The Physics of Music and Color PDF
Preview The Physics of Music and Color
Leon Gunther The Physics of Music and Color Sound and Light Second Edition The Physics of Music and Color Leon Gunther The Physics of Music and Color Sound and Light Second Edition 123 LeonGunther DepartmentofPhysicsandAstronomy TuftsUniversity Medford,MA USA ISBN978-3-030-19218-1 ISBN978-3-030-19219-8 (eBook) https://doi.org/10.1007/978-3-030-19219-8 1stedition:©SpringerScience+BusinessMedia,LLC2012 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewhole orpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof illustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway, andtransmissionorinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthis publication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesare exemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationin thisbookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublisher northeauthorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerial containedhereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremains neutralwithregardtojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Dedicatedtomymother,Esther(Weiss)GuntherWand, whonurturedmewithadeepappreciation ofmusicandthebeautyofnature, andtomywife,Joelle(Cotter)Gunther, whosustainsmewithherloveandwisdom Preface to the Second Edition Over the course of the years since the first edition was published in 2011, I havecomeacrossmanyfascinatingphenomenathatinvolveorarerelatedto soundandlight.Asaresult,Ihavefeltthedesiretopublishasecondedition. Highlights in this second edition are the addition of sections on the followingsubjects: • Onthebeatsofthesoundofabell • AMandFMradio • On the spectrogram, which can display the flow of the frequency of a waveintime.Itcancapturetheessentialcharacteristicsofawave,oftenof soundwaves—withapplicationsindiagnosingmedicalproblemswiththe voiceandinidentifyingbirdcallsvisually—butalsoofelectronicsignals suchasthoseproducedbyEKGsandmorerecentlyevenofgravitational wavesemittedbybinaryneutronstarsthatcollapsedbillionsofyearsago. • Onthediopter,whichisaparametercentraltoexpressingthepowerofa lens. • Ontheluminanceofabeamoflight,whichisrelatedtobrightness.Ifeel thatthissubjectisquitecomplexbutisnottreatedinaclearandaccessible waybyamultitudeofsourcesontheweb.Thisbookpresentsanessential explanationofluminancewithoutexcessivecomplexity. IhaveaddedtwonewAppendices: • OnNumbers:dealingmostimportantlywithorderofmagnitude,signifi- cant figures, and relative changes, all of which are important in making calculations in this book. Included are tricks (“shortcuts” might be a better word) for simplifying the calculation of the relationship between the relative change of one parameter and the relative change of another parameteruponwhichthefirstdepends.Asexamplesofusingatrick,we willbeabletoeasilydeterminetheeffectofachangeinthetensionofa violin string on its pitch or the effect of a change in temperature on the pitchofaflute. • On Photons: dealing with the mysterious, incomprehensible behavior of photons in a clear way. This behavior indicates that quantum theory requires a major change in the conduct of the discipline of Physics and changes the assumptions as to what Physics has to say about“reality.” It istheopinionofthisauthorthatPhysicshasnothingtosayaboutreality andthattheterm“reality”fallsonlywithintherealmofPhilosophy. vii viii PrefacetotheSecondEdition Ihaveaddednumerousproblemsattheendofthechapters.Andfinally,I haveclarifiedmuchofthematerialinthefirstedition. The second edition calls for me to express my deep gratitude to my friend and colleague Ivo Klik for reading through the new sections in this edition,providingmewithnumeroussuggestionsforimprovedwordingand correctingtypos. Preface to the First Edition ThistextbookhasitsrootsinacoursethatwasfirstgivenbyGaryGoldstein andmeatTuftsUniversityin1971.Weareboththeoreticalphysicists,with Gary focusing on the study of elementary particles and my focusing on condensed matter physics, which is the study of the fundamental behavior of various types of matter—superconductors, magnets, fluids, among many others.However,inaddition,webothhaveagreatloveandappreciationfor thearts.Thisloveisfortunatelyalsomanifestedinourinvolvementtherein: Gary has been seriously devoted to oil painting. I have played the violin since I was seven and played in many community orchestras. I am also the founder and director of a chorus. Finally, I am fortunate to have a brother, Perry Gunther, who is a sculptor and my inspiration and mentor in the fine arts. ItiscommontohaveacourseoneitherthePhysicsofMusicorthePhysics ofColor.Numeroustextbooksexist,manyofwhichareoutstanding.Whydid wechoosetodevelopacourseonbothmusicandcolor?Thereareanumber ofreasons: 1. The basic underlying physical principles of the two subjects overlap greatly because both music and color are manifestations of wave phe- nomena.Inparticular,commonalitiesexistwithrespecttotheproduction, transmission, and detection of sound and light. Our decision to include bothmusicandcolorwaspartlyduetothefactthatsomewavephenomena are relatively easy to demonstrate for sound but not for light; they are experienced in every day life. Examples include diffraction and the Dopplereffect.Thus,thestudyofsoundhelpsusunderstandlight.Onthe otherhand,therearesomewavephenomena—commontobothsoundand light—that are more easily observed for light. An example is refraction, wherein a a beam of light is traveling through air and is incident upon a surfaceofglass.Refractioncausesthebeamtobenduponpassingintothe glass.Refractionisthebasisfortheoperationofeyeglasses.Andfinally, there are wave phenomena that are easily observable for both sound and light.Interferenceisanexample. Twostereoloudspeakersemittingasoundatthesamesinglefrequency producedead(silent)regionswithinaroomasaresultoftheinterference between the two sound waves produced by the two loudspeakers; the colors observed on the CDs of the photo on the cover page are a result oftheinterferenceoflightreflectedfromthegrooveswithintheCDs. ix x PrefacetotheFirstEdition 2. The production of music and color involves physical systems whose behaviordependsuponacommonsetofphysicalprinciples.Theyinclude vibrating mechanical systems (such as the strings of the violin or the drum, vibrating columns of air in wind instruments and the organ), electromagnetic waves such as light, the rods and cones of the eye, and the atom. All manifest the existence of modes and the phenomena of excitation,resonance,energystorageandtransfer,andattenuation. CDs ’produce’ sound through a series of processes that involve many distinct physical phenomena. First, the CD modulates a laser beam that excitesanelectronicdeviceintoproducinganelectricalsignal.Thelaser lightitselfisamanifestationofelectricandmagneticfields.Theelectrical signal is used to cause the cone of a loudspeaker to vibrate and produce themotioninairthatisnoneotherthanthesoundwavethatwehear. 3. Thecoursethatledtothewritingofthisbookofferedustheopportunity to study a major fraction of the basic principles of physics, with an added important feature: Traditionally, introductory physics courses are organizedsothatbasicprinciplesareintroducedfirstandarethenapplied wherever possible. This course, on the other hand, is based upon a motivationalapproach:Becauseoftheeaseofobservingmostphenomena thatisaffordedbyincludingbothlightandsound,weareabletointroduce thevastmajorityoftopicsusingclassdemonstrations. We challenge ourselves by calling for a physical basis for what we observe. We then turn to basic principles as a means of understanding thephenomena.Astudyofbothsubjectsinvolvesprettynearlytheentire gamut of the fundamental laws of classical as well as modern physics. (Themainexcludedareasarenuclearandparticlephysicsandrelativity.) Ultimately, our approach helps us appreciate a central cornerstone of physics—to uncover a minimal set of concepts and laws that is adequate to describe and account for all physical observations. Simplification is the motto.Welearntoappreciatehowitisthatbecausethelawsofphysicsweave an intricate, vast web among physical phenomena, physics (and science generally) has attained its stature of reflecting what some people refer to as “truth”and,muchmoresignificantly,ofhavinganextraordinarilyhighlevel ofdependability. The prerequisites for the associated course were elementary algebra and a familiarity with the trigonometric functions. The only material in the textbook that requires a higher level of mathematics is the appendix on the TransformationofColorMatchingFunctions(AppendixM)fromonesetof primariestoanother—theanalysisrequiresagoodunderstandingofmatrices. I have never included this appendix in my course; it is available for those whomightbeinterestedinit.Thelevelofthetextbookissuchastoproduce questionsastowhetherastudentwithoutinclinationstomajorinthesciences canhandlethematerial.Ithasbeenmyexperienceinteachingtheassociated courseatTuftsUniversityforover35years,thatveryfewsuchstudentshave failed to do well in the course. In the Fall, 2009 semester, in particular, the fifteenstudentswhotookthecoursewereallmajoringintheArts,Humanities orSocialSciencesorasyethadnotdeclaredamajor.Theaveragescoreon theFinalExamwasarespectable73%,witharangefrom61%to94%. PrefacetotheFirstEdition xi NoteonProblemsandQuestions Whetheryouarereadingthisbookinconnectionwithacourseyouaretaking or reading it on your own, I strongly urge you to take the questions and problemsinthebookveryseriously.Totestyourunderstanding,tomeasure your level of understanding, you have to do problems. In all my more than 50 years of studying physics, I have never truly appreciated a new subject withoutdoingproblems. Therearemanyfinebooksalreadyavailablethatcovereitherthephysics ofsoundandmusicorthephysicsoflightandcolor.Someofthesebooksgo intogreatdepthaboutanumberofthesubjects,waybeyondthedepthofthis book.Forexample,youwon’tfinddetailsonthecomplexbehaviorofmusical instrumentsinthisbook.ThebookbyArthurBenade,listedinAppendixE ofreferencesisagreatresourceonthissubject,eventhoughitisquitedated. And, you won’t find in-depth coverage of the incredibly rich range of light and color phenomena that is treated in the wonderful book by Williamson andCummins.Theirsectiononoilpaintisoutstanding.Instead,youshould look on this book as a resource for gaining an in-depth understanding of therelevantconceptsandlearningtomakesimplecalculationsthatwillhelp you test hypotheses for understanding phenomena that are not covered in this book. You will be able to read other books and articles on the web, empoweredwithanunderstandingthatwillhelpyouappreciatethecontent. Oneoftheproblemsragingtoday(2011)istheproliferationofinformation. Ah yes, you can look up on the Web any topic in this book. Unfortunately, a huge fraction of the information is incorrect or unreliable.1 How can you judgewhatyouread?Theonlysolutionisforyoutoaccumulateknowledge andunderstandingofthebasicsandtocriticizewhatyouread.2 1Recently,theSharpCorporationannouncedthatitwasgoingtomakeavailableacolormonitorandTVthathasfour primarycolorsamongthecolorpixels,incontrasttothethreeprimariescurrentlyused.Asaresult,itclaimedthat thenumberofcolorsavailablewouldapproachone-trillion.[Seetheirwebsite:http://www.sharpusa.com/AboutSharp/ NewsAndEvents/PressReleases/2010/January/2010_01_06_Booth_Overview.aspx.] YetyouwilllearninChap.15 thathumanvisioncandifferentiateonlyabouttenmillioncolors.Therefore,eveniftheSharpmonitorwereableto produceonetrillioncolors,theviewerswouldn’tbeabletobenefitfromthisgreattechnology.Wecanstillaskwhat canpossiblybethegaininaddingayellowprimary?Istheirchosencoloryellowforthefourthprimarythebestoneto chooseinordertoimproveourcolorvision?SeeChap.15forinformationonthisquestion.Websitesabounddealing withthesignificanceofSharp’snewtechnology;thisbookwillhelpyouanalyzeandjudgewhatyouread. 2What applies to information on science applies to all subjects. If you are given a multitude of conflicting expert opinionsonasubject,youwilltendtochooseoneexpertwhoisclosesttoyourpointofvieworyouwillwanttothrow allthesourcesoutthewindowwiththeconclusionthatreliableinformationnotonlycan’tbefoundbuthasnomeaning. ThefascinatingbookbyNeilPostman—AmusingOurselvestoDeath:PublicDiscourseintheAgeofShowBusiness [PenguinBooks,N.Y,1986]—discussessomerelatedproblemsconnectedwiththisproliferationofinformation.
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