Sound and its Measurement CH 3

Lecture II: Acoustics Part 1 Simple Harmonic Motion and Sound (SHM) - Waveform repeats itself over time (periodic) - a SHM results in a pressure wave that repeats itself over time - Is a single frequency - Is a pure tone - Hooke's law: the restoring force is proportional to the displacement - compressions and rarefactions are steady - steady rhythmic back and forth movement, a SHM Sine Waves - the sound waves propagated through air occur in synchrony with the vibration of the tuning fork, or any vibrating body itself - sound does not actually look like this, just a graphical representation Sine Waves - the waveform - a plot of change in amplitude or displacement over time - the display is called the time-domain waveform, or waveform - air does not actually undergo this form of excursion: the waveform is a representation - Sine waves important bc they propagate without changing their form - single sinusoidal wave produces a pure tone Characteristics of Sine Wave 1) Displacement/Amplitude - Displacement of a vibrating body at any instant is the distance from equillibrium to the position of the body at that instant - at the top would be maximum displacement in the compression area - time - abscissa (x) - pressure - ordinate (y) - Amplitude describes distance from an object's rest position by a vibrating body or the magnitude of pressure change that occurs by that object's motion - the greater the distance from the point of rest, the greater the amplitude - Loudness is the psychological (subjective) parameter of amplitude - it's the impression we get from the strength of the sound pressure - the greater the amplitude, the louder the pure tone sounds - intensity describes the amt of sound that passes through given area - a pure tone's intensity is measured by the amplitude of its sine wave, and it varies with time - more displacement means more pressure and greater amplitude, and higher volume - Amplitude/Intensity of sound determines how much energy or force is imposed on the medium - Peak amplitude (vP) - from equilibrium to maximum displacment - Peak to peak amplitude (vPP) - maximum displacment in one direction, and plus the maximum displacement in the other direction - peak amplitude is half of the peak to peak amplitude - Wave with the larger amplitude corresponds to greater density of the air particles, or higher atmospheric pressure during compression, and less density or less atmospheric pressure during rarefaction, versus sound with lower amplitude

2) Frequency (f) - the number of complete vibrations or cycles per unit of time - measured in cycles per second (cps) - Cps represented by Hertz - 100cps = 100Hz - psychological (subjective) parameter of frequency is pitch - If you have sound that is 250 Hz and another sound that is 4000 Hz - the first is lower pitch - frequency and pitch are not the same thing - frequency is physical and pitch is psychological - the high frequency tone has more cycles per second, aka higher hertz than a lower frequency tone - Greater mass in an oscillating system results in decrease of frequency of vibration - Systems that have more stiffness (less compliance) will vibrate better at higher frequencies - incr stiffness, incr frequency/pitch - stiffness is opposite of compliance - human hearing range from 20 Hz to 20,000 Hz - day to day, we experience from 100 Hz to 6,000 Hz - infrasonic (lower) and ultrasonic (higher) - sounds that do not fall within this range of human hearing 3) Period (T) - time elapsed during single complete vibration - Frequency and period are reciprocals - T = 1/f - f = 1/T - T is period/time in seconds, f is frequency in Hertz - Low frequency sounds have long period - High frequency sounds have short period

Lecture 3: Acoustics Part 2 Phase - sound waves can differ in amplitude, starting phase, frequency - B is starting at 90 degrees in relation to A - interference - the interaction of waves at different starting phases - an interference happens when 2 or more waves come together, and depending on how peaks and troughs match up, the waves might add together or partially/completely cancel each other out Constructive Interference - occurs at any location along the medium where the two interfering waves have a displacement in the same direction - A +B, the medium has a displacement that is greater than displacement of the two individual pulses Destructive Interference - occurs where the two interfering waves have displacement in the opposite direction - cancel each other out, +1 and -1 - at the instant of complete overlap, there's no resulting displacement of the particles of the medium, because they've canceled each other out Phase - Interference - when two waves of equal frequency and amplitude are combined together: - If "in-phase" (have same starting phase), will reinforce each other and result in summation of the two waves, and a doubling of the waves - constructive inferference (reinforcement of waves when combined) - If 180 degrees out of phase, the two tones will cancel each other out, resulting in no sound - destructive interference (reduction of waves when combined) - must have same frequency and amplitude for this to work - In phase: waves add together - 180 degrees out of phase: waves cancel each other - Different waves: new wave created, combination of constructive/destructive interference

Beats - two ALMOST identical frequency tones are combined - increase and decrease in amplitude - these rapid fluctuations in amplitude are 'beats' - constructive interference, then destructive interference, and so on Noise - a sound that has little/no periodicity - can also mean a sound with an instantaneous amplitude that varies over time randomly White Noise - all frequencies within specified range are present, without regard to phase, and the avg power over a frequency range is constant- intensities for each frequency are the same Pink Noise - used in studies of audition - amplitude decreases by one-half with each doubling of frequency Passive Filters - 3 types 1) Low-pass filter - attenuates high frequency energy but passes low frequency energy 2) High-pass filter - attenuates low frequency energy but passes high frequency energy 3) Combination - results in filter that will pass signals within a certain frequency band, but attenuate others Ex. Narrow band noise

Lecture 4: Acoustics Part 2 Sound Pressure Level - pressure is force per unit area - dyne (d) - one dyne of force is sufficient to accelerate mass of 1 gram at 1 cm per second - Newton (N) - 1 Newton is a force that will accelerate 1 kg of mass, distance of 1 meter, per second - the greater the force, the greater the pressure, the greater the amplitude, the louder the sound - A unit of sound pressure is Pascal (Pa) - 1 Pascal = 1 N/m^2 - the smallest sound pressure required to produce barely audible sound is 0.00002 or 20 microPa = 0 dB SPL - reference for sound pressure level - Formula for intensity reference: dB = 10 x log(IO/IR) - Formula for sound pressure reference: dB = 10 x log(PO^2/PR^2) Or 20 x log(PO/PR) - intensity is proportional to pressure squared Reference Levels - A decibel is a ratio that does not have absolute or fixed value, it always has a reference level - Reference levels are: dB (IL) = 10^-12 watts/m^2 or 10^-16 watts/cm^2 dB (SPL) = 20 microPascals

Calculating dB (IL) dB = 10 x log(IO/IR) 0 dB is threshold of hearing - How many decibels is a sound that is 10^-8 Watts/m^2? - 40 Doubling dB - dB cannot be added because they are ratio and logarithmic - cannot do 60 + 60 = 120 - when sound pressure is doubled, dB increased by 6 dB SPL in perfect world - when sound intensity is doubled, dB increases by 3 dB IL

Lecture 2: Acoustics Part 2 Simple harmonic motion is depicted as sine wave Phase: 0 degrees, 90 degrees, 180 degrees, 270 degrees, 360 - phase is useful in describing relationship betw 2 or more vibrations/wave motions - waveform can be defined as portion of a circle in degrees - expressed as theta - phase change in a complete vibratory cycle is 360 degrees - starting phase - point in the displacement cycle at which an object begins its vibration - not always going to have the same starting phase Sound Velocity - the speed of sound C is: - dependent on medium elasticity and density - dependent on medium temperature - At sea level at 20 degrees Celsius, the speed of sound is 344 m/sec or 1130 ft/sec - the closer the molecules are to each other, the less time it takes for them to pass the sound to each other, and the faster the sound will travel - sound travels faster through mediums with higher elasticity such as steel, rather than rubber - If a material is more dense because its molecules are larger, will transmit sound slower - It takes more kinetic energy to make larger molecules vibrate than smaller molecules - sound travels at a slower rate than a more dense object if they have the same elastic properties - If they have the same elastic properties, sound travels faster through aluminum than gold because the aluminum molecules have less density than gold - the elastic properties have a larger effect than density - molecule density and air density are different - sound travels faster through denser air - sound travels faster through higher temperature - incr in temperature causes molecules to move faster - heat, like sound, is a form of kinetic energy - at higher altitudes where atmospheric pressure is decreased, density of medium is decreased, temperature of medium is decreased, and velocity is decreased - as elasticity increases, sound velocity increases - easier for sound waves to go through solid than through liquid because molecules are closer together and tightly bonded Characteristics of Sine Wave 4) Wave Length - wavelength is distance betw identical points on two adjacent waves - Wavelength (lambda) = C/f - Measured in units of length, ex. ft - the lower the frequency, the longer the wavelength - the higher the frequency, the shorter the wavelength - all sound waves are traveling at the same speed of sound, regardless of frequency - so waves with longer wavelength/lower frequency won't arrive to your ear faster than high frequencies - Longer wavelength/lower frequency sounds can bend around objects, while higher frequency sounds are absorbed by objects

Damping - sound energy dissipates with distance from a source - damping is reduction in amplitude during successive oscillations - amplitude decreases - this results from frictional resistance or absorption - damping does not affect the frequency Free Vibration Ex. tuning forks, pendulums, vibrating strings - Vibrate at natural/resonant frequency - vibrates periodically until energy is dissipated - pendulum - resonant frequency dependent on its length - Strings - dependent on tension, length, and mass - Tuning forks - dependent on mass and stiffness of tines - Frequency stays constant regardless of amplitude or damping - Resonance - Ex. tuning forks - Free vibrator absorbs sound energy best when the energy source has a frequency rate exactly the same as the vibrator Forced Vibration - An outside force is added to control the vibration - Swinging or vibration will continue until the outside force is removed - when outside force is discontinued, object will revert to free vibration - Where vibratory or sound energy is imparted to a structure at a frequency rate other than its own natural frequency - can transfer energy - usually vibration does not last and is highly dampened - human ear highly dampened to avoid continual vibration after sound

Sound is generated by vibrations and carries through pressure waves - human reactions to sound are psychological, subjective experiences of pitch, loudness, sound quality, and ability to tell direction of sound source Sound is both psychological and physical Psychological: sound is auditory experience - the act of hearing something Physical: sound is series of disturbances of molecules within elastic medium such as air Sound may travel through any elastic medium - the elasticity, or springiness, of any medium is INCREASED as distance betw molecules is DECREASED - if a springy object is distorted, it will turn to its original shape; the rate is determined by elasticity of object - solid is more elastic than liquid, liquid more elastic than gas - Brownian motion - rapid/random movement of air particles, affected by heat - as heat INCREASES, particle velocity INCREASES When molecules are pushed closer together, they are condensed/compressed When a space exists between areas of compression, this area is rareified Waves - the succession of molecules being shoved together and then pulled apart Waves through the air are made of successive compressions and rarefactions The molecular motion in transverse waves is perpendicular to the direction of wave motion - horizontal, circular movement - pebble in water Longitudal wave - wheat blowing in field - air molecules move along the same axis as the wave itself when a force is applied Sine waves/ sinusoidal motion - bucket of paint - cycle - consists of compression and rarefaction, function of time - if movement of paper takes 1 second, during which 2 complete cycles take place, the frequency is 2 cycles per second (cps) A body moving back and forth oscillates - one cycle of vibration, or oscillation, begins at any point on wave and ends at identical point on next wave - pure tone - when a body oscillates sinusoidally, showing only one frequency of vibration with no tones superimposed - frequency of wave - number of complete sine waves that occur in one second - compression of sine wave is shown by extension of curve upward, rarefaction by extension of curve downward - one cycle broken down to 360 degrees - cosine wave - when wave begins at 90 degrees rather than 0 degrees

Effects of energy on vibration - Fig 3.5 When an oscillating body has swung from point A to point B, must come to stop - no kinetic energy, all is potential - An object that is allowed to vibrate will encounter opposition to its movement by molecules in air - this small amt of friction converts some of the energy in initial movt of object into heat - friction slows down the swinging until it eventually stops - free vibration - if no outside force is added to continue the swinging - swings back and forth until it stops - heavy damping - causes oscillations to cease rapidly - critically damped - when oscillations cease before a single cycle is completed Forced vibration - if an outside force is added to the swinging that controls the vibration, swinging will continue unaltered until the outside force is removed - when external force removed, the object reverts to free vibration, decreasing distance of swing until it becomes motionless - in both free and forced vibrations, the number of times the weight moves back and forth (frequency) is unaltered by distance of swing (amplitude) - as amplitude DECREASES, velocity also DECREASES Duration usually used is second - if time required to complete a cycle is 1 second, then frequency is 1 cycle per second (cps) - also Hertz Period - time required for each cycle Period = 1/frequency Effects of length on frequency If length of string were shortened by holding it closer to weight, the number of swings per second would increase, weight would swing back and forth more frequently - Thus, as length decreases, frequency increases - as length increases, number of hertz decreases Effects of mass on frequency As mass INCREASES, frequency DECREASES Effects of stiffness on frequency - as a body vibrates, it exhibits certain amt of compliance/stiffness - as compliance INCREASES, resonant frequency (frequency at which body is most easily made to vibrate) decreases - systems w/ more elasticity vibrate better at higher frequencies than lower frequencies

Lecture 3: Acoustics Part 1 In daily life we seldom hear pure tone sounds from sine waves - usually they are complex sounds - speech, music - built from sinusoidal components that are taking place at the same time - sound is still periodic, but does not have pure tone quality Assume that amplitudes of these frequencies are equal, but not always - When amplitudes are not the same for the combining waves, waveform shapes change drastically depending on amplitude Periodic - wave repeat themselves over time, sound musical - pure tone Aperiodic - waves that vary randomly, do not have tonal quality (perceived as noise) - complex waves can be either periodic or aperiodic Harmonic Series - a periodic wave, however complex, has a fundamental frequency f0 at which the wave repeats itself - f0 is the greatest common divisor of the component frequencies - harmonic frequencies are whole number multiples of the fundamental f0 - f0 is first harmonic - harmonic - any whole number multiple of the fundamental - an octave is the doubling of a frequency Ex. if fundamental is 150 Hz, first octave is 300 Hz, second octave is 600 Hz

Partials and Overtones - overtone denotes any component in a complex tone that has a frequency higher than the fundamental frequency - all complex waves can be considered to consist of parts or partials - fundamental frequency is the first harmonic, it would also be the first partial - second frequency is the second harmonic and second partial, etc. - partials and overtones are numbered differently, but partials and harmonics are numbered the same - first overtone with second partial, second overtone with third partial, third overtone with fourth partial Complex sounds - harmonic structure - overtone - component of complex tone that has frequency higher than the fundamental frequency - Partial - any component in complex tone - octave - any interval of 2 frequencies having a frequency ratio of 2:1 Fourier Analaysis - Jean Baptiste Fourier discovered that complex waves are built of harmonic sine waves - Fourier analysis: acts like a prism - represented as line spectrum graph - amplitude, frequency, phase - human ear has ability to resolve varied frequencies that contribute to complex sounds, but not the individual frequencies - fourier analysis allows us to decompose a complex waveform into its pure frequencies - allows complex acoustic signal to be broken down into its actual frequency components - can reveal whether a sound is pure tone, which would only contain one frequency, or complex tone, which would contain multiple sine waves Complex Waveforms - Steady state sound (usually periodic) - frequency, composition, amplitude, and phase relationship of the partials of a tone are constant over time - Transient sound (usually aperiodic) - a change in steady state - musical tones are complex tones composed of fundamental frequency and harmonically-related series of overtones - vowels of speech are also composed of this fundamental frequency - but speech is rarely in steady state, constantly changing, so speech is transient sound

Lecture 4: Acoustics Part 1 Decibel scale represents amplitude of sound wave Scales - most measurement scales are absolute and linear - Decibel scale is relative and logarithmic - Range of hearing from just audible (threshold) 10^-16 watts/cm^2 to painful 10^-4 watts/cm^2 Log 1 = 0, because 10^0 = 1 Log 10 = 1, because 10^1 = 10 Log 100 = 2, because 10^2 = 100 We use logarithms to make large range of numbers more manageable - portrays how intensity differences are perceived in human ear - corresponds to our perception of loudness of sound Absolute vs Relative Measurement Relative Measurement: - needs a reference or zero point - comparison of 2 measures Ex. Mach Scale in reference to speed of sound - decible represents ratio of measured intensity to reference intensity

Reference of Zero - 0 dB does not mean absence of sound - It means the intensity you are comparing is the same as reference level (the threshold) - lowest point in intensity that a person can perceive the stimulus - threshold - Can be many different references that are used - Measured in various ways: IL (intensity level), Sound pressure level (SPL), Hearing level (HL), Sensation level (SL) The Decibel - Logarithmic intensity ratio = 10^14 - Decibel is a tenth of a Bel - usually measured in range of 0-140 dB - measurement unit for intensity - no fixed absolute value - decibel expresses ratio betw measured sound and set reference intensity Intensity Level (IL) - Intensity - amt of energy transmitted per second over an area of 1 square meter - Intensity = Energy/ (Time + area) or Power/area - watts/cm^2 - Intensity level only exists when there is a reference given - Therefore, dB IL should only be used when the reference is 10^-12 watts/m^2 or 10^-16 watts/cm^2 - the greater the amplitude of the particles of the medium, the greater the intensity IR = 10^-12 watts/m^2 = 10^-16 watts/cm^2 - dB (IL) = 10 x log (IO/IR) - can get negative dB

Lecture: Acoustics I - acoustics is study of sound - sound is psychological (subjective): pitch, loudness, timbre/quality - sound is physical (objective): frequency, intensity, spectrum - yes, there's always a sound made by a crashing tree - sound is the movement of a disturbance through an elastic medium - in equilibrium if there is undisturbed medium (air), with exception of Brownian movement and pressure variations - in order for sound to be perceived, there must be disturbance through medium caused by vibrating force Prerequisites for production of sound: 1) Medium must have mass/inertia - tendency of matter at rest to stay at rest and tendency of matter in motion to stay in motion - the greater the object's mass, the greater the inertia, takes a larger force to move it because it wants to stay at rest 2) Medium must have elasticity (in order to vibrate) - tendency of object to resist deformity and return to rest position - higher elasticity means higher resistance to deformity - steel has high elasticity than rubber - sound waves are not going to be propogated in vacuum or absence of air 3) Needs a source of energy (e.g. a force), cause of that vibrational disturbance - Force = mass x acceleration, needs to have mass and elasticity - force is push or pull on object - Newton's 2nd law: when force is applied to air particles by a moving object, the air particles will travel in the direction of the force, and amt of this distance is proportional to magnitude of that applied force - a large force will cause object to travel much further than a small force - the greater the force applied, the greater the distance the object will travel - the force is indirectly related to mass - if you exert same force to object of diff masses, the smaller mass accelerates greater than acceleration of larger mass - pushing a kitten has greater acceleration than elephant

Sound propogation - sound waves are propagated through air in all directions - 3 dimensional - sound does not just travel straight ahead, but also travel behind you, to the side, etc. so ppl all around you will hear that sound - if you strike tuning fork on high surface and set tines in vibration, air molecules are also set in vibration, which creates pressure wave - air molecules go in same direction as force that is applied - air molecules bump into neighbor molecules, get compression where they will keep bumping and moving in wavelike motion - because of elasticity, the original molecules will bounce back and create succession of molecules being shoved togheter and pulled apart, wave motion - compression/condensation - particles closer together than at equilibrium - higher pressure than surrounding atmospheric pressure - in equilibrium, molecules are spaced equally without Brownian motion - compression of air molecules move closer togheter, hit neighboring molecules to get area of compression - where compression is, air pressure is higher Rarefaction - particles farther apart than at equilibrium - lower pressure than surrounding atmospheric pressure - molecules less compressed than at equilibrium - pressure lower than normal atmospheric pressure - periods of compression and rarefaction repeated over and over - rareified air trails behind the compression - when source stops vibrating, source goes back to state of rest Sound Propogation - Important to note: the disturbed particles exhibit a minute forward and backward motion - the disturbance moves in a wavelike fashion NOT the air particles themselves - kinetic energy is moving outwards, not the air particles themselves - sound can be seen as transfer of energy from one place to another

Complex Sounds - pure tones seldom appear in nature - any complex wave can be analyzed in terms of sinusoidal components Fundamental frequency - lowest rate of a sound's vibration - determined by physical properties of vibrating body - periodic - some complex sounds repeat over time - Aperiodic sounds vary randomly over time, do not have fundamental frequencies, and perceived as noise Harmonics - all frequencies are whole number multiples of the fundamental - these tones, which occur over the fundamental, are harmonics or overtones - spectrum of sound w/ 100 Hz fundamental would contain higher frequencies of 200 Hz, 300 Hz, 400 Hz, so on - overtones and harmonics are numbered differently First harmonic is fundamental frequency, second harmonic is twice the fundamental, etc. First overtone is equal to second harmonic, and further overtones are numbered consequtively

Spectrum of a complex sound - read pg 40 - although fundamental frequency determines all harmonic frequencies, harmonics do not all have equal amplitude - in any wind instrument, fundamental frequency is determined by vibration - even though the fundamental and harmonic frequencies may be the same, the amplitudes of diff harmonics vary from instrument to instrument Altering the size and shape of vocal tract results in frequency and intensity changes that emphasize some harmonics and suppress others - resulting wave form has series of peaks and valleys - peaks - called a formant, and it is manipulation of formant frequencies that facilitates recognition of diff vowel sounds - peaks are numbered consequtively and expressed as lowest first, formant (F1), the second formant (F2), etc. - formant frequencies of the human voice are determined by vocal tract Intensity - how far a body vibrates - Fig. 3.12 - amplitude - the distance the mass moves from the point of rest - if a greater force is applied to air molecules, they will move further from their points of rest, causing greater compressions and greater rarefactions, and increasing therefore the amplitude - 2 sine waves may be contrasted by their differences in intensity, frequency, and phase Force - the greater the force, the greater the amplitude of the sound wave - because of human ear's sensitivity, only very small amts of force required to stimulate hearing - dyne (d) is unit for quantifying small changes in force - 1 dyne accelerates mass of 1 gram at 1 cm per second - if mass of 1 gram is held at sea level, force of gravity on this mass is 1000 dynes - Newton used as force measurement in U.S. - 1 Newton of force accelerates a 1 kg mass at 1 m/s^2

Pressure - pressure is generated whenever force is distributed over a surface area - Ex. pounds per square inch - measured in Pascals in SI system, and dynes/cm^2 in CGS system - if a given area remains constant, pressure increases as force is increased - because of sensitivity of human hearing, micropascals used to express sound pressure in audible range of intensities for humans and animals - smallest pressure variation... Work - when any mass is moved, certain amt of work is done as energy is expended - amt of work is expressed as force exerted times the distance the mass moved - 1 erg (e) is amt of work done when 1 dyne of force displaces an object by 1 cm; 1 Joule (J) is 10 million ergs Power - capacity to exert physical force or energy and is expressed as rate at which energy is expended - units are horsepower and watts, erg per second - power measures the magnitude of sound - as distance from source INCREASES, the sound energy DECREASES because the sound's power is spread through a larger area Intensity of a Sound Wave - intensity is amt of force per unit of area - inverse square law - intensity decreases proportionately to the square of the distance from the sound source - Intensity (in watts) = power(in watts)/(4pi x radius^2)

The Decibel - unit of measurement of intensity - five important aspects of decibel: 1) it involves a ratio 2) It uses a logarithm 3) it is therefore nonlinear 4) may be expressed in various reference levels 5) it is a relative unit of measure - decibels cannot be simply added or subtracted bc they are logarithmic Logarithms - simply a number expressed as an exponent (power) that tells how often a number (Base) is multipled by itself - Ex. in 10^2, the log (2) tells us that the base (10) is multipled by itself 1 time - base 10 most common - logarithm is useful in expressing ratio betw 2 numbers - ratios expressed without a specific reference are totally meaningless Table 3.1 Intensity Level - useful to express decibel with intensity reference - watt/m^2 is unit - intensity reference may be given as IR (the number of watts of reference intensity) - output (ex. loudspeaker) may be expressed as IO, so ratio is set up between intensity reference and intensity output - to solve for number of decibels using intensity reference: dB = 10 x log (IO/IR) - the usual intensity reference (IR) is 10^-2 watt/m^2, but can change - essential that the reference must always be stated - when the reference is 10^-12 watt/m^2, the term intensity level (IL) may be used as shorthand to imply this reference - if intensity output and intensity reference are exactly the same (IO = IR), ratio is 1:1 - because the log of 1 is 0, formula shows number of decibels is 0 - 0 dB does not mean sound is absent, but rather intensity output is same as intensity reference - If IO is changed to 10 watt/m^2, number of decibels (IL) would be 130 - Table 3.1 shows that as intensity output (C) INCREASES, the ratio (A) INCREASES, raising power of log (B) and INCREASING number of decibels (D) - remember that decibel is logarithmic expression - when intensity of wave is doubled, number of decibels is not doubled but increased by 3

Resonance - resonant frequency - natural rate of vibration of a mass - when external force is removed, oscillation will revert to resonant frequency until it is dampened - musical notes shatter glass - resonant frequency of glass is produced, and amplitude of the sound (pressure wave) is increased until the glass is set into vibration that is sympathetic to (the same as) the sound source - if the glass is made to vibrate w/ sufficient amplitude, its shape becomes so distorted that it shatters Sound Velocity Velocity - speed with which sound travels from source to another point - sound velocity is determined by density of the medium - the closer together the molecules, the shorter the journey each particle makes before striking its neighbor, and the more quickly the adjacent molecules are set in motion - because of this, sound travels faster through solid than through liquid, and faster through liquid than through gas - when temperature/humidity INCREASE, speed of sound INCREASES - at higher altitudes the speed of sound is reduced bc distance betw molecules is greater - Instantaneous velocity - velocity of sound determined by speciifc movement - sound velocity fluctuates as wave moves through medium - in such cases, average velocity of wave determined by dividing distance traveled by time interval (mph, m/s, cm/s) - when velocity is increased, acceleration takes place - when velocity is decreased, deceleration - sonic boom - as solid object moves through air, it pushes air molecules out of way - if object exceeds speed of sound, causes great compression ahead of itself, leaving partial vacuum behind - compressed molecules rushing in to fill vacuum result in sudden overpressure called sonic boom

Wavelength fig 3.8 - length of wave is measured from any point on a sinusoid (0 to 360 degrees) to the same point on the next cycle of wave w = v/f - as frequency INCREASES, wavelength DECREASES Longer wavelengths of lower-frequency sounds more easily move around obstructions than do shorter wavelengths with higher frequencies Phase - any point on a sine wave can be compared to a standard - standard is 0 degrees - if oscillation has a beginning at 0 (or 360 degrees), it is in phase with the standard Interferance pg 38 - whenever more than 1 tone is introduced, there are interactions among sound waves - such interactions are determined by frequency, intensity, and phase relationships of the diff waves - Beats - beats - changes in amplitude - when difference betw 2 frequencies is increased, number of beats per second increases - the number of beats per second is determined by differenece betw 2 frequencies - difference tone - when difference in frequency betw 2 tones becomes large enough, the ear recognizes a number of tones, including the higher one, lower one, difference tone, and summation tone, all expressed in hertz as multiples of two original tones