Lecture 10 Notes
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Lecture 10 Notes

Course Number: PH 2233, Spring 2011

College/University: Mississippi State

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Recap of last lecture v= v fluid = restoring force inertia resisting change B vsolid = Y v gas = RT M Intensity = <Power>av/area = BkA2 = B 2A2 = P2max/B = (10dB)log(I/I0) where I0 = 1x10-12W/m2 (I0 threshold for human hearing at 1000Hz) Applications such as sonar, ultrasonic imaging, ultrasonic surgery Problem 16.55 A soprano and a base are singing a duet. While the soprano sings a A# at 932...

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of Recap last lecture v= v fluid = restoring force inertia resisting change B vsolid = Y v gas = RT M Intensity = <Power>av/area = BkA2 = B 2A2 = P2max/B = (10dB)log(I/I0) where I0 = 1x10-12W/m2 (I0 threshold for human hearing at 1000Hz) Applications such as sonar, ultrasonic imaging, ultrasonic surgery Problem 16.55 A soprano and a base are singing a duet. While the soprano sings a A# at 932 Hz the base sings a A# but 3 octaves lower. In this concert hall the density of air is 1.2 kg/m3 and its bulk modulus is 1.42x105 Pa. In order for their notes to have the same sound intensity level, what must be a) the ratio of the pressure amplitude of the bass to that if the soprano, and b) the ratio of the displacement amplitude of the bass to that of the soprano? c) What displacement amplitude does the soprano produce to sing her A# at 72dB? Problem 16.55 Each octave lower corresponds to halving of the frequency. If the Soprano sings at 932 Hz the Bass must be 932/8 =116.5Hz I = P2max/B and it is related to the displacement as I = B 2A2 Intensity is related to pressure as a) Therefore if the intensities are the same the pressure amplitudes must also be the same b) For displacement amplitude IS = IB means s2As2 = b2Ab2 or sAs = bAb therefore if s/b = 8 means As/Ab = 1/8 c) An intensity of 72dB implies I/I0 = 107.2 or I = 1.585x10-5 W/m2 = B 42 f2A2 Therefore A =sqrt( 2*1.585x10-5/sqrt(B)/42f2) = 4.73x10-8m = 47.3 nm Standing sound waves Longitudinal waves can have standing waves just as transverse waves. For longitudinal waves displacement node = pressure anti-node. Video: http://www.doflick.com/ViewVideo.aspx?vid=203 http://lecturedemo.ph.unimelb.edu.au/Wave-motion/Standing-waves/Wb-3-The-Gas-Tube Sound wave resonance the depends on instrument The waveform must match the resonant container (open at both ends, one end, clamped at both) Open columns Closed columns Demo The speed of sound can be measured with a resonant pipe Vary the frequency of the sound introduced into the tube, and measure normal modes in a pipe of known length. The air in an organ pipe is replaced by helium (which has a lower molar mass than air) at the same temperature. How does this affect the normal-mode wavelengths of the pipe? A. B. C. D. The normal-mode wavelengths are unaffected The normal mode wavelength increases The normal mode wavelength decreases The answer depends on whether the pipe is open or closed Problem 16.28 The auditory canal of the ear is filled with air. One end is open, and the other end is closed by the eardrum. A particular persons auditory canal is 2.4 cm long and can be modeled as a pipe. a) What are the fundamental frequency and b) wavelength of this personss auditory canal? Is this sound audible? b) Find the frequency of the highest audible harmonic of this persons canal. Which harmonic is this? Problem 16.28 The auditory canal of the ear is filled with air. One end is open, and the other end is closed by the eardrum. A particular persons auditory canal is 2.4 cm long and can be modeled as a pipe. a) What are the fundamental frequency and wavelength of this personss auditory canal? Is this sound audible? b) Find the frequency of the highest audible harmonic of this persons canal. Which harmonic is this? a) f1 = v/4L therefore f1 =344/(4*0.024) = 3.58 kHz b) and fn = nf1 for n=1,3,5, since highest audible frequency is 20000Hz, n= 20000/3580 = 5.6 which means the highest audible harmonic is 5th with a frequency of 3580*5 = 17900Hz.

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Mississippi State - PH - 2233
Recap of last lectureStanding waves in longitudinal waves (sound waves)open columnsf1 = v/2L, f2 = v/L, f3 = 3v/2Lhttp:/The_Gas_Tubeclosed columnsf1 = v/4L, f3 = 3v/4L, f5 = 5v/4LWave interferenceDestructive interference when the distance between
Mississippi State - PH - 2233
Recap of last lectureJust like other waves sound waves interfereWhen the frequency of two sound waves is the same:Destructive interference when the distance between the speaker is /2, 3/2, 5/2Constructive interference when the distance between the spe
Mississippi State - PH - 2233
Recap of last lectureDoppler Effectfront = (v vS)/fSbehind = (v + vS)/fSfL = (v +/- vL)fS/(v +/- vS)Electromagnetic waves occur overa wide range Where wavelength is large, frequency is small. The range extends from low energy and frequency(radio
Mississippi State - PH - 2233
Recap of last lectureElectromagnetic waves do not need a medium to propagateTime varying E and B fields produce EM waves such as E &amp; B fieldsassociated with accelerating charged particles.They satisfy the wave equation and v = f, in vacuum v = c = 3x1
Mississippi State - PH - 2233
Recap of last lectureEM waves also satisfy the wave eqn. and the E &amp; B fields vary sinusoidallyWhen propagation through a medium the velocity changes from c tov = c/n where n is called the refractive index = KKm where =K0and = Km0Recap of last lectur
Mississippi State - PH - 2233
Recap of Mondays lectureEM radiation have both particle like and wave like properties. TheQuantum description of EM radiation takes into account both typeof behavior.Laws of reflection i= rReflection can be specular anddiffuse. When studying reflect
Mississippi State - PH - 2233
Recap of last lectureFor light traveling from a to b where na &gt; nb, as the angle ofincidence becomes more and more acute, the light ceases to betransmitted, only reflected. crit = sin-1(nb/na)Frustrated TIRTIRIn which of the followingsituations is
Mississippi State - PH - 2233
Recap of last lectureThe wavelength dependence of refraction is called dispersionna = c/va = 0/aThere are two states of linear polarization of lightCertain materials block EM waves polarized light in a particulardirectionIf the angle between the pol
Mississippi State - PH - 2233
Recap of last lectureLight can also be polarized by reflection. It is 100% polarized inthe direction parallel to the reflecting surface when the angle ofincidence = brewster angle = tan-1 (nb/na)Scattered light perpendicular to the direction of propag
Mississippi State - PH - 2233
Recap of last lectureparticlesdsin = m (maximas)dsin = (m+ ) (minimas)For small sin ~ tanor d.ymax /R = mor ymax = mR/dI = 0cE2p= I0 cos2/2wavesIn Youngs experiment, coherent light passing throughtwo slits (S1 and S2) produces a pattern of dark
Mississippi State - PH - 2233
Recap of last lectureFor small the maximas are at 2t = mn wheren = 0/nMaxima for 2t=(m+ ) m=0,1,2Minima for 2t = mPhase shift of /2An air wedge between two glass plates Just like the thin film, two waves reflect back from the air wedgein close pro
Mississippi State - PH - 2233
Recap of last lectureBright rings when net phase shift = 2t+ /2 =m or 2t = (m+ )dark rings when 2t = m m=0,1,2,Thin film coatings can make perfectreflectors or perfect absorbersDiffractionandFraunhofer DiffractionP will be a dark band ifasin = O
Mississippi State - PH - 2233
Recap of last lecturew1/a85% ofthe powerP will be a dark band ifasin = Orsin = m/a m =1, 2, For small sin ~ ~ tany = xm/a with m =1, 2, Intensity in a single-slit patternEp = E0sin(/2)/(/2) sin/2 I = I0 /2 2 = (2/)*[path difference] = (2/
Mississippi State - PH - 2233
Recap of last lecture sin/2 I =I0/2 2 = (2 / )asinThe first minima is at 1 = / 2 /( Two slit interference sin /2 I =I0 /2 d = 4adsin = m (maximas)dsin = (m+ ) (minimas)I = I0cos2/22 sin /2 I = I 0 cos 2 /2 = (2 /)2 = ( 2 /)2Diffra
Mississippi State - PH - 2233
Recap of last lectureRevisit 2 slit interference: actually diffraction pattern from eachslit interfere to produce the pattern seen which is a little differentfrom the idealized 2 slit pattern we saw in the last chapter.I I0 cos2 sin /2 22 /2 f = (
Mississippi State - PH - 2233
Recap of last lecture.When light has a wavelength l much smaller than objects that itinteracts with, we can treat light as composed of straight-line rays.This regime is called geometric optics.Reflections from a spherical mirrorsa + b = 2ftan a = h
Mississippi State - PH - 2233
Recap of last lectureSpherical reflecting surfaces can be concave orconvex. (concave is when the mirror is silveredon the outer surface while convex is the otherkind.)Under the paraxial approximation (smallangles or light almost parallel to the opti
Mississippi State - PH - 2233
Recap of last lecturena/s + nb/s = (nb-na)/Rm = y/y = -nas/nbsA pair of spherical surfaces can form concave orconvex lenses. Light refracting through thesespherical surfaces tend to converge in convex lensesand diverge in concave lenses.For thin le
Mississippi State - PH - 2233
Recap of last lectureHuman eye: most of the bending (refraction) due to the cornea which has asmall focal length.The lens is used to get additional variable focusing so that near and far objectscan be on focus at the retinaNormal eye near point = 25
Mississippi State - PH - 2233
Recap of last lectureMagnificationby a simplemagnifier'Mh/ fh/ NNfIf eye focuses at near p oint,achieve slightly greater power :MN1fN = near point , 25 cmMicroscope magnification = M1*M2 = s25/f1f2Telescope magnification = -f1/f2Microsc
Mississippi State - PH - 2233
Recap of last lecturePostulate of Classical relativity:Laws of mechanics (Newtons laws ) are invariant in all inertial reference framesCrisis in classical relative: In classical relativity the velocity of light would bedifferent in a frame moving with
Mississippi State - PH - 2233
Recap of last lectureConsequences of the postulates of special relativity:1. Speed of light is a constant2. Simultaneity of events is frame dependent3. Time intervals are frame dependent4. spatial intervals (length) is frame dependent5. Space-time i
Mississippi State - PH - 2233
Recap of last lectureConsequences of the postulates of special relativity:1. Time in moving frames is dilated t = t2. Length in moving frames is contracted l = l/3. = 1/(1-u2/c2)1/24. The complete Lorentz transforms are given by:t = (t - ux/c2)x= (
Mississippi State - PH - 2233
Recap of last lectureLooked at 4 phenomena which are problematic for classical physicsLine spectra seen for different elements when they are heated/energizedPhoto-electric effect (electrons emitted from metal when light withFrequency above a threshold
Mississippi State - PH - 2233
Recap of last lectureLooked at 4 phenomena which are problematic for classical physicsLine spectra and black body radiation spectrum can be explained interms of discrete energy levels in atoms where E1 E2 = hf;Ephoton = hfThe same particle like prope
Mississippi State - PH - 2233
Recap of last lectureEvidence for wave like behavior of particles:Diffraction and two slit interference patternsThese are a consequence of the uncertainty principleDpDx hParticles can be described by wave-functions y (x,y,z,t)Particle wave-functions
Mississippi State - PH - 2233
Recap of last lectureSolving the wave equation (Schrdinger Eq.) for the most simpleproblem a particle in a box (infinite potential well) shows thatthe particle can only occupy discrete energy levels. The wave fn.for each of these energy levels resembl
Mississippi State - CH - 1213
John W. MooreConrad L. StanitskiPeter C. Jurswww.cengage.com/chemistry/mooreChapter 12Fuels, Organic Chemicals andPolymersPetroleumPetroleum is a complex mixture of: alkanes cycloalkanes alkenes aromatic hydrocarbonsIts composition and color
Mississippi State - CH - 1213
Chapter 13Chemical Kinetics: Rates ofReactionsChemical KineticsThe study of speeds of reactions and the nanoscalepathways or rearrangements by which atoms andmolecules are transformed from reactants toproducts.Chemical kinetics is also called reac
Mississippi State - CH - 1213
Chapter 14Chemical EquilibriumCharacteristics of Chemical EquilibriumMany reactions fail to go to completion.[Reactants] stop decreasing, and[Products] stop increasing.The reaction reaches equilibrium.If there are more:products than reactants = pr
Mississippi State - CH - 1213
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Mississippi State - CH - 1213
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Mississippi State - CH - 1213
Chapter 17Additional Aqueous EquilibriaBuffer SolutionsBuffer = chemical system that resists changes in pH.ExampleAdd 0.010 mol of HCl or NaOH to:1 L SolutionInitialpHafter HClpure H2O7.002.0012.00[CH3COOH] = 0.5 M+ [CH3COONa] = 0.5 M4.74
Mississippi State - CH - 1213
Chapter 18Thermodynamics:Directionality of ChemicalReactionsReactant- &amp; Product-Favored Processes Why are equilibria product- or reactant- favored? Why do some reactions occur spontaneously? Why do others require help (heat, spark)? Exothermic rea
Mississippi State - CH - 1213
Chapter 19Electrochemistry &amp; itsApplicationsElectrochemistryElectrochemistry is the study and use of e- flow inchemical reactions.Redox reactions generate (and use) e Those e- can be harnessed (batteries). Corrosion is an electrochemical reaction.
Mississippi State - CH - 1213
Chapter 20Nuclear ChemistryThe Nature of RadioactivityHenri Becquerel (1896): U salts emitted rays that fog a photographic plate. U metal was a stronger emitter.Marie and Pierre Curie: Isolated Po and Ra that did the same. Marie Curie called the p
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