The Science of Sound
The Science of Sound ISP 215
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This 10 page Class Notes was uploaded by Ms. Mckenzie Labadie on Saturday September 19, 2015. The Class Notes belongs to ISP 215 at Michigan State University taught by William Hartmann in Fall. Since its upload, it has received 8 views. For similar materials see /class/207728/isp-215-michigan-state-university in Integrative Studies Physical at Michigan State University.
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Date Created: 09/19/15
ISP 215 Science of Sound Chapter 3 Vibrations 11 Book Notes 31 7 Damping decay Ideal simple ha1monic motion goes on forever Vibrations of a real free mechanical system are damped by frictional forces including air resistance Decreases gradually with time Possible to compensate for damping by adding energy to the system from outside System is then active not passive or freely vibrating 32 7 Natural Modes of Vibration A mode is described by its properties Frequency 9 a specific frequency 1 5 o 15 s 9 stiffness of spring Newtons per meter m 9 mass kilograms o i 0159 272 Shape Amplitude 33 7 Multimode Systems A system of two masses and two springs has two modes of vibration Two separate and distinct natural frequencies for the system One for each mode The shapes of the two modes are quite different 34 7 The Tuning Fork Several modes of vibration one more important than all the others Main mode 9 frequency stamped on the fork Other modes 9 their frequencies are higher than the main mode first clang mode is particularly evident Mode addition 9 when a physical system vibrates in several modes at once resulting vibration is just the sum of individual modes Addition property superposition After adding main mode and clang modes of the tuning fork coeXist hear all modes Damping 9 clang modes don t interfere due to rapid damping 1 minute after fork is struck 9 only main mode heard Effectively becomes a single mode system ISP 215 The Science of Sound Chapter 9 Fourier Analysis and Synthesis Book Notes o JBJ Fourier 1768 71830 Any waveform is just a sum of sine waves 0 Fourier synthesis Complicated vibrations can be created by adding up simple ha1monic motions of various frequencies 0 Can make any waveform your heart desires o Fourier analysis Begin with a complex wave and discover what the sine waves are that make it Any complex wave can be analyzed in only one way Only one set of sine wave frequencies amplitudes and phases that can come out of the analysis Any waveform is a unique sum of sine waves 91 7 The sine wave 0 Pure sine wave Single component Simplest wave 92 7 Complex Waves 0 2 components 0 Q 200 Hz A 45 units 600 Hz A 15 units 0 phase both Signal 45 sin 360 200t 0 15 sin 360 600t 0 93 7 Periodicity 0 Find the fundamental frequency Greatest common divisor 0 Period 9T i f0 94 7 The sawtooth 0 Periodic waveform Sine wave components will be harmonics o Fundamental l A 2 harmonic i A 3 harmonic A 95 7The sounds o 3 kinds of periodic signals 0 The 1000 Hz sine Starting phase affects the sound for ony an instant cannot possibly matter in the long run Somewhat piercing and unpleasant Dull tone color 0 2 components complex 200 plus 600 Hz Can hear both harmonies separately ISP 215 Science of Sound Chapter 5 Sound Waves Book Notes 0 Different kinds of waves Radio waves Light waves Xrays Waves on the surface ofa lake 0 Can be characterized by Direction of propagation Speed of propagation 0 Different kinds of waves 0 Waves Physical means of propagating energy Momentum Information without transporting mass 51 7 Polarization 0 Two directions associated with any wave Propagation Displacement 0 Transverse wave 9 direction of displacement is perpendicular to the direction of propagation 0 Longitudinal wave 9 direction of displacement is parallel to the direction of propagation Sound waves can be eitheror 52 7 The Speed of Sound 0 Speed of sound 9 3437 g in room temperature 1128 ff 769 0 Speed of sound depends on air temperature Higher the temperature the faster the sound 0 Y 3317 06 Tc y9 speed of sound in meters per second Tc 9 temperature in Celsius degrees 0 Speed of sound does not depend on air pressure 53 7 Sound Waves in Space and Time 0 Waves are functions of the dimension of time o 3 different dimensions of space Two of them are space and time ISP 215 The Science of Sound Chapter 10 Sound Intensity Book Notes 101 7 Pressure power and intensity 0 Sound waves have pressure power intensity and energy 0 Pressure wave is both positive and negative 0 Power is strictly positive Focus on intensity 7 I 0 Sound wave travels outward from source power in the wave spreads out over space 0 If a certain amount is spread over a large area weak sound 0 Ifsame amount is spread over a small area strong sound These are both measured by intensity 0 Physical dimensions 9 power per unit area 0 Power is expressed in metric unit ofwatts area is m Intensity 9 watts per square meter Refer to power and intensity as P I o Intensity is proportional to the square of the pressure A chAZ 0 prressure is doubled intensity increased by 4 times 0 prressure becomes 10X larger intensity becomes lOOX larger Increased by a factor of 100 102 7 The inverse square law 0 Inverse square law When further away from a sound it tends to be less loud Refers to intensity of the sound wave Intensity at a receiver depends inversely on the square of the distance from the source 2 0 10 d Z o Spherical source Pulsating sphere o Radiates a sound wave equally in all directions Isotropic 5 4nd2 0 S 9 surface area of a sphere o d 9 square of the radius P m o P 9 power ofthe source 0 Application of the inverse square law There s a source a receiver and nothing else but air Recapulation 0 Pressure Positive and negative ISP 215 Science of Sound Chapter 4 Instrumentation Book Notes 41 7 Transducers o Transducers 9 device that converts a signal from one form to another amp Microphone 9 converts a signal from an acoustical pressure wave to an electrical voltage 0 Loudspeakerheadphones do the opposite Microphoneloudspeaker 9 analog devices 0 Output of the device is analogous to the input 0 Linear transducer 9 doesn t distort the signal A change in the input to the devices causes a proportional change in the output 42 7 The Oscilloscope Instrument that displays waveforms is function of time Horizontal aXis 9 time Vertical aXis 9 voltage Analog and digital scopes Analog 9 use cathode ray tube CRT Digital 9 use CRT or liquid crystal display LCD 43 7 The Spectrum Analyzer Displays amplitudes as a function of frequency Horizontal aXis 9 frequency Vertical aXis 9 amplitude of the component whose frequency corresponds to the value of the horizontal aXis Displayed in decibels 44 7 The Frequency Counter 0 Does not have a screen 0 Numerical readout with half a dozen digits Indicates the frequency Hz in a signal 0 Mindlessly counts the occurrence of a particular feature in the signal voltage 0 Next is the electronic gate 9 tells the counter when to count Precisely one second long 45 7 The Function Generator 0 Creates a signal in electronic form 0 User must specify frequency and amplitude and waveform 0 Digital function generators 9 waveform synthesizers Allows user to generate complicated waveforms of any desired shape ISP 215 The Science of Sound Chapter 11 The Auditory System Book Notes 0 Physiology begins with anatomy Science of where things are in the body what they look like how they are connected and how these facts give clues about physiological function 0 Consists of peripheral elements called the ear Peripheral elements 0 Near the skull o Comprise what is commonly called the ear Central elements 0 Located in the brain 0 Brainstem midbrain cortex 111 7 Auditory anatomy 0 Peripheral auditory system 9 3 main divisions Outer ear middle ear inner ear 11117 The outer ear 0 Part that you can see 0 Consists of Pinna o Fleshy homlike protuberance from the side of the head Often used for hanging decorations Ear canal external auditory meatus o Duct about 25 cm long 0 Runs from pinna to eardrum 0 Sometimes accumulates ear wax o Eardrum tympanic membrane is end of outer ear Beginning of middle ear 1112 7 The middle ear 0 Consists of 3 bones and several muscles in a small cavity in the temporal bone 0 Bones act as lever that conducts sound vibrations from eardrum to oval window Oval window 9 point of contact with inner ear 0 3 bones 9 ossicles little bones Smallest bones in the body From eardrum to oval window in order 0 Malleus 9 the hammer o Incus 9 the anvil o Stapes 9 the stirrup o Stapes presses on oval window and transmits vibrations to the inner ear 1113 7 The inner ear 0 Where the real action takes place Possible to hear without outer ear and middle ear Not possible to hear without inner ear Converts acoustical signals into signals that the brain can understand A cavity inthe skull s temporal bone called the cochlea Snail shaped Divided into 3 canals by 2 membranes 0 Canals lled with uid Main membrane 9 basilar membrane Other membrane 9 Reissner s membrane So light unimportant mechanically Doesn t affect the way uid moves in the cochlea Important electronically o Separates ions in canal called scala media from ions in scala vestibule 0 Different in ionic concentration provide the energy source for the action of the hair cells Ionic differences serve as the ear s battery 0 Source of electrical energy Pressure pulse from oval window travels down duct made from scala vestibule and scala media to end of snail shell cavity small opening helicotrema There pulse can turn around and come back on the other side of the bascilar membrane through scala tympani 0 End of scala tympani 9 round window another membrane that acts as pressure relief mechanism Motions of the uids in the canals causes the basilar membrane to move Organ of Corti 0 Filled with hair cells Vital role in hearing 0 Hair cells are transducers Convert mechanical motion into neural impulses 0 Electrical spikes 9 language of the brain 1114 7 The semicircular canals Contiguous with cochlea Share the same uids Nothing to do with hearing Origin of sense of balance vestibular system Sensitive only to low frequencies of whole head motion Mostly below 10 Hz Neural messages travel on VIIIth nerve Auditory nerve Cochlear nerve Eighth cranial nerve 112 7 Auditory Function 1121 7 Outer ear function Pinna gathers sound Directs it into ear canal It s shape gives an uneven frequency response o Captures some frequencies better than others 0 Uneveness has a big effect on high frequencies above 5 kHz Frequency response depends on direction of sound origin 0 Ear canal 25 cm long Tube that s open at one end closed at the other 0 Closed by ear drum Auditory system most sensitive to frequencies 3000 7 4000 Hz 1122 7 Middle ear function 0 Ear canal sound waves are pressure waves in the air 0 Inner ear sound waves are pressure waves in cochlea uid 0 Middle ear function Form an efficient coupling of the waves in the air of the uids Without the bones waves in the air of the ear canal would be re ected from denser cochlea uids 0 Little of the sound energy would be coupled into the motion of the uids 0 Only 1 of sound energy would be transmitted from outer ear to inner ear Can reduce efficiency of the coupling between outer and middle ear by 2 muscles 0 Stapedius muscle 0 Tensor tympani Contract to make coupling less efficient in the presence of loud sounds 0 Automatic volume control 9 protects inner ear Incompletely evolved rather slow 0 Too slow to react to impulsive sounds 0 Also contract to make middle ear coupling less efficient when you begin to vocalize Defends inner ear against your own voice 1123 7 Inner ear function 0 Converts sound vibrations into neural impulses that the brain can understand 0 Cochlea gains sensitivity and sharp frequency tuning from internal electromechanical feedback 0 Cochlea is responsible for encoding signals 2 different ways Place encoding o Basilar membrane vibrates due to uid vibrations in cochlea Heavier near the apex than at the base Vibrations maximally at different places for tones of different frequency 0 Highfrequency tone causes vibration near the base Little vibration anywhere else 0 As a result hair cells next to basilar membrane fire off Hair cells elsewhere on the membrane are silent Encodes the fact that frequency is high Location of active hair cells transmitted because each hair cell is connected to higher auditory centers by about 10 nerve fibers in auditory nerve ISP 215 The Science of Sound Chapter 6 Wave Properties Book Notes Properties of waves Interference Beats Re ection Refraction 61 7 Wave Addition When waves from 2 sources are added in the air Ear is only exposed to a single wave Single wave is sum of 2 sources Pressure waves Can be either positive or negative 0 Lead to reinforcement or cancelation Reinforcement 2 waves are added and they have the same sign 0 Both positive or both negative Summed wave is more positivenegative than constituents Cancelation Constituents have different signs 62 7 Interference Both sources emit the same waveform and frequency Dramatic events can occur Simplicity leads to power Constructive interference 2 sources add up to reinforce one another 2 waves have the same phase Destructive interference 2 sources ass up to cancel one another 2 waves have opposite signs Key to complete destructive interference is to delay by half a period 63 7 Beats Also a form of interference Maxima and minima Takes place in time not space Occurs between 2 sine tones Almost the same frequency but not exactly the same Beat rate difference between 2 frequencies fbeats fZ f1 64 7 Audio Analogies 0 Audio signals 0 Mixer Electronic device that adds signals together If there s same frequency same amplitude but are 180 out of phase then it will cancel Iffrequencies of 500 and 510 Hz 9 will beat 10x per second 65 7 Generalization Telephone dial tone 9 sum of 2 sine waves 350 Hz and 440 Hz Electronic inversion 500 Hz tone can be cancelled by adding another 500 Hz tone if one is delayed by 1 ms compared to the other 0 1 ms is onehalf ofthe period Makes the 2 tones 180 out ofphase Inverter 9 has an input and an output 0 If input voltage is positive output voltage is negative If input voltage is negative output voltage is positive Always the same magnitude Noisecancelling headphones Active noise cancellation 9 pick up annoying sound with a microphone to convert it to audio signals invert the signal and play it back through a loudspeaker this should cancel the annoying sound 0 Almost impossible to achieve active noise cancellation Active noise cancellation can be possible Ducts 9 sound is con ned only one important direction of propagation along the length of the duct Headphones 9 another con ned environment contain little drivers with diaphragm that reproduced speech and much Noisecancellation headphones Each ear contains a tiny microphone to pick up outside noise signal from the microphone is inverted and sent back and mixed up with the desired speechmusic 66 7 Re ection o Waves can be re ected when it abruptly changes its direction of propagation 0 Can be re ected from wall because the material is different than ordinary air 0 2 kinds of re ection Specular ex mirror Re ecting surface has irregularities that are much smaller than the wavelength 0 Preserves the orders of the rays preserve the image on re ection Diffuse wall Bumps on the surface are comparable to the wavelength or larger than the wavelength
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