental quantity which characterizes the physical state of a substance. In the microscopic statistical theory, we understand temperature as the average energy per degree of freedom of motion of th
Old Dominion - PHYS - 111
ThermodynamicsWalker, Chapter 18 Physics 111 Autumn 2003 Prof. C.E. Hyde-WrightThermodynamics The 19th century industrial revolution was powered by the practical applications of the new understanding of the theoretical connection between heat and
Old Dominion - PHYS - 111
Physics 111 Semester Review Kinematics Dynamics Work, Kinetic Energy, Potential Energy Momentum, Collisions Gravity Oscillations Waves Fluids/Kinetic Theory ThermodynamicsKinematics, Constant Acceleration Position: x = x0 + v0,x t + (1/2)
Old Dominion - PHYS - 332
Physics of MusicProf. Charles E. Hyde-Wright Physics 332 Old Dominion University Autumn 2002Aesthetics in Art and Nature Physical &amp; mathematical attributes of music and sound Acoustics of Musical Instruments Electronic sound recording and g
Old Dominion - PHYS - 332
Physics of Music Lecture 2: Waves and SoundPhys 332W Prof. Charles E. Hyde-WrightDemonstrationsMass on spring w/ PASCOX(t), V(t), A(t), V vs X Torsion Wave Machine PVC version on Quinckes Tube Speaker w/ and w/out baffle03 Sept 2002
Old Dominion - PHYS - 332
Physics of Music Lecture 3: Standing WavesTraveling Waves, Reflections Standing Waves Prof. Charles E. Hyde-Wright Autumn 2002Standing Electron Waves in an Atomic Corralwww.almade n.ibm.com /vis/stm/co rral.html10 Sept 2002Phys 332W2Refle
Old Dominion - PHYS - 332
Physics of Music Lecture 4: Analysis and Synthesis of TonesBerg &amp; Stork, Chapter 4 Fourier Analysis Pure Tones NoiseFrequency and Intensity scalesFrequency:Each Octave is a factor of two change in Frequency (Pythagorous) Musical Octave sou
Old Dominion - PHYS - 332
Physics of Music, Lecture 5: Human Perception of SoundProf. Charles Hyde-WrightReference materialsThe Physics of Sound, R.E. Berg, D.G. Stork The Science of Sound, T.D. RossingLaboratory Projects in sound perception &amp; discrimination Just
Old Dominion - PHYS - 332
Physics of Music: Lecture 6 The Human Vocal TractFormants &amp; Harmonics Vowels &amp; Consonants Prof. C. E. Hyde-Wright Oct 1, 2002Anatomy of the vocal tractThe [adult] vocal tract is a tube 17-18 cm long, closed at the vocal folds, open (or closed)
Old Dominion - PHYS - 332
Physics of Music: Lecture 7October 8, 2002Sound Recording and Reproduction Berg &amp; Stork, Chapter 7 Prof. C.E. Hyde-WrightAnalogThe sound amplitude is recorded by a continuously varying signal: Shape of groove cut in wax/plastic on 78/45/
Old Dominion - PHYS - 332
Physics of Music Lecture 9Room Acoustics Prof. Charles E. Hyde-Wright Berg &amp; Stork Chapter 8Reverberation Sound bounces off the walls. The listener hears both direct sound and (multiply) reflected sound. With each bounce, the intensity I0 d
Old Dominion - PHYS - 332
Physics of Music Lecture 10Tuning and TemperamentBerg &amp; Stork, Chapter 9 Prof. Charles Hyde-Wright Old Dominion UniversityTuning Concert A = 440 Hz Historic pitch: Large variations in custom with period and location. Gradual historical ten
Old Dominion - PHYS - 332
Physics of Music Lecture 11Woodwind Instruments Berg &amp; Stork Chapter 10. Prof. Charles Hyde-Wright Old Dominion UniversityWind InstrumentsWoodwinds Resonant Tube Sound made byBrass Edge toneRecorder, Flute, Organ Clarinet, Saxophone,
Old Dominion - PHYS - 332
Physics of the PianoPiano Tuners Guild, June 5, 2000Charles E. Hyde-Wright, Ph.D. Associate Professor of Physics Old Dominion University Norfolk VA chyde@odu.eduJune 5, 2000Piano Tuners Guild1ODU PHYS 332W The Physics of Music and Musical
Old Dominion - PHYS - 332
Violin AcousticsPhysics 332 Prof. HydeWrightBowingStick-Slip FrictionBow at position L/n suppresses mode nVibrations of Sounding Board and Back plateViolin ArchitectureViolin AcousticsHarpC-major scale (multiple octaves) Shift a
Old Dominion - PHYSICS - 332
Physics 332W Prof. C.E. Hyde-Wright Name SignatureQuiz 1IDNovember 7, 2002 1:30 2:45 pmFrequency times Wavelength = Wave Velocity: f=v Wave Velocity for waves on a string = square root of Tension divided by the mass per unit length of the str
Old Dominion - AO - 03
Old Dominion University Headcount by Domicile, Campus, and LevelSemester Fall 2003Domicile Campus Out of On Off In State State Campus Campus Total Level First-time Freshmen Attendance 1,821 178 Full Time 34 14 Part Time 1,855 192 Total Other Attend
Old Dominion - AO - 93
Old Dominion University Headcount by Domicile, Campus, and LevelSemester Fall 1993Domicile Campus Out of On Off In State State Campus Campus Total Level First-time Freshmen Attendance Full Time Part Time Total Other Freshmen Attendance Full Time Pa
Old Dominion - PHYS - 332
Physics 332W Physics of Music &amp; Music Reproduction Laboratory Safety Autumn 2006This class will use familiar household items, and some specialized electronic equipment. It is very important exercise due safety procedures.Electrical Safety.Ordinar
Old Dominion - PHYS - 332
Physics 332Physics of Music &amp; Music ReproductionAutumn 2002Laboratory 1 Sound, Vibrations, &amp; OscilloscopeIn this lab, you will observe the wave forms of some simple sound sources: Whistling, singing, noise, etc. You will also become familiar w
Old Dominion - PHYS - 332
Harmonic Analysis with CoolEdit2000Phys 332W Lab 3 Sept 14, 2006 Goals: To familiarize yourself with the tools of harmonic analysis in CoolEdit2000. To analyse the harmonic structure of several tones and noise from real sound sources. Musical i
Old Dominion - PHYS - 604
Homework 1, Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Sept 12, 2006)1.1. A solid sphere of radius a has total charge Q. Use Gausss theorem to obtain the electric eld E as a function of the distance r from the center of the sphere, for b
Old Dominion - PHYS - 604
Homework 1, Physics 604 SolutionProf. Charles E. Hyde-Wright(Dated: Due: Sept 12, 2006)1.1. A solid sphere of radius a has total charge Q. Use Gausss theorem to obtain the electric eld E as a function of the distance r from the center of the sphe
Old Dominion - PHYS - 604
Homework 2, Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Sept 26, 2006)2.1. A grounded, metal sphere of radius R is centered at the origin. The sphere is in the presence of an electric eld with asymptotic boundary condition E(x, y, z) E0
Old Dominion - PHYS - 604
Homework 2, Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Sept 26, 2006)2.1. A grounded, metal sphere of radius R is centered at the origin. The sphere is in the presence of an electric eld with asymptotic boundary condition E(x, y, z) E0
Old Dominion - PHYS - 604
Homework 3, Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Oct 3, 2006).NOTES:Some useful integrals:+dx ex + 2/2= 2(1) (2)2 1 dx iqx x2 /2 ee = eq /2 2 2The Dirac -function, is not a function, but a distribution. Let L
Old Dominion - PHYS - 604
Homework 3, Physics 604Prof. Charles E. Hyde-Wright(Dated: Due: Oct 3, 2006).NOTES:Some useful integrals:+dx ex + 2/2= 2(1) (2)2 1 dx iqx x2 /2 ee = eq /2 2 2The Dirac -function, is not a function, but a distribution. Let L
Old Dominion - PHYS - 604
7(x, z)l lH Q IS A Ug H G V E Y B G H G C Q X A CB D G I A R D S Q I G Q A U G C Q X A H G Y R D V G C Q G E D Q D C f a B` g H G V E Y B G H G C Q X A CB D G E A X H G c D I R D B S Q D c G C Q D c G C Q G E D Q D C f a e` 8 P ID E Y AX G C Q
Old Dominion - PHYS - 604
7q 4 1 1 2R/a 2R/a + |r a/2| |r + a/2| |r z 2R2 /a| |r + z 2R2 /a| z z a7`u GR A US P G QS I d c A E X R D S Q I G Q A xu P A C Q G c G F E D CB G F D cS G C Q W e P I Y A X G e I D B W QS V D B G C Q G P S H I S R D S Q I G Q A U G C 9 8
Old Dominion - PHYS - 604
PHYSICS 604, Homework 6Due: Thursday November 16, 20066.1. A charge Q is at the center of a dielectric sphere of radius R and permittivity . (a) Find the electric eld, as a function of radius r &lt; R (inside the sphere). (b) Find the electric eld, a
Old Dominion - PHYS - 604
PHYSICS 604, Homework 6Due: Tuesday November 15, 20056.1. A charge Q is at the center of a dielectric sphere of radius R and permittivity . (a) Find the electric eld, as a function of radius r &lt; R (inside the sphere). (b) Find the electric eld, as
Old Dominion - PHYS - 604
PHYSICS 604, Homework 7Due Tuesday, Nov 29, 20051. A capacitor is made out of two parallel plates of surface area A. The gap, of width d is lled with a homogeneous isotropic linear dielectric of permittivity &gt; 0 (in Gauss units, (Gauss) = (M KS)/