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This 5 page Class Notes was uploaded by Leah Dunn on Sunday August 30, 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 78 views. For similar materials see Sound and Music in Science at University of Colorado.
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Eugh...this class is soo hard! I'm so glad that you'll be posting notes this semester.
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Date Created: 08/30/15
Sound and Music 08262015 Introduction 0 This chapter will lay a foundation for the others to follow by introducing some of the basic concepts of sound I Acoustics and Music 0 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 ll Organizing Our Study of Sound 0 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 0 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 0 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 0 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 0 the density and pressure of the air are greater than they would be in the absence of the sound wave 0 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 0 Sound in air is longitudinal the vibration of each particle or air is parallel to the direction of the wave 0 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 0 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 a 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 0 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 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 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 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 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 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 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 Formula that produces the day lengths Simple Harmonic Oscillation any system con guration for which all forces are precisely balanced when placed in this con guration the system will remain at rest 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 o 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 0 an object is the energy that it possesses due to its motion o 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 o 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 0 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 ef cient 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