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This 36 page Class Notes was uploaded by Eleazar Batz on Wednesday September 30, 2015. The Class Notes belongs to PHYS 130 at Western Kentucky University taught by Ting-Hui Lee in Fall. Since its upload, it has received 49 views. For similar materials see /class/216681/phys-130-western-kentucky-university in Physics 2 at Western Kentucky University.
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Date Created: 09/30/15
2909 Doppler Effect You hear the high pitch of the siren of the approaching ambulance and notice that its pitch drops suddenly as the ambulance passes you That is called the Doppler effect mzvsgztsgrmsziirgrzse frequency at sound even Inuugh 9 some realism and wave in 179le6 T somce maves velocity am Glaser by m so nan ed Siaimnary some or lrequency 1mm Movmg somca ul requancv me v H Z A A Sunm velocity v A VT v v5 n A w r VSJT Doppler Effect fJ fofo 5 i V V a Vfor approach b 7 Vfor separation A girl is sitting near the open window of a train that is moving at a speed of 10 ms The girl s uncle stands Shook Wave near the tracks and watches the train move away The MM girl s brother also stands near the tracks but ahead of the train and watches the train getting closer The train is blowing a whistle with a frequency of 500 Hz What frequency does the girl hear Her uncle Her brother mm 12de WWW lhm39hnqadnlmd Somc Boom Interference Wave interference is the phenomenon which occurs Sm39dmm when two waves meet while traveling along the same H WWW medium mll rg lln mpinngup d HWW am The interference of waves causes the medium to take on m 39 a shape which results from the net effect of the two individual waves upon the particles of the medium mummquwn Principle of Superposition When two waves interfere the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location Superposition ABCDEFGHI J KLMNOPQRSTU Superposition ABCDEFGHI J KLMNOPQRSIU Interference and Phase Two traveling waves which exist in the same medium will interfere with each other If their amplitudes add the interference is said to be constructive interference and destructive interference if they are quotout of phase and subtract fl In phase Constructive interference Destructive 180 out Interference of phase m Constructive Interference We Interference Dimslum Destructive Interference Be ue mm During luminance 1 2909 Destructive Interference ltgt 7 Before and After Re ne hnterfexenoe A erlnterfererwe 39 The two circular waves undergo interference and create the pattern represented in the diagram The thick lines in the diagram represent wave crests and the thin lines represent wave troughs Several of positions in the water are labeled with a letter Categorize each labeled position as being aposition where either constructive or destructive interference occurs 4 i i H Jlmmlnu Johnny Interference with a Tuning Fork Each tine of the fork roduces a pressure wave whic trave s outward at the speed of sound One part ofthe wave has a pressure hi er an atmospheric pressure another ower At some angles the high amp Maw pressure areas of the two swam waves coincide and you hear a louder sound w V 3 5quot At other angles the high ressure part of one wave coincides with e low pressure part of the other Interference of two identical sound Figure 413 Figure 414 Figure 415 Interference and Phase n L1 7 L2 n 0 i1 i2 i3 i4 for constructive interference n ilZ i32 i52 for destructive interference 2909 Beats I When two sound Waves of different frequency approach your ear the alternating constructive and destructive interference causes the sound to be alternatively so and loud a phenomenon Which is called quotbeatingquot or producing beats Beats Wve 1 mi uni Wve 2 blue f H 1c In ICL IDJi ICL HHI HHHHHHHHHHHH HHHHHHHHHHHHHHHI 1c In 1 In 1c But mm in gram Beat Frequency I The beat frequency is equal to the absolute value of the difference in frequency of the two Waves 39 fbeat ifl fzi I Used by musicians in tuning their instruments 2909 Combined Sound Level Add intensity not SILII When two sounds have very different frequency you can Find their intensities respective then add them together Find the intensity ratio of these two sounds then use it to nd the total intensity 22509 Example Flute 60dB clarinet 63 dB Interference When the two sounds have frequencies very close to each other Need to nd their amplitudes Example A1 3AZ Itotal 10 12 Constructive interference 1516 I2 Destructive interference I01 4 12 If SILZ 77 dB SIL1 865 dB s1Ltotal 87 dB SILC 89 dB s1Ld 83 dB 22509 Chorus Effect The continual ebb and ow of multiple beats when three or more instruments play in unison No two instruments can produce precisely the same frequency each pair produces a beat Add a sort of warmth to the sound The longterm average intensity is just the sum of the separate intensi es as if they frequencies had been quite different Types of Waves Longitudinal the motion of the medium is parallel to the direction of wave propagation Transverse the motion of the medium is perpendicular to the direction of wave propagation Wave Graphs Displacement vs position A snapshot at a certain time Inform ation can be extracted from the graph amplitude and wavelength Displacement vs time The motion at a single position Inform ation can be extracted from the graph amplitude and period Simple Harmonic Motion Amass bouncing up and down on the end of a spr1ng Apendulum Figure 212 Sound Wave 0 Sound is a longitudinal wave 7 Composed of compressions and rarefactions Lnuulkudlnul Wm Hill NIH II M www h Sicsclassroomcom mmedia waves tfcfm Amplitude displacement amplitude pressure amplitude N 001 to l Nm2 10397 to 10395 atm Recall that Pressure is forcearea Nmz 1 atmosphere Z 105 Nm2 Sound Wave Sound is n We Wave 53 quot 2209 Sound Wave Frequency 7 pitch Amplitude 7 loudness Waveform 7 tone color timbre Demonstration Tuning fork Oscilloscope Function generator Figure 24 25 amp 26 Speed of Sound Speed ms distance In time s Air is a nondispersive medium VT 344 06 T 20ms Compare Thunder and Lightning Speed oflight 3x108 ms Speed of sound 344 ms at 20 C Suppose athunderstorrn is 1 km away Classi cation of Sound Frequencies lnfrasound 7 below 20 Hz Audible sound 7 20 Hz to 20 KHZ Ultrasound 7 above 20 KHZ Wavelength of Sound Frequency Wavelength 10 Hz 34 m 100 HZ 34 m 1000 HZ 034 m 10000 HZ 0034 m 2209 Sound Spectra The frequencies of all the sinusoidal component that make it up The amplitude of each sinusoidal component present Periodic Complex Waves The repetition frequency determines the pitch The Fourier componenm of a complex wave belong to a harmonic series with the repetition frequency of this complex wave as the fundamental frequency The repetition frequency is the largest common factor of all the frequencies present in the spectrum What are the repetition frequency of the following waves A 10 20 30 and 40 Hz B 5610and12Hz C 612andl8Hz D 18 24 and 60 Hz What is the spectrum of the complex wave thick dotted line What is the spectrum of the complex wave thick dotted line 39u A a W N 39x d t3 Vgrw f J quotiv va y Mm y E Ohm s law of hearing The ear is sensitive to the amplitudes but not the phases of the harmonics of a complex wave 4609 4609 Musical Instruments Percussion Instruments Percussion Striking a hard object String Deformation of the object Wind Pass on to adjoining material Human voice Indude Membranophones Vibration of a exible membrane mounted on some rigid frame Metallophones Vibration of metallic objects Xylophones Vibration of wooden objects Drumhead Timpani http mu ith 4 39 quot 39 yLEMLTimnanihfml httpwwwketteringeduNdrusseIIDemosMembraneCircIeCirclehtm Vibraphone Cowbell http mII irm 39 quot 39 yTnytr nwhnll hfml h u 39 mmwatchvth7VvSrAEE Cymbal httpwwwmusicvtedumusicdictionarvtextcCrashcvmbaIshtml httpwwwmusicvtedumusicdictionarvtextsSusgendedcymbahtml Xylophone or Marimba 0 22012 1 a c Marin 64 Xylophone httpWwwyoutubecon watch vBHP5xiBP9Iampfeaturerelated Human Xylophone httpwwwyoutubecon watch vlS52az4SZlAampfeaturerelated Mouth Percussion httpWWWyoutubecomWatch vEYVKEOWfqp8ampfeaturerelated 4609 Temple Blocks httpwwwmusicvtedumusicdictionarvtexttTempleblockshtm Wood Blocks httpwwwmusicvtedumusicdictionarvtextwWoodblockhtml Wood Fish Properties of the Sound Loud or Soft Amplitude of the strike Surface area Transient No clear pitch in most cases Specific shapes Frequency depends on Size Vibration speed material mass or inertia Two bars of different length but made of the same material Short one has higher frequency Two bars of the same size and shape but different material Steel and cast iron steel is stiffer Natural modes of Vibration The frequency or frequencies at Which an object tends to Vibrate With When disturbed 39 Musical instruments and other objects are set into Vibration at their frequency When a person hits strikes strums plucks or somehow disturbs the object The input of energy disturbs the particles and forces the object into Vibrational motion at its natural frequency 4609 Natural modes of a circular membrane Node point of no displacement Nodal diameter Circular nodal lines Figure 916 7 move at opposite direction Figure 917 mmenwikigediaogwikiVibmtions of a circular dmm hmWwwyoutubecomthch7Fs9GB18201Y0 Drums don t produce de nite pitch The many natural mode frequencies do not belong to a harmonic series Tympani Membrane on kettle Mode 1 dissipates fast Mode 4 6 8 9 with circular nodal lines are less excited striking point at half to threefourths of Air lowers the frequencies produces frequencies within aharmonic series Striking points and Vibration recipes Strike in the center 7 dull thump The center is on the nodal lines of may natural modes 2 3 5 6 7 839 onlythose few circularly symmetric modes 1 4 9 are excited Therefore the soundlacks richness and brightness because so many ofthe drum s natural frequencies are missing Striking points and Vibration recipes A large soft object hits a drumhead wntirely within one or 7 region of some mode the mode is strongly excited If the area struck includes both and 7 regions the mode is excited little Striking points and Vibration recipes Hard mallets exert a large pressure on a tiny area and excite many modes 7 bright sound Soft mallets exert smaller pressure over a larger area of contact and excite only the lower modes 7 duller sound 4609 2509 Sound Propagation Re ection Refraction Diffraction Re ection The change in direction of a wave front at an interface between two different media so that the wave front returns into the medium from which it originated Common examples include the re ection of light sound and water waves The re ection of Mount Hood in Trillium Lake The Law of Re ection Angle ofincidcnce Angle ofre ection A ray oflight is incident towards a plane mirror at an angle Ono deng wim the mirror surface What will be the angle ofre ection lerur Specular vs Diffuse Re ection 2509 2509 Driving at night on a Wet road Ad39YuPM mW Mammy m m Smooth or Rough Smface Depends on the wavelengths Op mtlhmeter u t m t Lowest bass notes 71 or 2 meters Re ection of a pulse at a fixed end WM Invalde The string exerts a upward force on the end ofthe string The wall exens an equal downward force on the end ofthe which one might have changed Speed wavelength amplitude for the re ected pulse 2509 Re ection of a pulse at a free end mm mm The end of the string moves up and comes to rest The re ected Wave pulse propagates from right to le With the same speed and amplitude as the incident Wave and With the same polarity right si e up A less to a more dense medium Annmvding umludzn emmmdzn ema um n he bundaryinmthcmma ummxdxlnipulzisinve ni A more to a less dense medium Amvemvelingfmmnmmedengmnlasdmma umm we lucid nd MmeDuse laiDuse me o 9 MM Imuni nl lln wi1bexe adedo thehuumiuyuuihuum haiwwlhe bounduyinmthzmmedium Thmisminvenixm ht wwwketlerin edu drussell Demos re ect re ecthlm 2509 Amplitude Changed upon Re ection Part of the sound energy is absorbed at the re ecting surface Heavy drapery vs plaster wall Echo vs Reverberation Echo 7 the original sound and re ected sounds are separate Reverberation 7 the original sound and re ected sounds are mingled Human brain keeps a sound in memory for up to seconds In a small room S 17 m the re ected sound wave reach the ear Within 01 seconds Reverberation in a room Listener Plane Wave Re ecting from a Plane surface Emma WM I mam mm wmwmn Point Source Re ecting from a Plane Surface p0 he mlwr mu a m wall 2509 Plane Wave Re ecting from a Concave Surface Incident plane wave suund Reflected sound focuses toward Refraction of Sound Refraction is the bending of waves when they enter a medium where their speed is different As a toy Car rolls turn a Lees mm ggum hard floor onto carpal As a column cl ll changes direction matching troops became the wheel that i NB the carpet llrst l5 crosses from a 3935 slowed down rst medium to 3 slaw medium the direction v of march Visualizations chanQBS of Refraction 310 Fast w M 039 Concrete Swamp e 39um Medium Sound bends when parts of wave travel at different Warm Refraction of Sound in Air speeds Sound traveling in air of uneven temperature warm cold wind COId L A i Upwa I d Refraction Downward Refraction 2509 2509 Diffraction Diffraction the bending of waves around small obstacles and the spreading out of waves beyond small openings small compared to the wavelength Z H yw weveaulsms an J Wavelength dependence of Diffraction The long wavelength sounds of the bass drum will diffract around the comer more efficiently than the more directional short wavelength sounds of the higher pitched instruments It a matching band is appmaching an a class stveeL which lnsmrnenls wul you hear lirsn mun waned mm A 5mquot wavnicngm th pitched sounds lend to be male mmana Question 44 A partially open Window presents an opening 20 cm Wide What kind of sounds from outside will go across the room in a wellde ned beam What kind will spread evenly throughout the room Question 42 Discuss how much the sound is blocked off if you sit behind a large pillar N 05 m in a conceit hall Is the answer different for treble and for bass Is the problem alleviated by re ections from the walls Sound loss over distances Attenuation of sound depends directly on frequency2 Lightning cracks Lots of high frequencies nearby but rumbles when distant only low frequency This is why fog horns are low frequency n Outdoor Music No repeated re ections Weaker No reverberation Hard to distribute evenly Reduce the problems with having some re ecting structure Shell roof 2509 5109 Air Column Vibrations Boundary Conditions thsgzzrbzttrssifr mama Open end is maxrmum vibration does not move N Displacement antinode N N A Pressure node Nodes and Stretched string antinodes for displacement The existence of nodes A and antinodes iS Inherent In the standing waves which constitute the resonant modes of acoustic A pen an r em co A Cylindrical air column with both ends open Closed end is Displacement node Plot of vibrational amplitude by analogy systems like strings open and closed air f t g39 l gne columns and beanode tor the aquot motion Tube open at both ends Tubedosed atoneend A1r column open at both ends I messquotquot mm 8 Displacement of air b Pressure variation in the air 39 i I L r l i i 7 I A 1st mode 1 EIM L 1211 nOde antinode A Ode 13 f1 V2L B ewnmms ltgtogtoo areabsent A 2Ild mode A 04 3916 39 98 1 B f2 vL 2f B A 3rd mode A Wphysvnsweiiuaulmusic L 2 23 B B f3 3v2L 3f Air column open at both ends Air column closed at one end 3 Displacement of air b Pressure variation in the air L0nl2 inn 123 t L tumode A L 14 xi Waves travel at speed of sound gt f ML B Allowed wavelengths M 12 M 13 k1 A 2Ild mode Allowed frequenc1es f1 2 f1 3 f1 gt0 L 3422 06 B f2 3v4L 3f A 3rd mode A L 54 13 B B f3 5v4L 5f Air column closed at one end LC 2n7114 Ah n 1 2 3 Waves travel at speed of sound Allowed wavelengths A 13 A 15 X1 Allowed frequencies f1 3f1 5f1 Evennumbered harmonics are missing Ear sensitivity The ear canal is open at the outer end and closed by the eardrum on the other end Length is roughly 25 cm to 3 cm lst mode of closed tube 9 9 4L 10 cm f 344 KHZ corresponds to the dip at 3 to 4 KHZ on the FeltcherMunson diagram How about the 2 1 mode 5109 Musical Instruments Percussion String Wind Human voice Example Problem 920 http 39 39 nmvir lpn nhnepi id131 4809 4809 String Instruments Striking or plucking A string hit with a hammer could be called just another metallophone Number of strings To create a loud sound Electronic guitar Mechanical resonator The motion of the strings is transmitted to a box or soundboard Harpsichord Violin 4809 Standing Waves in Ropes and Sm39ngs A standmg Wave 15 the Wave formedby two aves of eq a1 amphmde and frequency traveling m opposne duecuons 10 1 Re ection ofa pulse at a xed and Wm r A mmmdm n v 39u The smug Exms supwem fume nn une md nnhe smug The Wall exens an sequ duwnward fume nn me and er e smug s new um Crates a Wavepulsethat pmfagzles rum nghl u left wnh me me weed and amphde as me Eldemwave but wnh nppnsne pulanly upsme dawn Natural modes for a 511ng Node pomt of zero duplacement Antmode pomt ofmaxlmum duplacemen For a stxmg xed at both ends the fundamental mnee the length othe stnng 4809 L 2 ill 2 4 First overtone or second harmonic f2 2f1 f Second overtone or third harmonic f3 2 3f 4809 Frequencies form a harmonic series 12239 5 L n 12 in f22f1 1 szn 2 f nf1 Perfect sine wave 9 e e 3 Pitch corres onds to the p 6699 4 fundamental e e 0 e e 5 frequency 6 G G 9 O G 6 Frequency of the string Frequency depends on Length of the string String s mass per unit length Tension of the string Vt x TM f112L Tu 4809 Vibrating String How to play different notes one string Fundamental l touch 12 way octave touch 13 a pluck 23 end plucking the 23 end gives a note a fifth higher than the fundamental Examples 39 Problem 101 39 Problem 102 39 Problem 103 4109 How to make a complex wave Is the red wave periodic Displacement Em For example add two sine waves together quot Principle of superposition the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location Time sec Is the red wave periodic Is this red wave periodic Displacement cm Displacement cm 5 Periodic Complex Waves Fourier s theorem Any set of sine waves whose frequencies 0 Fourier synthesis 7 putting sine waves together belong to a harmonlc ser1es w1ll comblne to Fourier analysis 7 taking complex waves apart make a periodic complex wave whose repetition frequency is that of the series fundamental Fourier spectrum 7 the recipe of sine wave amplitudes involved in a complex wave Fourier component 7 each sine wave Any perlodlc waveform of perlod P may be ingredient built from a set of sine waves whose frequencies form a harmonic series with f1 IP Nonperiodic Complex Waves I Any set of sine waves whose frequencies do not belong to a harmonic series will combine to make a complex wave that is nonperiodic and will generally sound impure or unsteady in one way or the 0 er I Any nonperiodic waveform may be built from a set of sine waves but their frequencies will not belong to a harmonic series Nonperiodic Complex Waves I Transient sounds 7 only a few frequency components that are not all multiples of any single number I Continuousnoise sounds 7 continuous spectrum with components present at every frequency Waveforms and Spectra I Figures 86 corresponds to Figure 81 Sine wave 7 fundamental I Square wave 7 oddnumbered harmonics Trangular Wave 7 oddnumbered harmonics I Sawtooth Wave 7 both odd and evennumbered harmonics White noise 7 equal strength at all frequencies I Pink noise 7 equal amount of energy in each octave lower frequency is louder I Square wave httpidmind net7zonamstmphysicswaves waveAdderWaveAdderl html httpwwwyenkacomfreecontenU itemactionguickgh I White noise httpenwikipediaorgwikiWhite noise I Pink noise httpenwikipediaorgwikiPink noise Waveforms and Spectra I Figure 87 corresponds to Figure 25 I Harmonics in all instruments shown I Bassoon 5Lh harmonic is strongest Ohm s law of hearing I The ear is sensitive to the amplitudes but not the phases of the harmonics of a complex wave 4109 31809 FletcherMunson Diagram Figure 612 Example Recorded 90 phons both at 1000 Hz and 50 Hz and played back with reduced intensi es at 001 Timbre and Instrument Recognition Waveform Transients the beginnings attacks and endings decays htt andasmasthm video I1 e i id131 Limitations in Music Movement 7 how fast can you play Perception 7 what do you really hear 31809 Musical events in Time Tempo 7 the pulse rate ofthe music Meter Rhythm 7 patterns of strong and weak beats Questions 71 amp 73 Melody and Harmony Melody 7 a succession of different pitches in time 7 horizontal structure Harmony 7 the combination of several notes at one time 7 vertical structure 31809 Scales and Intervals Scales 7 sets of allowed pitches Chromatic scale Diatonic scale piano Without black keys Interval 7 the perceived spacing between two pitc es Melodic interval Harmonic interval Chord Chromatic scale in equal temperament 12 equal semitones per octave f0 Xfo Xzfo X3f0 X1sz one octave higher X122 X 105946 Harmonic Series All the frequencies are simple multiples of a single frequency fl 110 Hz mdamental frequency fZ 2fl 220 Hz 2m1 harmonic 1st overtone f3 3fl 330 Hz 3 1 harmonic 2m1 overtone fA 4fl 440 Hz 43911 harmonic 3m1 overtone Octaves and Harmonics f 7 fundamental frequency If2f3f4f5f6f7f8f I Atunjng fork only plays one frequency I Amusical Instrument plays the fundamental frequency and all other higher harmonics 31809 Pleasing Intervals Table 72 1 octave ex Cto c1 c1 to G f5 f7 ef Not there discordant f7 not on piano hammer hits near note off7 I Note When a single note is played do not ONLY play fundamental frequency Also get higherhaxmonics Ratio between these 2 also must be pleasing Steps in Musical Interval and Harmonics Fifth Maanhiid Minanhiid 3 5 4 a 5 m 1 2 3 4 5 6 7 8 9 10 Musical Interval Octave anh anh szurThn39d z 1 4 3 4 3 54 one G c2 E G C
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