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by: Carlotta Dare DVM


Carlotta Dare DVM
GPA 3.68


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This 59 page Class Notes was uploaded by Carlotta Dare DVM on Saturday September 12, 2015. The Class Notes belongs to Physics 15 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/201925/physics-15-university-of-california-irvine in Physics 2 at University of California - Irvine.




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Date Created: 09/12/15
The Physics of Music Physics 15 InsTrucTor David Kirkby UniversiTy of California Irvine dkirkbyuciedu Miscellaneous I will be Traveling on Nov 26 Tuesday before Thanksgiving There will be a guesT lecTure Prof David Casper LecTure 13 I Woodwinds air reeds Thursday Nov 21 buT noT due for Two weeks Problem SeT 7 The lasT one will be handed ouT nexT I Brass Inglrumenls No office hours 1011am on Wednesday Nov 27 afTernoon hours are sTill OK InsTrucTor David Kirkby dkirkby uci edu Physics of Music LecTure 13 D Kirkby 2 Air Reed Air JeTs and Turbulence Examples of air reed insTrumenTs include The fluTe As fasT air is forced ouT Through your recorder and whisTIes lips iT comes in conTacT wiTh The sTaTionary surrounding air This conTacT Triggers TurbulenT eddies To form which in Turn disTurb The flow paTTern In an air reed insTrumenT a Thin JeT of air plays The role of The cane reeds of oTher woodwind insTrumenTs The air reed has Two main componenTs Air JeT Sharp edge PhysicsofMusicLecTure13DKirkby 3 Physicsof MusicLecTure 13D Kirkby 4 Air JeTs and Edges An air JeT sTriking a sharp edge will be deflecTed To one side of The edge When an air JeT and edge are coupled To a resonaTor such as an air column The frequency selecTiviTy of The resonaTor can harness The chaoTic JeTedge vibraTions To If The JeT is cenTered on The edge Turbulence can sTore energy aT harmonic frequencies cause H To swiTch back and forTh beTween sides in a Chmllc way The JeTedge air reed vibraTions are reinforced and synched To The air columns vibraTions by a feedback The Coupling of an air Jel Wllh an edge pmduces mechanism similar To The oTher reed insTrumenTs sound of iTs own which we describe as wind whisTling or aeolian Tones These gm Tones are inharmonic and noisy 13131 W H H femof u PhysicsofMusicLecTure13DKirkby 5 Physicsof MusicLecTure 13D Kirkby e In This case The feedback relies on The direcTion of air flow in The sTanding wave raTher Than pressure pulses The Physics of Music Physics 15 Universify of California Irvine Insfrucfar David Kirk dkirkby ucie Air Reed Insirumems Fime Air Reed Insirumems Recurder w quotmy s simiiur my um um ym m bum m zhnnmi in mm my my m and mm y m untdgt m quotman is unmud nmm g wamwims mm y ym m ymms miym hm mm my mmmyvymm m mmmymm Fime bemunsiraiiun Lisnnm m mmmm mm mm in v 5m m Dws mm mm mm indudt mmymmmm HW an m by hang my mm is mm mmmym HW ats in mm hang my mm HW dots mm warw Insirum ems gyms mmymmqs m mm mm mm mumps mm m mm bybiawng mm my my graup s waadwmd iymymmms Emmpits mm mmymmqs m m qymmpm rmbam my my um mbn m mmmm quotmums m m brass mmymmm m A mmmys warming pm A mmqymmmm mmmymp An my miumn my m m m mm A and mu A Manny ym duudyitantd my mama hm mm m nisa 5mm smpym mm mm mm mm 9 5mm HW an m mm mm mm mm m ubmss mmymmm mm M mm A qymmpm s mam 3 W imgv Mun m mmmm Haw mm mm urn uwnyda wamwims ym mmyomw hm brass mymmqs my m an um aniy 3 mm Energy Fiuw and Feedback vyyyymmmysmmms nnbrms m mmmys up 0quot mmmymm and my pp and m m miumn mymmm ymmmmmm m Mimw hplm m mm m in mm mymmmm m ymymm m w my zaiumn um m m w by du The Physics of Music Physics 15 InsTrucTor David Kirkby UniversiTy of California Irvine dkirkbyuciedu Brass Families Brasses in The OrchesTra Brass insTrumenTs can be grouped according To wheTher They are mosle cylindrical or conical Cylindrical TrumpeT Trombone french horn Conical corneT bariTone Tuba Physics of MusicLecTure 13DKirkby 13 Physics of MusicLecTure 13D Kirkby 14 Cylindrical Brasses TrumpeT LisTen To These samples of orchesTraI brasses from piccolo TrumpeT Physics of MusicLecTure 13DKirkby 15 Physics of MusicLecTure 13D Kirkby 16 Cylindrical Brasses Trombone Cylindrical Brasses French Horn Physics of MusicLecTure 13DKirkby 17 Physics of MusicLecTure 13D Kirkby 18 The Physics of Music Physics 15 InsTrucTor David Kirkby UniversiTy of California Irvine dkirkbyuciedu Conical Brasses Tuba Family H m STanding Waves in The Air Column uge am The air column in a brass insTrumenT is open aT The bell sh end and closed aT The mouThpiece end If H were sTraighT a brass insTrumenT should be similar To a clarineT ignoring The difference beTween a reed and a mouThpiece for now BuT brass insTrumenTs have Their air columns coiled up in many loops in order To make Them more compacT for Their lengTh How does This affecT Their sound LisTen To The PVC quotbrassesquot To hear The effecT of adding TwisTs and Turns To The air column Sousaphone bariTone Physics of Music Lecture 13 D Kirkby 19 Physics of Music Lecture 13 D Kirkby 20 Comparison of Air Columns Since The TwisTs and Turns do noT maTTer we can unroll The TrumpeT is abouT 3 Times longer Than a clarineT and The brasses To compare Their air columns bells omiTTed has The same boundary condiTions openclosed This means ThaT The frequency of a TrumpeT39s lowesT noTe 39 should be abouT 13 of The frequency of The clarineT39s TrumpeT 53872140cm Iowesf n016D3 Trombone 170105275cm InsTead The TrumpeT39s lowesT noTe E3 is sligthy higher Than The clarineT39s lowesT noTe French horn 19318 2375cm Why Tuba 05362536cm Physics of Music LecTure 13 D Kirkby 21 Physics of Music LecTure 13 D Kirkby 22 FirsT check The frequency specTrum of a PVC TrumpeTquot The imporTanT differences beTween a real TrumpeT and The PVC TrumpeT are WhaT is The lowesT harmonic Does iT agree wiTh The 39 The m Uthlece and quotmum T39Jbe expecTed f1 v4L The bell Are even harmonics suppressed as expecTed for BoTh of These feaTures change The effecTive lengTh of The openclosed boundary condiTions air column Since The PVC TrumpeT plays as expecTed whaT is BuT whaT really maTTers is ThaT They change The effecTive differenT abouT a real TrumpeT lengTh differenle for differenT frequencies Physics of Music LecTure 13 D Kirkby 23 Physics of Music LecTure 13 D Kirkby 24 The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu The bell on a brass instrument behaves like the open holes on a woodwind instrument and shortens the instrument39s effective length for low frequencies while leaving the high frequencies alone Both of these elements subtly adjust the oddharmonic spectrum to give an almost evenodd spectrum at a new fundamental frequency A trumpet would be out of tune inharmonic overtones if we removed either the bell or the mouthpiece The trumpet39s lowest resonance is out of tune with the ther overtones and so is not musically useful or physically sustainable The lowest harmonic resonance of a trumpet is about 3 times higher in frequency than the fundamental frequency we woul expect for a simple air column of the same length mm M MusicLchr113D Why 27 1 2 3 4 6 7 8 9 10 11 The mouthpiece and mouthpipe are a constriction of the Cylinder I I I I frequency air column and have the opposite effect they resonate around 800 Hz and increase the instrument39s effective length at high frequencies while leaving the low I I f frequencies alone t be renluenw 1 2 3 How do these two effects work together to fill in the mouth I I I even harmonics iece frequemv P mm mm is mm 25 mm mm is mm EA Pedal Tones What have we learned It is actually possible to play a note that is perceived to have the pitch of the mistuned fundamental by exciting the 2nd 3rd 4th harmonics and letting your brain fill in the missing fundamental This is called a m play these overtones 1 2 3 4 5 e frequency You will perceive this pitch mm M MusicLchr113D Why 2x Playing Different Notes So far we have focused on the air column and not mentioned how different notes are selected One method for playing different notes is to adjust the tension your lips which increases their r h in esonant frequency and t en In turn excites a higher overtone of the air column This is the only option on a bugle but still allows you to play a limited selection of music For example 9 mm M MusicLchr113D mm at Why isn39t there an instrument like the bugle for the woodwinds The reason is that reed instruments are optimized to play pitches corresponding to low harmonics of the air column while brasses are optimized to play high harmonics As a result a woodwind buglequot would have its notes too spread out to be usefu 39 wind buglequot 9quot f 2 f3 4 f fa 5 mm M MusicLchr113D Why an The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu Valves An empty bottle is essentially a woodwind buglequot The second method for changing the pitch is to alter the physical length of the instrument Try to blow overtones on one How many can you get Most of the brasses do this with fingeractuated valves that add an extra length of tube when they are pressed down I Rotary style Piston style french horn trumpet tuba Physics of Music Lecture 13 D Kirkby 31 Physics ofMustc Lecture 13 D Ktrkby 32 Trumpet Valve Fingerings Brass instruments traditionally have only 3 valves Why is Pressing down a valve makes the instrument longer and so this enough if the woodwinds need gt10 to cover each lowers the fundamental frequency This is opposite to register what happens with a woodwind where finger holes make the instrument shorter and raise the fundamental The reason is that the size of a register is determined by frequency the spacing of the harmonics being used lt trumpet 7 semitones you s cm A Ann is c cunt n ma clar net 19 semitones L 395 fluteoboe 12 semitones tsjeltzl actlc F lc j F39ej u I h f3 f4 f6 fa Physics of Music Lecture 13 D Klrkby 33 Physics otMustc Lecture 13 D Klrkby 34 Trumpet Fingerings Compromises How much should each valve increase the length of the The fingering chart tells us to press down valves 1 and instrument by 2 to reach the third semitone down Pressing down valve 2 should lower the pitch by one We have already calculated that this adds 612 18cm to semitone This is equivalent to stretching the length by the length 2112 106 So if the original length is 100cm the extra lenglh ShOUld be 6cm But three semitones requires a stretch of 2312 119 or an extra 19cm Pressing down valve 3 should lower the pitch by two semitones This is equivalent to stretching by 2212 112 What went wron Intervals re uire multiplying b some or adding 12cm 9 q Y ratio but valves involve adding some length These are impossible to reconcile exactly so some compromise is necessary just like for the woodwind register holes Physics of Music Lecture 13 D Kirkby 35 Physics otMustc Lecture 13 D Kirkby 3o 39 9 KISS Dark Matter Workshgp mthan Feng 15 July 2003 UC Irvine O EVIDENCE FOR DARK MATTER 3 l y There is now overwhelming evidence NoBigBang a391 r302 05I that normal standard model matter is not all the matter in the Universe 2 Dark Matter 23 i 4 Supe39quot vae Dark Energy 73 i 4 1 g 7 Normal Matter 4 i 04 Neutrinos 02 ZmVO1eV 7 threw EE Wdlrf To date all eVIdence is from dark matter s gravitational effects and tillquot mm 9 insensitive to many of its particle 22 00 properties 1 One w w ilw Wewouldliketodetectitinotherways O 1 2 3 to learn what it is QM 15 Jul 09 Feng 2 A PRECEDENT In 1821 Alexis Bouvard found anomalies in the observed path of Uranus and suggested they could be caused by dark matter In 184546 Urbain Le Verrier determined the expected properties of the dark matter and how to find it With this guidance Johann Gottfried Galle discovered dark matter in 1846 Le Verrier wanted to call it Le Verrierquot but it is now known as Neptune the farthest known planet 18461930 197999 2006present DARK MATTER CANDIDATES The observational 131 i constraints are no 1312 i match for the creativity 13 fibaquot i of theorists 32 S 039 39 neutrings WLMPs gquot a 33 rst Masses and Interaction bi grams strengths span many 1218 Q many orders of 1037 SuperWIMPs magnitude but not all mfgny CDM gram candidates are equally i3 10 16431 1317101 16 Iii 16451641 16 166164 1oquot to3 lo 1o lento 1o mass GcV HEPAPAAAC DMSAG Subpanel 2007 15 Jul 09 Feng 4 THE PLAN WIMP Dark Matter Direct Detection Indirect Detection Colliders discussions on Friday and next week Beyond WIMP Dark Matter Astrophysical Signals 15 Jul 09 Feng 5 WIMP DARK MATTER Fermi s constant GF introduced in 19303 to describe beta decay n gtpe T2 6 11105 GeV392 9 a new mass scale in nature mweak 100 GeV 15 Jul 09 Feng 6 THE WIMP MIRACLE 1 Assume a new heavy l I particle X is initially in thermal equilibrium xx lt gt 7f 2 Universe cools xx 7 7f 3 XS freeze out 1 10 100 woo xzmT time gt xx Zeldovich et al 19605 15 Jul 09 Feng 7 THE WIMP MIRACLE The resulting relic density is 1 1 m2 Increasing UAVgt QC N lt0 Ugt 9X w X qr f l I X J f For a WIMP mX 100 GeV and gX 06 9 QXO1 iiil I l l l I D 100 1000 xmT time gt Remarkable coincidence particle physics independently predicts particles with the right density to be dark matter 15 Jul 09 Feng 8 l lllllll l l WIMPS FROM SUPERSYMMETRY The classic WIMP neutralinos predicted by supersymmetry Goldberg 1983 Ellis et al 1983 Supersymmetry extends rotationsbooststranslations string theory unification of forces For every known particle X predicts a partner particle X Neutralino x e y Z Flu Fld Particle physics alone 9 x is lightest supersymmetric particle stable mass 100 GeV All the right properties for WIMP dark matter 15 Jul 09 Feng 9 QDM 23 i 4 stringently constrains models 500 Focus Coannihilation 39 re ion Too much p039nt 9 dark matter reglon 393 Bulk g Yellow preWMAP reglon g Red postWMAP 500 1000 1500 2000 2500 1110 Gov Cosmology excludes many possibilities favors certain regions 15 Jul 09 Feng 10 WIMP DETECTION Correct relic density 9 Efficient annihilation then E g A 2A cc X X 2 50 0Q 91 79 quot5quotquot 0 CD9 50 3 3900 Q2 92 SR 92 CDQ J Et 13 a 539 q q 29 3 V a o LU g Efficient scattering now Direct detection 15 Jul 09 Feng 11 DIRECT DETECTION WIMP properties v 10393 0 Kinetic energy 100 keV Local density 1 liter Detected by recoils off ultra sensitive underground detectors Area of rapid progress CDMS XENON LUX Theory predictions vary but many models 9 1044 cm2 15 Ju09 2 Crosssectlon cm nonnahsod to nucleon 39 39 39 httpl39l d11itoolsbeVynle GaitskelllVIandionlippin WIMP Mass lGeV02 CDMS 20042005 reanalysis 2008 Ge XENONIO 2007 Net 136 kg SuporCDMS Promoted 25kg 7STSnolab L X 300 kg LXe P1 o1ect1on Jul 2007 Baltz and Jondolo 2003 Baltz and Gondolo 2004 Markov Chain Monte Carlos Feng 12 DIRECT DETECTION DAMA Annual modulation Collision rate should change as Earth s velocity adds constructivelydestructively with the Sun s Drukier Freese Spergel 1986 DAMA 86 signal With T 1 year max June 2 26 keV g DAMANa0L29tkmxj39r 39 339 3 lt lAl 39lALIBRA05339toanlE a target niass 873 kg 3 target mailss 2328 kg l t 9 l1 1 1 e 39 a g c f ll 31 1 it 1 3 1 Bi 3 j g g E iV Tl vEIT LNJ I 3 3 2 ET LL LE 1 1411411 quotit s 1 W 1 I i Q a 1 it up i 1 N i i 1 2 3 o g l T l j l i i i o a a i oo 8 1 3 i v z a 1 I 39 1 i I at 1 i i ll i 3l 1 I C r o F v 3W 11 39m 1 1m 1 Time day 15 Jul 09 Feng 13 CHANNELING DAMA s result is puzzling in part because the favored region was considered excluded by others This may be ameliorated by Astrophysics K Channeling in crystalline detectors 39 efficiency for nuclear recoil energy 9 electron energy depends on direction ETEXONO 2007 10 Gondolo Gelmini 2005 1 99 Drobyshevski 2007 DAMA 2007 Um39mne39ed XENDNIO I allowed region to Rather low WIMP masses GeV Very high 0839 103939 cm Channeled 39 ion O Channeling reduces threshold shifts O O 15 Jul 09 Feng 14 INDIRECT DETECTION Dark Matter annihilates in the halo to a place some particles an experiment 15 Jul 09 Feng 15 PAMELA AND ATIC 2008 1000 39 39 we r oe pre 41 5H 35 o o Positron fraction Ep3UdNdEp m4 5 H r rrPAMELWOQBX M ATC2008 391 1v 10D Energy Gav 70 100 1000 Energy Gav Solid lines are the predicted spectra from GALPROP Moskalenko Strong 15 Jul 09 Feng 16 ARE THESE DARK MATTER Must fit spectrum not violate other constraints photons antiprotons Neutralinos in supersymmetry XX 9 ee suppressed by angular momentum conservation XX 9 WW 9 e gives softer spectrum also accompanied by large antiproton ux KaluzaKlein dark matter from extra dims Appelquist Cheng Dobrescu 2001 3181 9 ee unsuppressed hard spectrum 31 couples to hypercharge Bee39 20 81 mass 6001000 GeV to get right Q BUT flux is a factor of 1001000 too big for a thermal relic requires enhancement astrophysics very unlikely particle physics 15 Ju09 1000 E KK dark matter with m 600 GeV E D a l i we 2 E uf ATIC 2008 10 n 1 0 100 1000 Energy GeV 0 010 I l I I 1115 300 9 o 0 an 0 o o a E3 5d edOdE cm zsAsrTlGeVz39B FERMI AND HESS 2009 Fermi and HESS do not confirm ATIC no feature consistent with background with modified spectral index i rHEAT 2001 ABETS 2001 0 AM 2002 5 01 I ATIC12 2008 x FPB BETS 2008 v HESS 2005 O u E3JE GeV m39Zsquotsr I y v HESS 2009 FERMI 2009 Fermi 2009 i i t 4 I 1 HI 15Ju09 102 E oev 1Os th m e e equot 3 Pulsars can explain PAMELA Zhang Cheng 2001 Hooper Blasi Serpico 2008 C 10392 Yuksel Kistler Stanev 2008 Profumo 2008 Fermi 2009 HEAT 9495 ICAPRICE 94 AMS 01 PAMELA 08 Fermi 2009 ll 1 illllll iiill r Iiillii 10 1039 102 103 E Gev Feng 18 14 I39eV 106198 t6 Dquotquar R39s73 2 TeV Re t r hfg gqarb WHAT THEN What LHC actually sees Ch 5 3 Eg do pair production Each quot1 9 neutralino x 2 X s escape detector missing momentum This is not the discovery of dark matter Lifetime gt 10397 s 9 1017 s 15 Jul 09 Feng 20 THE EXAMPLE OF BBN LIB r22 0005 on 002 003 0 b 025 gt 024 023 022 HH InquotE llr5 109 LiIlll a Ifr10 l l l 2 3 l 3 U T 25 LI 1 Bar39yonto plloton ratio 1110 15 Ju09 Nuclear physics 9 light element abundance predictions Compare to light element abundance observations Agreement 9 we understand the universe back to T1MeV t1sec Feng 21 DARK MATTER ANALOGUE Particle physics 9 39 dark matter abundance prediction 0 Compare to dark matter abundance observation o How well can we do xmT time gt 15 Jul 09 Feng 22 Contributions to Neutralino WIMP Annihilation l X W V quot A i r 2 if HMquot z 4 4 r A A 7 H i W X w r x l 3911 4 r H V 5 1 W X Z 739 7 A v F l x V x M X n x X x W Z W x m 1 X I r gtf11f5 J 1 li Jungman Kamionkowski Griest 1995 15 Jul 09 Feng 23 RELIC DENSITY DETERMINATIONS 30 quot39quotquotquotquotquotquot LHC best case scenario L001 m 20 g N gt v ILC is N 10 8 8 g 539 o N u 8 c 0 a 3 A N lt quotEL 1Q 5 PI k 3 g i gg WMAP anc Ev current 2010 9 I II I I II I I II I I I I I I I I I I I 90 95 100 105 mx GeV level comparison of predicted Qcomder with observed Qcosmo 15 Jul 09 Feng 24 BEYOND WIMPS The WIMP miracle seemingly implies that dark matter is Weaklyinteracting Cold Collisionless Are all WIMP miraclemotivated candidates astrophysically equivalent No Recently have seem many new classes of candidates Some preserve the motivations of WIMPs but have qualitatively different implications 15 Jul 09 Feng 25 SUPERWIMP DARK MATTER Feng Rajaraman Takayama 2003 A new class of candidates An example Supersymmetry Graviton 9 Gravitino G Page39s Primack 1982 Mass 100 GeV Interactions only gravitational supenNeak GnotLSP GLSP SM SM G LSP G Assumption of most of Completely different literature cosmology and particle physics 15 Jul 09 Feng 26 SUPERWIMP RELICS Suppose gravitinos G are the LSP Increasing lt17Avgt 1 WIMPs freeze out as usual l In WIMP Gye 77777777777 a But then all WIMPS decay to gravitinos after 39 MPIZIMW3 seconds to months xmT time a Gravitinos naturally inherit the right density but interact only gravitationally they are superWlMPs also KK gravitons quintessinos axinos etc Feng Rajaraman Takayama 2003 Bi Li Zhang 2003 Ellis Olive Santoso Spanos 2003 Wang Yang 2004 Feng Su Takayama 2004 Buchmuller Hamaguchi Ratz Yanagida 2004 Roszkowski Ruiz de Austri Choi 2004 Brandeburg Covi Hamaguchi Roszkowski Steffen 2005 15 Jul 09 Feng 27 SUPERWIMP COSMOLOGY Late decays can modify BBN Late decays can modify CMB Resolve 6397Li problems black body spectrum p distortions tau12 I norm 101 LUZ 003 i VCfusimc Miuwwwa BACKGROUND SrEyrRUM mom C933 I x m m 3 D N m s A 4 LO LO 9 Intentw 1nhrgscmisr mam zooz odd JexJes spieizi i 3 n 7 x mm mnunm 11 Dec 08 Feng 28 2 It Baryonrtorpimton WARM SUPERWIMPS SuperWIMPs are produced in late decays with large velocity 01c c Suppresses small scale structure as determined by Ms Q Warm DM with cold DM pedigree Dalcanton Hogan 2000 Lin Huang Zhang Brandenberger 2001 Sigurdson Kamionkowski 2003 Profumo Sigurdson Ullio Kamionkowski 2004 Kaplinghat 2005 Cembranos Feng Rajaraman Takayama 2005 Strigari Kaplinghat Bullock 2006 Bringmann Borzumati Ullio 2006 15 Ju09 luuu A m 0 eV Tl dlleCl Function lkl 800 400 7cm 10 04 Mpc 9003 1219 soueiqweo 1500 2000 2500 quot1 SWIM Gav 300 O Sterile v 7 Dodelson Widrow 1993 SuperWlMP 9003 19H5UId9gtl lo 4 I n k m Mpc lieng 29 HIDDEN DARK MATTER Start over What do we really know about dark matter All solid evidence is gravitational Also solid evidence against strong and EM interactions A reasonable 1St guess dark matter has no SM gauge interactions ie it is hidden Kobsarev Okun Pomeranchuk 1966 many others What one seemingly loses Connections to central problems of particle physics The WIMP miracle Signals 15 Jul 09 Feng 3O CONNECTIONS TO CENTRAL PROBLEMS IN PARTICLE PHYSICS We want hidden sectors SUSY Breaking Consider SUSY Connected to the gauge hierarchy problem Hidden sectors are already X required to break SUSY Hidden sectors each have their own particle content mass scale mX Interactions gauge couplings 9X 15 Jul 09 Feng 31 What can we say about hidden sectors in SUSY SUSY Breaking Generically nothing But in the attractive SUSY models that solve the flavor problem gauge mediated models anomaly mediated models the superpartner masses are determined by gauge couplings mXgX2 0X QC This leaves the relic density invanan Hidden 15 Jul 09 Feng 32 THE WIMPLESS MIRACLE Feng Kumar 2008 Feng Tu Yu 2008 The thermal relic density 10 I u constrains only one i combination of gX and mX 2 10392 m a 9X X N TX 10 3 00gt 9X These models map out the I I WlMl3less oM remaining degree of 10 106 10 4 102 10 102 104 freedom candidates have a mxleevl range of masses and couplings but aways the Naturally accommodates right relic density multIcomponent DM all with relevant Q 15 Jul 09 Feng 33 HIDDEN CHARGED DM How is hidden dark matter stabilized Ifthe hidden sector is standard modellike the most natural possibility is that the DM particle has hidden charge and so is stabilized by charge conservation cf the electron m GeV q MSSM W sparticles W Z t N O p ey VG Hidden flavorfree MSSM mX sparticles W Z q I quotror 239 N O gyvG 15Ju09 Feng 34 HIDDEN CHARGED DM Feng Kaplinghat Tu Yu 2009 This scenario shares all WIMP motivations but now 39 39 quotquotquotlnx39 391quotiquotev39 there are strong DMDM taneRHlto8o8l 133 iii interactions with many 100 novel astrophysical 5 implications 5 l 10391 l e l Eg Compton scattering 3 Mquot e Mquot 2 r l delays kinetic decoupling 9 10100 101 102 103 104 105 106 small scale structure k lMpc 15Ju09 Feng 35 DM SELFINTERACTIONS Also have DM selfinteractions through Rutherford scattering Highly velocitydependent y constrained by existence of non IQ 4quotquot3 U4 51114 6 spherical halos bullet cluster 2 do ot39X 10O 10 1 g If dark sector has only EM hard 10 a X to get correct thermal relic denSIty 04 Ackerman Buckley Carroll Kamionkowski 2008 if 10 10 10 7 E With dark SM weak interactions 13 39 E can give the right Q lots of 10 1502 W 100 m 10 103 104V freedom m GeV 15 Jul 09 Feng 36 The Physics of Music Physics 15 Insfrucfar David Kirkby Universify of California Irvine dkirkby uciedu Midierm m m tsmrtan htmmnm was My mmmg m t g an in NW m stdmn 731mm mo Marian m Wmquot quotanquot M Lecture 10 m m mm a war m i m M m m m m W m up w i m aquot m Wm 39Sm es quot 392 mumm kngmmqmms an Pyvhagur 5 i mum unmmmmms Macawquot EquaiTemperamemScaie NW NW Ummmux 5mg mmquot may in mde mmquot 25v in W mummy mmm mmw s w mum is 35v Drup imam u n m Qadny H mm sgnumrts 5 in mm Undngmd m W W A ms mam minimum m m mde mm mquot Ladgnrd mgmmmu m MSYB Hamtwmk m mde mm m Wm an m m m W quot100 Review uf Lemme 9 Mume mm m pmmn 01 mmm Vans 1 Wm mm D i adtsa quotWWWmm mm 01 pm pmmn m mum impar mu 01 mum and Vriqumzyzuts The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu Musical Scales Harmonic Timbres There is an infinite continuum of possible frequencies to Most musical sounds have overtones that are use in music approximately harmonic Ge equally spaced on a linear requency axis But in practice most music uses only a small finite number of specific frequencies This is most likely due to a combination of two related factors We call each of these special frequencies a musical um The resonant frequencies of many naturally occurring and call a set of notes a musical scale 39 resonant systems are approximately harmonic Different cultures have adopted different scales The your bmm ls ophmlud far llSTenmg TO Tlmbres Thu are approximately harmonic choice of scale Is primarily aesthetic but some aesthetic judgments are heavily influenced by physical considera ons 23 dissonance Note that there are examples of naturally occurring I Inharmonlc sounds eg a hand clap but we do not perceive What can physics tell us about musical scales These as bemg mus39cal39 physmi annm l D Why 7 physmi annm l D Why h Octaves Rule Two notes played together on instruments with harmonic The correct answer to the octave test was 4 although timbres sound most consonant least dissonant when their most people prefer a slightly bigger octave with a fundamental frequencies are an exact number of octaves frequency ratio of about 2021 that corresponds to 6 apart This preference for slightly stretched octaves may be due to our familiarity with listening to pianos which are usually I I I I I I frequency deliberately tuned to have stretched octaves more about this in Lecture 14 In this sense an octave is a special interval that we can expect will play a special role in any quotnaturalquot scale although it is certainly possible to invent unnatural scales Try this demonstration to see if you can pick out octaves whysmi Inch ml Why v whysmi Inch ml Why In Subdividing the Octave Scales and Timbre In practice this means that if a particular frequency is The choice of a scale subdivisions of an octave is included in a scale then all other frequencies that are an intimately related to the timbre of the instrument that exact number of octaves above or below are also included will be playing the scale Therefare changing The 52 Of quotDIES In use in a scale The scale and timbre are related by dissonance the notes boils down to the problem of how to subdivide an octave if a ale Shauld quotOT saund unpleasam when Played oge er For example most people listening to an instrument with no overtones e a pure SHM sine wave will have no preference for how to subdivide an octave and the octave is no longer a special interval Is the choice of how to subdivide an octave purely est etic or are there physical considerations that prefer certain musical intervals r these o learn more about the connection between scales and timbre why hi Mm Inch l D Why 11 why hi Mm Inch l D Why 12 The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu How Finely to Chop the Octave However most people listening to an instrument with Minimizing the dissonance of notes played together on harmonic timbre Ge most quotmusicalquot instruments will have instruments with harmonic timbres gives us some guidance a definite preference for certain intervals where on how to create a scale with a given number of notes but overtones coincide exactl not on how many notes to use y Different instruments with harmonic timbres have Some of the conventional choices are different strengths for the various harmonics These Penfafanic fave is divided in 5 nofgs 2939 Ancienf differences af ect how consonant th preferred intervals Greek Chinese Celtic Na ve American music are but do not change their frequencies Diatonic Modal octave is divided into 7 notes eg Indian traditional Western musi ThEFEFOT E The is 0 universal 52 0f Pr f rr d Chromatic octave is divided into 12 notes modern subdivisions of the octave for instruments with harmonic Wesfern music timbres based on a physical model of dissonance WNWmic mum l D Why WNWmic mum l D Why A Primer on Musical Notation The white notes on the piano are named ABCDEF gt 90mg up quotl frequencyllawards The gm 0quot le keybaard from a white note to Its adJacent black note gives a sharp 3 After 6 we start again at A This reflects the special role C 9 25 TO C 39 D 9 25 TO bu39 539 of the octave we give two frequencies an octave apart the Similarly Being down in frequency gives a at D goes To same note name U E goes to E etc I EL 9ND D E 9ND CM Fwy A c D new i t C C and U are necessarily the same note on the piano but this is not generally true for all possible scales mm mm ml mm mm mm ml mm Pentatonic Scales The usual choice of 5 notes in a pentatonic scale iano Other choices of 5 notes are also possible corresponds to the black notes on the p Examples Indian music 3927 Chinese music Q39 Celtic music Auld Lange Syne My Bonnie Lies Over the Ocean This scale includes the dissonant whole tone 98 interval but leaves out the less dissonant major 54 and minor 65 third intervals Why Presumably because music limited to just 5 notes would be boring without some dissonance to create tension WNWmic mum l D Why WNWmic mum l D Why The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu Diatonic Scales The major and minor scales of Western music are diatonic Most Western music since the 17th century is based on scales in which the octave is divided into 7 steps major and minor scales The notes of the major scale correspond to the white Earlier music was Primarily modaL notes on a piano starting on C The natural minor scale corresponds to the white notes starting on A Example gregariaquot chums I Diatonic scales can also start on any other white note of the piano The results are the modes with names like Dorian Phrygian Lydian mm a Music Lawn NJ mm W mm a Music Lawn NJ mm at Chromatic Scales Although most Western music is based on diatonic scales The main reason for adopting a chromatic scale is to be it frequently uses scales starting on several different able to play pieces based on different scales with the notes in the same piece of music as a device for adding same instrument interest and overall shape Ari octave divided into twelve notes includes all possible A major scale starting on C uses only white notes on the seven quotOle d39afamc scales piano but a major scale starting on B uses all five black quot012 Not all instruments adopt this strategy For example harmonicas are each tuned to specific diatonic scales To play in a different key you need a different instrument or else to master bending techniques What exactly should be the frequencies of the 12 notes that make up a chromatic scale mm a Music Lawn NJ mm at mm a Music Lawn NJ mm 22 The Circle of Fifths Is there an obvious way to subdivide an octave into twelve We can reach all 12 notes of the chromatic scale by notes walking up or down the piano in steps of a fifth 32 Yes the notes should be equally spaced and include all of Going up we reach all the special consonant frequency ratios 32 43 white notes of the piano To what extent is this actually possible lmth The Sharps After the octave the fifth 32 is the most cahsahaht 90mg dOWquot W hquot F rst interval for harmonic timbres The fourth 43 is really 1quot Thequot 9 hmugh quot392 just a combination of the octave and fift als39 llllll l mm a Music Lawn NJ mm 23 mm a Music Lawn NJ mm 24 Either way we eventually get back to a6 7 octaves away if we start on a 43 32 x 12 The Physics of Music Physics 15 Insfrucfar David Kirkby Universify of California Irvine dkirkby uciedu Using ii siisi in iiiiis w mi mimisi ii Wtqunry A siiiiisi mnhad is ii mm siP mi byu iiiii sisiyisiwnmsigsingspss i vimmam x3Z22 2 WW 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nuiiii im ii ddmis ii mi imwismi ssa ms up si iiyig is iiiik siyiiinisis siin iim ii miiiiomisiiyiimi hm imima quotmas ii misus tqmiiyspxtd si 1 isgsiiiiiit Ms sssis issii ipiii ii isiiig si iiinias hm ssa swig d ntmiydtpmdng si ii sisis sisiiiiiig isi isi sanimis sssi suiisim ssim minim iis msiis mm iiismpismimsissgii aimimi musisms isi um D is iisim is ii swim b wun qudiyrspuud mus si imnrum isssiiiiiiisssm 4 ssiss msys iisymi s Vipptd ssssmins si ii sssssiX ssisii sis usisiis s an is sissism sis is ssssiisss sysi xmisiiisi ssssxiss ave minim Limninchises Wis nsissssiiixinsiississiiisiss ssiissi A ssssiisisis smisi sssisssi is sissisismss smiisi isquot si simimi iiisssssgt ssmsisxsisimi sysism s is minY is iiiiiis msss A iiiiins sss s sisi ssi Psismisi siii sysisii is ism is si xiisiisisis swiiiismssssissiisi sssssii is smsisi s ms iisi is siisssyssii sissisisss wiii ii iimiiissssss issiiim ism sissisisss ws isquot iss iiiik aHM ssisisi sss iiisims siiss is ii iii ssss ssisssi iiiiiiins sssss The Physics of Music Physics 15 InsTrucTor David Kirkby UniversiTy of California Irvine dkirkbyuciedu LimiTing Cases for Rope Waves NegaTIve reflecTIon 1 If The exTra rope is heavy enough This N T 39 39 Is essenTIally The same as flxmg The end 0 rmsmlssmn wave passes Through The Join unaffecTed TransmiTTed unchanged 39vv 3 If The exTra rope is much lighTer Than The original rope This is essenTially same As leaving The end free a whip PosiTive reflecTion No Transmission 2 If The exTra rope is The same as The original rope The 2 k No reflECllon Physics of MusicLecTure4D Kirkby 7 PhysicsofMusicLecTure4D Kirkby 8 Try This or To find ouT In addiTion To The reflecTed wave we find a TransmiTTed wave WhaT did ou learn y The process of TransmiTTing a wave Through an inTer face where The wave speed changes is called refracTion If The exTra rope is heavier slower Than The original rope The reflecTed pulse is a negaTive of The original The refracTed wave is always a smaller version of The pulse and Smaller original pulse iT is never flipped To be a negaTive pulse If The exTra rope is lighTer fasTer Than The original rope The reflecTed pulse is The same as The original buT smaller Physics of MusicLecTure4D Kirkby 9 PhysicsofMusicLecTure4D Kirkby 1o ReflecTion amp RefracTion ReflecTion and refracTion are complemenTary processes ThaT boTh occur aT The boundary beTween Two differenT media The reflecTion coefficienT R measures The ampliTude of The reflecTed wave compared wiTh The incidenT wave A negaTive coefficienT indicaTes a negaTive reflecTion The Transmission coefficienT T measures The ampliTude of The TransmiTTed wave IT is always posiTive The incidenT wave is converTed enTirely inTo TransmiTTed and reflecTed waves T R 1 wwwmwv Physics of MusicLecTure4D Kirkby 11 PhysicsofMusicLecTure4D Kirkby 12 The Physics of Music Physics 15 UniversiTy of California Irvine InsTrucTor David Kirkby dkirkbyuciedu InTo The Second Dimension UnTil now we have only considered one dimensional wave even when we looked aT Two dimensional represenTaTions such as The air parTicles How are Things differenT in Two dimensions The main difference is ThaT you can Travel in more Than one direcTion Special Cases of 2D Sources Plane waves are really JusT one dimensional waves since The disTurbances aT differenT places are all in parallel direcTions d irecTion of Travel Plane waves are a maThemaTical idealizaTion since They require an infiniTely long source Physics of MuslcL2clur24DKrkby 13 Physics of MuslcL2clur24DKrkby 14 Circular waves or spherical waves originaTe from a poinT source and spread ouT in circles or spheres Circular waves look like plane waves up close anoTher limiTing case Principle of SuperposiTion in 2D The PoS holds JusT as well in any number of dimensions Example DisTurbance A circular wave cenTered aT 10 DisTurbance B circular wave cenTered aT 10 WhaT does The combined wave moTion look like Physics of MuslcL2clur24DKrkby 15 Physics of MuslcL2clur24DKrkby 16 See also of mulTipole sources ReflecTion ltS RefracTion in 2D When we considered reflecTion amp refracTion of Transverse waves on a rope we were only considering one dimensional propagaTion aT The inTerface beTween Two media A pulse reaching a one dimensional inTerface can eiTher bounce back reflecT andor keep going refracT In Two dimensions a wave can also change iTs direcTion of propagaTion q x Physics of MuslcL2clur24DKrkby 17 Physics of Music L2clur24 D Kirkby 18 The Physics of Music Physics 15 UniversiTy of California Irvine InsTrucTor David Kirkby dkirkbyuciedu WhaT deTermines any change of a wave39s direcTion of propagaTion aT an inTer face LisT The variables in This problem The angle aT which The incidenT wave hiTs The inTer face The wave39s speed before The inTer face The wave39s speed afTer The inTer face v before Physics of MusicLecTure4 D Kirkby 19 ReflecTion in 2D ReflecTion from a smooTh surface is specular The angle of incidence equals The angle of reflecTion This simple rule sTill leads To some complex effecTs For example a disTance lighT source reflecTed from a sphere has highlighTs Physics of Music LecTure4 D Kirkby 20 AnoTher complex effecT occurs when lighT on The inside of a circular or cylindrical objecT Try This demo The resulTing pileup of reflecTed rays produces a characTerisTic shape called a causTic curve Physics of MusicLecTure4 D Kirkby 21 RefracTion in 2D Toy Analogy WhaT happens when The Toy enTers The grass where iTs wheels will Turn slower Physics of Music LecTure4 D Kirkby 22 FirsT whaT happens if The Toy hiTs The grass head on nor a incidence lllllll l BoTh wheels enTer The grass and slow down aT The same Time The Toy does noT change direcTion When leaving The grass The Toy speeds up buT again does noT change direcTion Physics of MusicLecTure4 D Kirkby 23 WhaT if The Toy enTers The grass aT an angle so one wheel hiTs The grass and slows down before The oTher M i During The TransiTion period when one wheel Turns fasTer Than The oTher The Toy will roTaTe Physics of Music LecTure4 D Kirkby 24 The Physics of Music Physics 15 Instructor David Kirkby University of California Irvine dkirkbyuciedu Refraction Lenses The amount that the toy rotates depends on If a wave passes through a pair of parallel interfaces it 39 how different the speeds are in and out of the grass emerges 0quot 1 Pall ParallEl 0 lls original Pal 39 how long the wheels are turning at different speeds Who if The inferfaces are quotof parallel The length of time the wheels are turning at different speeds depends on the angle at which the toy approaches the gross I 7 Waves arriving at an interface where their propagation speed changes undergo exactly the same change in W 39 a direction r l l 391 T mm of Music mm 4 I mm 25 mm of Music mm 4 I mm 2a Refraction Prisms The air near the surface of the earth can act as a sound What if the speed of wave propagation depends on the lens if the speed of sound varies with elevation frequency A continuous change of the speed with elevation causes The frequency of visible light corresponds to its color t e wave directions to be continuously deflected In a smooth curve The speed of light in air is almost independent of frequency but varies in glass This leads to prism effects Eg if speed of Tr Ylhis sound increases with elevation Mini Mini due to increasing temperature or winds v w u w if H 4 mm of Music mm 4 I mm 27 mm of Music mm 4 I mm 28 Refraction Water Waves Diffraction Ocean waves are often approximately plane waves Reflection and refraction are universal properties of wave propagation at an interface where the medium changes As they approach the shore the wave speed decreases in shallower water causing the waves to become more parallel Anofher universal feufure is diffruc on39 With the shoreline Diffraction results in waves spreading out from any discontinuity eg and edge or isolated point they find Diffraction allows waves to bend around an obstacle When ou hear someone talking around the corner you are hearing diffracted sound and possibly also reflecte sound mm of Music mm 4 I mm 29 mm of Music mm 4 I mm 3n The Physics of Music Physics 15 UniversiTy of California Irvine DiffracTion and WavelengTh DiffracTion is imporTanT for how sound spreads ouT from a source The amounT of spreading increases when sound passes Through a narrow opening narrow compared To The wavelengTh Ill allqu him Ilg 39 39 39lj uh InsTrucTor David Kirkby dkirkbyuciedu Physics of MusicLecTure 4DKirkby 31 Try This demo To see diffracTion of high frequency sound produced by a TweeTer speaker Physics of MusicLecTure 4DKirkby 32 ReflecTion and refracTion can boTh be ThoughT of as limiTing cases of diffracTion we can approximaTe a smooTh inTerface wiTh many poinT like sources caccgcccnccgo Physics of MusicLecTure 4DKirkby 33 AnoTher 2D EffecT Doppler EffecT Things geT more inTeresTing when The source of a wave is moving This is parTicularly True for sound waves where a source can easily reach speeds near or even exceeding The speed of sound 1 This resulTs in The Doppler effect ill NoTe ThaT The source in This example is generaTing sound aT a consTanT frequency The apparenT change of piTch is enTirely due To The source s moTion ChrisTian Doppler 1803 1853 Physics of MusicLecTure 4DKirkby 34 WhaT do we observe The sound appears To have a higher frequency as iTs source approaches and Then a lower frequency as iT recedes Try changing The source s speed in This demo and waTch whaT happens To The spacing of The wave cresTs Physics of MusicLecTure 4DKirkby 35 CaTching Up Shock Waves Things geT even more inTeresTing when a source of sound Travels aT The speed of sound or fasTer This causes a pileup of The wave cresTs or shock wave Shock waves are imporTanT for music also We will see laTer ThaT shock waves occur when playing a brass insTrumenT Physics of MusicLecTure 4DKirkby 3e The Physics of Music Physics 15 UniversiTy of California Irvine LecTure 15 Percussion InsTrumenTs PIaTes I Keyboard InsTrumenTs Piano The Human Voice InsTrucTor David Kirkby dkirkby uci edu Review of LecTure 14 We covered Those percussion insTrumenTs based on vibraTing barsrods and membranes We saw ThaT The common feaTure of percussion insTrumenTs is Their inharmonic Timbre and ThaT is due To The more complicaTed naTure of Twodimensional resonance Some percussion insTrumenTs eg xylophone make adapTaTions so ThaT They sound more harmonic and can be used melodically Physics of Music LecTure 15 D Kirkby 3 Cymbals Gongs and TamTams Cymbals are circular plaTes usually made of bronze wiTh an almosT flaT saucer like shape Gongs and TamTams are similar To cymbals buT wiTh more curvaTure aT Their edges Physics of Music LecTure 15 D Kirkby 5 InsTrucTor David Kirkby dkirkbyuciedu Miscellaneous We agreed ThaT Problem SeT 7 is worTh 75 poinTs insTead of The usual 50 poinTs We agreed ThaT The final exam will cover all The lecTures 118 and MT JusT Those since The midTerm 918 I will be Traveling on Tuesday nexT week Prof David Casper will give The firsT lecTure on Music and Technologyquot covering Topics such as Loudspeakers microphones Amplifiers Special effecTs The lasT Two lecTures will cover compression eg MP3 and Techniques for synThesizing music elecTronically Physics of Music LecTure 15 D Kirkby 2 VibraTions of PIaTes A plaTe is a solid objecT whose Thickness is small compared wiTh iTs oTher dimensions A plaTe has The same relaTionship To a membrane as a rodbar has To a sTring Tension force is replaced by sTiffness and oTher dimensions e g Thickness influence The sound The sTanding waves on a flaT circular plaTe are similar To Those of a circular membrane buT Tend To be higher in frequency PIaTes are noT necessarily flaT in Their resTing posiTion unlike membranes Physics of Music LecTure 15 D Kirkby 4 STeel Drums STeel drums are a recenT invenTion developed by Trial and error using The 1000s of oil drums lefT on The beaches of Trinidad Si Tobago by The BriTish Navy afTer World War II The playing surface pan of a sTeel drum is hammered inTo a concave shape wiTh individual noTe areas LisTen To an example 395 1 Physics of Music LecTure 15 D Kirkby e The Physics of Music Physics 15 Universi ry of California Irvine Ins rruc ror David Kirkby dkirkbyuciedu Bells and Carillons Bells are an0139her form of vibra139ing pla139e in 139his case 139he pla139e is curved info a bell shape A carillon is a se139 0f 139uned bells c0n139r0lled from a keyboard Lis139en 1390 an example g Handbells were developed 1390 allow church bell ringers 1390 prac139ice wi139h0u139 dis139urbing 139he whole neighborhood Keyboard Insfrumenfs Keyboard ins139rumen139s c0nsis139 0f 139uned s139rings coupled 1390 an airfilled cavi139y S139rings are s139ruck 0r plucked by a mechanical ac139i0n which is c0n139r0lled from a keyboard Pianos clavichords and harpsichords are all examples of keyboard ins139rumen139s Physics of Music chfurz 15 D Kirkby 7 Physics of Music chfurz 15 D Kirkby 8 Piano Consfrucfion Piano Sfrings Piano s139rings are made from highs139reng139h s139eel and usually s139re139ched 1390 ab0u139 half of 139heir breaking s139reng139h on a me139al frame The s139rings of a piano are alm0s139 ideal onedimensional s139rings bu139 have some inharmonici139y 139ha139 ge139s worse a139 higher harmonics Pianos cover 139he frequency range from 27 5 Hz A 0 1390 4186 Hz wi139h 88 keys a ra139i0 of 15221 Ra139her 139han have 139he l0nges139 s139rings 152x longer 139han 139he sh0r139es139 ones 139he 139ensi0n and mass are varied in differenf ranges Physics of Music chfurz 15 D Kirkby 9 Physics of Music chfurz 15 D Kirkby 10 Piano Tuning A piano sounds bes139 in 139une when i139s 0c139aves are s139re139ched 1390 ma139ch 139he inharmonici139y 0f 139he s139ring 0ver1390nes M0s139 n0139es 0n 139he piano have 139hree corresponding s139rings The piano sounds bes139 when 139hese s139rings are sligh139ly 0u139 0f 139une wi139h each 0139her 139his delibera139e mis139uning allows 139he vibra139i0ns 0f 139he s139ring 1390 las139 longer 0139herwise 139hey 139ransfer 139heir energy 13900 efficien139ly 1390 139he soundboard When 139he s139rings are 13900 far 0u139 0f 139une 139he resul139 is a h0nky1390nkquot piano sound HammerSfring Inferacfions The mechanical ac139i0n 139ha139 139ransla139es a key press in1390 139he hammer hi139139ing 139he s139ring is surprisingly complex This mechanism has 3 main purposes 1390 provide a lever ac139i0n s0 139ha139 139he hammer 139ravels fas139er 139han 139he key 1390 provide an escapemen139 ac139i0n s0 139ha139 139he hammer moves independen139ly 0f 139he key 1390 raise and lower a fel139 damper 139ha139 allows 139he s139rings 1390 vibra139e freely Physics of Music chfurz 15 D Kirkby 11 Physics of Music chfurz 15 D Kirkby 12 The Physics of Music Physics 15 UniversiTy of California Irvine InsTrucTor David Kirkby dkirkbyuciedu Piano Pedals A piano usually has 2 or 3 fooT operaTed pedals The righT mosT pedal raises The dampers on all sTrings so ThaT They conTinue To vibraTe afTer a key is released and are also free To vibraTe sympaTheTically when oTher noTes are played The lefT mosT pedal makes The insTrumenT quieTer by eiTher shifTing The hammers To miss one sTring or else by moving The hammers closer To The sTrings A cenTer pedal if presenT usually susTains only Those noTes being played Physics of Music Lecture 15 D Kirkby 13 Piano Soundboard The sound board plays a similar role To The fronT and back plaTes of a sTring insTrumenT and is responsible for producing mosT of The sound ThaT you hear VibraTions of The sTrings are TransmiTTed To The sound board via a bridge AlThough The meTal frame hold The sTrings does mosT of The work some of The sTring Tension is TransmiTTed To The sound board via The bridge This force ToTals 300 lbs Physics of Music Lecture 15 D Kirkby 14 The Human Voice Your voice is primarily for communicaTing buT is also a very versaTile musical insTrumenT Some of The quesTions we will address nexT are WhaT is The insTrumenT39s energy source WhaT are The resonaTors in The voice insTrumenT39 WhaT is The difference beTween vowels and consonanTs WhaT is The difference beTween spoken and sung words Is The voice more like a sTring brass or woodwind insTrumenT Physics of Music Lecture 15 D Kirkby 15 The Voice InsTrumenT The source of energy is The air in your lungs ThaT you force ouT under pressure Through your vocal TracT The main chambers of your vocal TracT are your larynx ml cayiTy and nasa cayiTy Physics of Music Lecture 15 D Kirkby 16 Vocal Chords The word chords suggesTs a sTring insTrumenT buT in facT The vocal chords are more like a TrumpeT player39s lips Your vocal chords are locaTed JusT behind your Adam39s apple The chords are normally open so you can Vi I breaThe buT can be 39 39 9 JP Pm closed under muscle l L 3 l39Him i1 mills I39H39 15117 conTrol For a movie of The vocal chords in acTion see Physics of Music Lecture 15 D Kirkby 17 There are 3 main ways ThaT you use your vocal chords To conTrol The sounds you produce Leave The chords open sss or parTially open quothuhquot Suddenly opening The chords produces an explosive coughlike sound say ldioT vehemenle Rapidly open and close The chords To produce repeTiTive pulses of air compare 222quot and sss wiTh your finger on your Adam39s apple 7397 quoti 4 J39s 31 The lasT Technique is The mosT versaTile and is similar To how a brass insTrumenT is played Ill L fl is Physics of Music Lecture 15 D Kirkby 18 The Physics of Music Physics 15 InsTr39LlcTor39 David Kirkby Universi ty of California Irvine dkirkbyuciedu An important difference between a brass player39s lips and The sound produced by the vocal chords alone depends on the vocal chords is the absence of strong feedback from how much force you use to try and close them against the the rest of the instrument pressure ofair from your lungs Whisper This means the frequency at which your chords vibrate is Emmy under your direct muscle control and not determined by the resonances of your vocal tract 3 Normal e normal range of chordvibration frequencies used by women is 140400 Hz and 70 200 Hz for men The upper end of these ranges is extended about an octave for 9 Air flow through vocal chords singin What sound do the vocal chords produce on their own s39mimd ine The Vocal Tract Forman ts The total length of the vocal tract is 1718Cm It is closed The broad resonances of the vocal tract are called at the vocal folds and open at the mouth and nose forinants ey are driven syinpathe ically by the e result is that the vocal A halfopen air column of the same length has resonant My frequencies at about 500 1500 2500 Hz lorinant resonances The vocal tract has resonances at similar of vocal tract frequencies but unlike an ideal pipe these resonances are of low quality and requmv inquot v so spread over a wide range 0 Tlmbr39e of normal frequencies mostly because the walls of chord Vlbrutlons the vocal tract are soft kesulting im re The Vocal Trust In Mo tion What does all this motion of the vocal tract do to the 7 It39s 10 below outside quot quotquotd Wquot Pmduce39 You control the central frequencies of each forinant by making adjustments to the s ape of your vocal tract The changes are most y to the crosssectional area and not to Le boulanger the 392quot H but one bieres 9 The main articulators that can vary the shape of the vocal tract are the Lips Tongue Why did Ken set the soggy soft palate gateway between oral and nasal cavities net on topof his deck The Physics of Music Physics 15 University of California Irvine Instructor David Kirkby dkirkbyuciedu Speech Articulation block the passage of air through the v c An articulator can partially fricative or completely stop o al tract A partial blockage fricative causes a noisy hissing sound b erve how changing the shape of your vocal tract articulation determines the sound that you produce PhysicsoMu5icLlc ml15D Why The building blocks of speech are called W A simple classification of phonemes groups them into vowels and consonants For acoustical study a more useful classification is Plosives Fricatives consonants Other consonants Pure vowe s Dipthongs vowels mm M Mm Llc ml 15D Why 2 Plosives and Fricatives air is release determines resulting consonant sound flow throug PhysicsoMu5icLlc ml15D Why Plosive sounds think aplosive result from a sudde release of air he 39 Fricative sounds think frying result from turbulent air h a narrow constriction The location of the constriction determines the resulting consonant sound Voiced Sounds Plosives are transients try sustaining a single p39 sound but fricatives can be sustained Both have the characteristic timbre of noise a range of frequencies are produced with none standing out in particular Plosives and fricatives come in unvoiced and voiced forms the first and second of each pair of examples Unvoiced sounds are produced with the vocal chords o en The chords vibrate during voiced sounds Compare sss39 and 22 mm M Mm Llc ml 15D Why 2x Other Consonants The other consonantsquot include the analyzer to see why they are called glides Liquids I r Nasals m ring voiced through the nose only Glides or semivowels w y look at the frequency PhysicsoMu5icLlc ml15D Why Vowels Vowels are sustained voiced sounds with a definite pitch Their timbre is determined by the formants You produce different vowel sounds by adjusting the shape of your vocal tract to change the frequencies of these formants The pitch of a vowel is determined by how fast you vibrate your vocal chords while the timbre is determined by the formant frequencies This is the reason why the same vowel can be spoken or sung at different pitches mm M Mm Llc ml 15D Why an InsTrucTor David Kirkby dkirkbyuciedu The Physics of Music Physics 15 UniversiTy of California Irvine Vowels and FormanTs Here are some examples of The vocal TracT shape and corresponding Timbre for some vowels Vowel IdenTificaTion Look aT The specTrum of differenT vowels wiTh The analyzer Can you idenTify The formanTs How do They change for differenT vowels r2 lurk Physics of Music Lecture 15 D Kirkby 31 I I rim 39 lt To a good approximaTion m Q 1700 we can characTerize each Fl H17 vowel by The frequenc1es quotquot D hitti 1 a pu of The lowesT Two F1 F2 3 5 he formanTs W iii 1 fan39th AMERICA ENGLISH Dam PEWYSOHampBarmy 1952 9m F2 Hit 7 Physics of Music Lecture 15 D Kirkby 32 There is a universal seT of vowel sounds ThaT can be produced we all have The same vocal TracT alThough noT all languages use all possible vowels Compare American and BriTish english vowels r2 our r2 our n am in 6 mm 7 m quot quot bgu pm m Fl 7 Hz 596 bwk H W mm 6 t W caught Pu 7 bird be e i 7 he 6 5quot V m um pol hot 9 e m bum s e m h l lul quot I e m bet fest e m farther AMERICAN ancusn Date Peterson8ltBam2y 1952 gun RRITI H FNI I I H Date Deterdmg t997 e m snn lSnn 72m zsnn 2m mu s u 2m zsnn m s u 2 Hz F2 H DipThongs Finally The lasT caTegory of sounds are dipThongs DipThongs are sounds ThaT morph from one vowel sound To anoTher vowel sound due To The moTion of The Tongue Some examples are nghTquot ahee mgTe ehee quotmt l39quot awoo mgnT aou oilquot awee Look aT some dipThongs on The specTrum analyzer Physics of Music Lecture 15 D Kirkby 33 Physics of Music Lecture 15 D Kirkby 34 The Singing Voice The main challenge for producing musical sound wiTh The voice is ThaT The formanT frequencies are noT harmonically relaTed To The vibraTion frequency of The vocal chords When singing you make several adapTaTions To adjusT The frequencies of your formanTs To be more harmonic Larynx is lowered 39 Jaw is opened wider Tip of Tongue andor lips are pushed forward Singer39s FormanT The lowering of The larynx helps To produce a new singer39s formanTquot aT high frequency 25003000 Hz near The resonanT frequency of The ear canal The origin of This formanT is a narrowing of The larynx beTween The vocal chords and The epigloTTis WaTch This demo To see how The narrowing of This caviTy alTers The formanTs and The resulTing sound 47 Compare The frequency specTrum for spoken and sung vowels Physics of Music Lecture 15 D Kirkby 35 Physics of Music Lecture 15 D Kirkby 3e


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