Chapters 3,5,7 Phys 1240
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This 12 page Class Notes was uploaded by Leah Dunn on Thursday September 17, 2015. The Class Notes belongs to Phys 1240 at University of Colorado taught by John Price in Spring 2015. Since its upload, it has received 104 views. For similar materials see Sound and Music in Science at University of Colorado.
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Date Created: 09/17/15
Sound and Music 08262015 Introduction This chapter will lay a foundation for the others to follow by introducing some of the basic concepts of sound I Acoustics and Music the science of sound and traditionally the term has meant especially the study of the physical nature of sound 0 One of the main divisions of classical physics along with motion mechanics heat thermodynamics light optics electricity and magnetism As technology has advanced the meaning of acoustics has gradually broadened includes those intentional combinations of sounds that we choose to hear for esthetic enjoyment and usually depends on an orderly pattern of sounds for a pleasing effect 0 sounds communicate the entire range of human ideas through word symbols rather than by conveying emotions directly 0 encompasses all other sounds unorganized unpleasant unwanted Organizing Our Study of Sound Sound 0 1 how it is created o 2 how it travels from one place to another o 3 how it affects the senses and emotions of a listener Your ears detect sound but it is not at all obvious how they do it or how much your nerves and brain modify the sound information they receive 0 u sensation of how high or quotlowquot a sound is o the sensation of strength or weakness in a sound Propagation is the simplest for physicist 0 Sound traveling through air obeys linearity light waves also have the same property of traveling through space wout altering one another Ill The Physical Nature of Sound Sound in air consists of longitudinal waves carrying energy outward from their source 0 We take to mean a rapid back and forth movement of an object o Awill mean a disturbance traveling outward in all directions from a vibrating source The passage of a wave through any region causes each little piece of material in that region to vibrate 0 That vibration doesn t carry any material very far and after the wave has passed each piece returns to its original position the density and pressure of the air are greater than they would be in the absence of the sound wave the density and pressure are reduced below their normal values 0 Each compression is created by temporarily moving air into that region from the adjoining rarefactions on both sides 0 A short time later this compressed air will reexpand Waves can be classi ed according to whether the local disturbance is or 0 When shaking a horizontal rope you set up a transverse wave whether shaking it side to side or up and down it vibrates perpendicular to the length of the rope Sound in air is longitudinal the vibration of each particle or air is parallel to the direction of the wave Wavelength the distance from one crest to the next along the direction of travel 0 Lambda A is used to represent wavelength 0 Wavelengths for sound range from A2cm to A 20m IV The Speed of Sound The speed of sound in dry air at room temp 20C is v20344 ms 0 At this rate the time it takes to travel 1 km would be 1000m344ms 3 seconds Air is a all sounds travel through the air at the same speed 0 if the air temp changes so does the speed of sound 0 speed increases about 06 ms for each degree of temp rise on C V Pressure and Sound Amplitude the distance each bit of air moves to either side of its normal position during its vibration the max increase of air pressure in a sound wave compression 0 pull or push upon anything measured in Newtons N 412N 1 pound of force 0 force per unit area pFSsurface area Introduction 0 Sound waves are dynamic they evolve in time The Time Element in Sound o If we try to stretch out a musical experience to discern more detail we change its quality o If we rush through it we again destroy one of the most important properties of performance 0 After dividing it into movements sections and phrases we come down to individual chords and notes this is like dividing a book into chapters paragraphs sentences words and letters 0 Each music note contains many individual sound vibrations and their rate is too rapid for us to recognize them separately 0 Galileo Galilei made sound by rubbing a card along the serrated edge of a coin to measure the exact nature of each vibration o rate of repetition of vibrations 0 Symbol fmeasured in Hertz Hz 0 The pitch to which most orchestras tune has f440 Hz and is called A440 because it causes your eardrums to vibrate 440 persecond P length of time taken for a single complete cycle of motion o P 1f The range of audible frequencies covers about 10 octaves and is conveniently remembered as extending from approximately 20 Hz up to 20000 Hz 0 Frequencies of radio waves are much higher AM radio is around 1 MHz and FM is around 100 MHz v A f o or cresting space Lambda must mean not just the distance from one crest to some subsidiary one but to the next corresponding crest where the entire pattern begins to repeat ll Waveforms A key role is played by the a device for displaying how an electrical signal changes with time 0 There is an endless variety of audible waveforms o It takes only a little experimentation with a microphone and oscilloscope to see that those waves that have several subsidiary peaks within each cycle deserve to be called complex lll Functional Relations 0 General concept called by mathematicians 0 Relationships involve or quantities that may have several different values under different circumstances 0 an expression of how one variable is related to another Scientists are always concerned with underlying physical relationships especially of cause and effect 0 One way to express these relations is by listing various pairs of corresponding values of the variables in a table with two columns 0 The important point about all such tables is that whenever we nd one particular value of either variable to be of special interest we can consult the table to nd the corresponding value of the other variable 0 0 Formula that produces the day lengths IV Simple Harmonic Oscillation o any system con guration for which all forces are precisely balanced when placed in this con guration the system will remain at rest 0 any force whose action is always in such a direction as to return an object to an equilibrium position the tendency of any body to continue whatever motion it already has only the action of forces can change that motion the maximum displacement A to either side of equilibrium occurs whenever the restoring force is of the uniquely simple kind called linear o SHM is especially important because suf ciently small vibrations of natural systems usually are of this kind The frequency of simple oscillation is determined by the strength of its restoring force and by its inertia o This formula says that the vibration will be more rapid on a stiffer spring but slower if the mass is increased An equivalent term for SHM is Will only become apparent when we see how other complex motions can be understood as combinations of several simple harmonic motions V Work Energy and Resonance done whenever one object exerts some force upon another while it moves in the direction of that force 0 W F x D an intangible property gained by anything upon which we do work 0 A quantity that is transferred from one body to another by the process of doing work an object is the energy that it possesses due to its motion the energy that an object has due to its position in a force eld or that a system has due to the con guration of its parts 0 ENERGY MAY BE TRANSFERRED FROM ONE BODY TO ANOTHER OR IT MAY CHANGE FROM ONE FORM TO ANOTHER BUT THE GRAND TOTAL NEVER CHANGES The continual competition between restoring force and inertia in any harmonic oscillator can also be described as an interplay of potential and kinetic energy 0 Restoring force does negative work on the mass reducing kinetic energy During vibration energy shuttles back and forth between kinetic and potential forms but the total energy remains the same In continuous excitation an external agent does more and more work on the string while it vibrates o This continuing energy input makes up for the losses to friction and radiation and thus maintains the vibration energy at a constant level An especially efficient way to deliver energy continuously to an oscillator is through which occurs when the driving force cooperates with the oscillator by alternating at about the same frequency that the oscillator would naturally prefer I Classifying Sound Sources Natural vs Arti cial sounds Not limited to original sounds but now have the opportunity to hear reproduced sounds as well Transient vs Steady sounds o temporary and quickly die Occur when sources are set in vibration at one moment but left alone thereafter 0 continue at same level as long as we choose to sustain them Classifying sounds according to the means of production families ll Percussion Instruments You can make a sound by striking any hard object against another The solid material is capable of carry a wave disturbance back and forth within itself 0 Includes possibility of both longitudinal and transverse waves Can be divided into 3 classes 0 Drums have membrane fastened to a circular hoop Used to be animal skin now plastic 0 De nite or inde nite pitch Vibraphones bells chimes triangles cymbals and gongs Vibrations generally die away slowly unless they are deliberately damped out by contact with some soft object Xylophone and marimba Hollow wooden instruments like temple blocks lll String Instruments A long thin string has very special properties that give its sound a much more de nite pitch than most percussion instruments 0 Can get a somewhat different quality of sound from the same strings by plucking rather than with the percussion instruments 0 An entirely diff approach is to have only a few strings but to obtain several notes from each by using different portions of its length Guitar lutes mandolins balalaikas vihuelas and the like 0 Energy must be passed through the air Louder soundmoving larger amounts of air IV Wind Instruments A narrow airstream directed against a sharp edged rigid obstacle at the right speed and angle will not just ow smoothly past the edge it will ow rhythmically o vibration produced by uid ow instability when a narrow stream of air is directed against sharp edge If there is an adjacent nearly enclosed air reservoir of proper size and resonance modi es and reinforces the edgetone vibrations giving a much louder sound and identi able pitch le blowing over a jug or a bottle 0 While ute family uses an edgetone the reed and brass families make use of air ow through a narrow opening of variable width Flexible boundary may be a thin piece of cane reed in which case we have the reed woodwind instruments In all instruments the reed itself can be made to sound at many different pitches Also possible to let a vibrating reed be the principal determiner of pitch 0 Brass instruments also have exible opening that controls their air input but it is formed by the player s lips Resonant action of the long tube back upon the lips that forces them to vibrate in a much more regular way Human voice operates somewhat like a brass instrument a Vocal cords buzz like a trumpet player s lips but aren t attached to a highly resonant tube V Source Size natural unit of measurement for the separation of two notes in pitch Size of instrument changes octaves but will still play the same note 0 Le the cello and violin ute and clarinet etc Vl Sound from the Natural Environment lf musical composition consists primarily of natural sounds and their derivatives it is sometimes called by the French term musique concrete meaning quotthe music of real objectsquot 0 Distinctions between natural and arti cial are not especially important to our study of acoustics because the same concepts we use in understanding the production of sound by traditional instruments are he ones we would use to analyze sound from any other source 0 l Amplitude Energy and lntensity What is the appropriate physical measure of sound strength or weakness 0 Amplitude Displacement vs Velocity Amp mean pressure amplitude whenever referring to sound 0 Energy The energy of oscillation is proportional to the square of the amplitude Any statement about the strength of a sound wave is imprecise unless we specify whether we mean amplitude or energy 0 Energy is usually of more direct interest than amplitude 0 Because the energy is traveling and is spread throughout the region where the wave exists we do not attempt to measure the total amount Measure energy ow P Et Ppower Etotal energy t time Power is measured in Watts 1 W 1 Js Power per unit area PS ESt n l intensity S size of sensitive area ll Sound Level and the Decibel Scale The loudest sounds we encounter rarely exceed 1 Wmquot2 in intensity It has become customary to use the sound level scale which is labeled in decibels dB 0 Practical sound measurements are routinely made with sound level meters that give readouts in decibels Sound level intensity SIL 0 There is always a correspondence between this code and the intensity but they are not the same The bel is de ned to represent a ration of 10 to 1 between two intensities o A BEL IS NOT AN AMOUNT OF SOUND IT IS A RELATION BETWEEN TWO SOUNDS Ill The Inverse Square Law Whatever energy passes across the inner surface we must have exactly the same amount of energy crossing the outer surface a little later 0 The reason the intensity is less on the outer surface is merely that the same total energy has been spread over a larger area A more general expression is the formula l2l1 r1r2quot2 OR SL2 511 20logr1r2 known as the IV Combined Sound Levels and Instruments Each source continues to supply energy in the same way just as if the other were not there 0 Matters become more complicated when we consider two sources whose frequencies are the same or nearly so Because the waves now maintain the same phase relation over a long period of time and the total disturbance is entirely different depending on whether the interference is constructive or destructive The continual ebb and ow of these multiple beats when three or more instruments play in unison is called o Adds warmth to the sound 0 Having several instruments together does not merely produce louder sound it also changes the quality of sound I Organizing Musical Events in Time No accident that we use the second as our basic unit measurement o If we went much smaller we couldn t count them one by one with unaided human perceptions 0 Units much larger we would soon nd ourselves subdividing them Nervous system also poses limitations on both movement and perception o The progression of major events of a piece such as the the sequence of signi cantly different chords ignoring ornamentation is generally in the neighborhood of one or two per second the quotpulse ratequot of the music 0 Le MM 120 which means it s played at a rate of 120 per minute or 2 per second 0 metronomes can be set to produce audible clicks at any desired rate and thus set a uniform tempo for practicing the way the basic tie units are arranged in groups measures 0 Le duple meter triple meter denotes patterns of strong and weak beats or subbeats 0 Le 44 time 68 34 o Rhythmic patterns in European classical and American popular music tend to be simple and straightforward 0 Common rhythmic device is deliberate disturbance of the normal pulse of accented beats Music from certain other cultures African and Indonesian use much more complex rhythmic patterns ll Melody and Harmony succession of different pitches in time that are perceived as continuing line the combination of several pitches at one time gives a vertical structure a cooperative effect from several notes sounding simultaneously 0 simultaneously highly structured both vertically and horizontally ie Writing a pleasing 4 part harmony so that each of the four players have an interesting melody of their own the controlled manner in which successive notes are joined to one another by a performer 0 Stress by articulation has a solid acoustical foundation Ill Scales and Intervals With pianos guitars and standard orchestral instruments we are heavily committed to using only 12 distinct pitches per octave any deviation is considered out of tune o allowed pitches Chromatic scale 12 familiar pitches per octave found on a keyboard a One note to another half step a Two white keys whole step a Standard orchestral instruments tuned to chromatic scale perceived spacing in between two pitches third fth octave and so on o Melodic interval one note following another 0 Harmonic interval both notes sounding simultaneously 0 Chord three or more notes sounding together Intervals just a way to tell how far apart they are written on the musical staff or how many white keys they span on the piano 0 IV The Harmonic Series 0 out of the vast numbers of possible combinations most of which would sound rather strange let us investigate the special case in which all of the frequencies are simple multiples of a single frequency 0 a harmonic series that can be constructed on any frequency
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