CHAPTER 1: FUNDAMENTALS OF SOUND
* Sound either stimulus (physics) or sensation (psychoacoustics)
o Ex. freq vs. pitch; intensity vs. loudness;
Sine wave: In order to conduct sound media must have elasticity and inertia, causes sinusoidal motion. For sin all energy concentrated at one frequency
Sound in Media:
* elastic forces of air restore displaced particles
* Without a medium sound cannot be propagated
Particle Motion:
* individual particles displace about 10-thousandth of an inch
* Three forms of particle motion: concentric waves (stone falling in water), waves from strings, longitudinal waves (traveling thru gas)
Propagation of sound:
* compressions vs. rarefactions
* will propagate at different speeds depending on medium
* more dense the medium, easier for sound to propagate
Speed of Sound: 1,130ft/sec; 770mph; 1240km/hr; ~5sec/mile
Wavelength: distance wave travels to complete 1 cycle (peak-peak)
Frequency: cycles per sec; λ= speed of sound / frequency
Complex Waves: complex waves can be reduced to sin waves
* Fundamentals + harmonics
* Harmonics vs partials (music term): partials of instrument not always correlated to harmonic fundamental (ex. church bell)
* Harmonics linearly related (integer multiples)
* Octave defined as 2:1 ratio between frequencies
Ex. low freq limit of band is 20hz, wat is high-freq limit of band that is 10 octaves wide? f/20hz= 2010= 20480hz
Spectrum: audible spectrum is 20Hz-20kHz
Electrical, Mechanical, Acoustical Analogs:

CHAPTER 2: SOUND LEVELS AND THE DECIBEL: ratios are more closesly related to human perception than linear numbers. Ratios are dimensionless which is important since logs are also dimensionless
SPL= 20log10 (pressure/pressure reference)dB
ex. an SPL is 78dB, what is sound pressure?
78dB=20logp / (20E-6)= 0.159Pa
ex. input of 1w produces SPL of 115dB at 1m, what is SPL at 6.1m?
SPL= 115-20log(6.1/1)= 99.3dB

CHAPTER 3: SOUND IN THE FREE FIELD: since in reality acoustic systems are really complex (with thousands of reflective surfaces etc.) so to make problems practical we consider sound in the free-field. Analysis is useful because it allows us to understand nature of sound waves in undisturbed state
Free Field: theoretical space
* sound travels in straight lines and is unimpeded
* unreflected, unabsorbed, undeflected, undiffracted, unrefracted, undiffused, not subjected to resonance effects
Sound Divergence:
* the farther we are from sound source, the more It behaves like a point source
* uniform intensity (power per unit area) in all directions when radiating from point source in free-field
Sound Intensity in Free Field: doubling distance from source quarters intensity
I= W/4πr2, I= intensity of sound/unit area, W= power source (constant), r= distance from source (radius);
I= W/2πr2 for hemi-spherical radiation
Sound Pressure in Free Field: doubling distance from source halves pressure
P= k/r, P= sound pressure, k= a constant, r= distance from source
Ex. when SPL L1 at distance r1, the sound pressure at another distance r2 can be calculated: L2= L1-20log( r2/r1 )dB (only true for free-field)

Chapter 4: The Perception of Sound
 
Ear Anatomy
The ear is made up of 3 principal parts: the outer ear, middle ear, and inner ear.
 
Outer Ear
-Composed of the pinna and the auditory canal. The auditory canal is terminated by the tympanic membrane (ear drum).
-Controls the apparent loudness by an amount varying with frequency.
-Pinna also imprints directional information on all sounds picked up by the ear.
-Ear canal also increases loudness of the sound
-The resonance effect of the ear canal increases sound pressure at the eardrum at certain frequencies. The maximum frequency at which the 2.5-cm pipe is one quarter wavelength, about 3,000 Hz.
-Primary pipe resonance amplifies the sound pressure at the eardrum by approximately 12dB at the major resonance at about 4,000 Hz.
-There is a secondary resonance nearer 9,000 Hz of lower peak pressure.
-These effects combine to make the ear most sensitive to mid-range frequencies, the frequencies occupied by speech.
 
Middle Ear
-An air filled cavity spanned by three tiny bones, called the hammer, anvil and stirrup. The malleus is attached to the ear drum and the stapes is attached to the oval window of the inner ear. These bones form a mechanical connection between the air actuated eardrum and the fluid filled cochlea of the inner ear.
-The area of the ear drum is about 80mm2, and area of oval window is 3mm2, which means a given force on the eardrum is reduced by the ratio of 80/3, or 27-fold
 
Inner Ear
-Terminated in the auditory nerve, which sends electrical impulses to the brain
-The leverage of the ossicles bones of the middle ear and the ratio of area of the ear drum and oval window efficiently match the impedance of air to the fluid of the inner ear.
-Waves set up in the inner ear by vibration of the oval window excite the sensory hair cells, which direct signals to the brain. There is a place effect, the peak of hair cell agitation for higher frequencies being nearer the oval window, and low frequencies at the distal end.
 
Loudness vs. Frequency
Based on the fletcher munson curve, each equal loudness contour is identified by its value at the reference frequency of 1 kHz, and the term, loudness level in phons, is defined. For example, the equal loudness contour passing through 40-dB sound-pressure level at 1kHz is called 40-phon contour. The line of each contour shows how loud sound-pressure level must be varied at different frequencies to sound equally loud as the 1-kHz reference loudness.
 
Loudness vs. Sound-Pressure Level
Many experiments have been done to find that a 10-dB increase in sound pressure level doubles the loudness. For a 10-dB decease, the subjective loudness is cut in half. The sone is a unit of subjective loudness.
 
Loudness Level (Phones)	Subjective Loudness (Sones)	Typical Examples	
100	64	Heavy Truck Passing	
80	16	Talking Loudly	
60	4	Talking Softly	
40	1	Quiet Room	
20	0.25	Very Quiet Studio	
 
Loudness vs. Bandwidth
-Bandwidth of noise affects the loudness of the sound.
-There is a critical band for every frequency.
-The equivalent rectangular bandwidth (ERB) can be calculated by the equation:
ERB = 6.23f2+93.3f+28.52 Hz
Where f =frequency, HZ
 
-Short bursts of a sound do not sound as loud as loud as longer ones.
 
-Only when tones are shorter than 100msec do they need to have their sound pressure level increased to produce a loudness equal to that of long pules or steady tones or noise.
 
-Steps of 5dB are audible, however steps of 0.5 dB may be inaudible. These vary with different frequencies.
 
-Because pitch is different from frequency, it needs another subjective unit, the mel. A reference level of 1,000 mels is defined as the pitch of a 1 kHz tone with SPL 60.
 
-If tones such as 1,000; 1,200; and 1,400 Hz are played together, a pitch of 200 Hz will be heard. The 200 is the fundamental and the others are harmonics above that, and the brain will perceive the fundamental.
 
Binaural Localization
-Signals from both ears are combined in the brain. Two factors are involved, the difference in intensity and the difference in time of arrival (phase)
-The head acts as an acoustic shadow. Acoustic shadows are lower at low frequencies, however it is stronger for higher frequencies.
 
Law of the First Wavefront
The sound that arrives first creates in the listener the perception of direction. The direct sound a person hears travels the shortest distance, thus providing a steady way to perceive where the sound is coming from
 
The Haas (Precedence) Effect
Describes the ability of the ear to integrate all sound arriving within the first 50msec, giving the perception that the sounds originate from the earlier source, and making the sounds seem louder.
 
The Franssen Effect
Exhibits auditory memory. If one sound is played through loudspeakers and the left loudspeaker plays the sound first, and slowly dies out as it fades into the right loudspeaker, you will continue to “hear” it from the left.
 
Reflection delay = (Reflected path) – (Direct Path)
                                                        1,130
This assumes 100% reflection at the reflecting surface. Both path lengths are measured in feet; the speed of sound is measured in feet per second.
 
Reflection level at listening position = 20 log Direct distance
                                                                                       Reflection Distance
This assumes inverse square propagation. Both paths are measured in feet.
 
Chapter 5: Signals, Speech, Music, and Noise
 
Speech
-Speech is highly variable and transient in nature, comprising energy moving up and down the three-dimensional scales of frequency, sound level, and time.
-There are two quasi-independent functions in the generation of speech sounds: the sound source and the vocal system.
-There are three different sources of sound that are shaped by the vocal tract: First is the sound we normally think of, sounds emitted by vocal chords (Voiced). Second source is that made by forming a constriction at some point in the vocal tract with teeth, tongue, or lips and forcing air through it under high enough pressure to produce significant turbulence (Fricative). The third is produced by the complete stoppage of the breath, usually toward the front, building up of the pressure, and then the sudden release of the breath (Plosive).
-Production of voiced sounds has 3 steps: 1. Sound is produced by the vibration of the vocal tract, with a spectrum that falls off at about 10dB/Octave. 2. Sounds pass through the vocal tract, acts as a time varying filter. Acoustical resonances, called formants, are characteristic of the vocal pipe. 3. Output voiced sounds are shaped by the resonances of the vocal tract.
-Speech sounds do not have the same strength in all directions. This is due to directionality of the mouth and the sound shadow cast by the head and torso.
 
Music
-Musical string instruments produce their tones by the vibration of strings. On a stretched string, the overtones are the exact multiples of fundamental, lowest note produced. The overtones can be called harmonics.
-For wind instruments, resonance in pipes or tubes can be considered primarily one-dimensionally. If air is enclosed in a narrow pipe closed at both ends, the fundamental (twice the length of the pipe) and all its harmonics will be formed. Resonances are formed in a pipe open at only one end at the frequency at which the pipe length is four times the wavelength, and results in odd harmonics.
 
Number of Binary Digits	Dynamic Range (dB)	
4	24	
8	48	
12	72	
16	96	
24	144	
  Theoretical Dynamic Ranges for Digital Word Lengths
 
Signal Distortion
·      Bandwidth limitation If the passband of an amplifier attenuates low or high frequencies, the signal output differs from the input by this bandwidth limitation
·      Nonuniform response Peaks and valleys within the passband also alter the signal waveshape
·      Phase distortion any introduced phase shifts affect the time relationship between signal components
·      Dyanamic distortion A compressor or expander changes the original dynamic range of a signal
·      Crossover distortion In class-B amplifiers, in which the output devices conduct only half of the cycle, any discontinuous near zero output results in what is called crossover distortion
·      Nonlinear distortion Human ear is not linear. When a pure tone is impressed on the ear, harmonics can be heard.
·      Transient distortion Transient intermodulation (TIM) distortion, slew induced distortion, and other measuring techniques evaluate transient forms of distortion.
 
Harmonic Distortion
 
Total Harmonic Distortion = Square root ((e2)2+(e3)2+(e4)2…(en)2) X 100
                                                                                   e0
Where e2, e3, and en = voltages of second, third and fourth etc. harmonics
    	e0 = fundamental

Resonance
-Amplitude of vibration of any resonant system is maximum at the natural frequency or resonant frequency and is less at frequencies below and above that frequency. A modest excitation signal at that response frequency will result in a high amplitude.

Chapter 6 – Reflection
 
·         Angle of incidence = angle of reflection
·         Parallel surfaces produce annoying flutter echoes
·         Energy is lost at reflection, continuing until the original sound is inaudible
·         Larger objects can reflect lower frequencies
·         Pressure at a reflective surface is double that of the incident wave
·         Large convex surfaces spread out sound
·         Large concave surfaces focus sound to a point
·         Parabolic surfaces also focus sound
o   Two across from each other create a whispering gallery
·         Standing waves created by parallel surfaces
o   Two waves, starting from each of the parallel surfaces, interact, forming the standing wave itself
o   Distance between walls = wavelength of standing wave
·         Corners reflect sound back where it came from, after losing intensity b/c of hitting two surfaces
·         Mean free path (MFP): average distance that sound travels between reflections
o   MFP = 4V / S
o   V = volume of the space, S = surface area of the space
·         Perception of reflections depends on delay time and dB level
o   Spaciousness vs. echo
o   Above 20 ms, it sounds more echoey unless at lower levels

Chapter 7 – Diffraction

·         Low-frequency sounds bend (diffract) more easily around obstacles
·         The smaller the size of the obstacle relative to the wavelength of the incoming sound, the easier the sound will bend around it
·         Behind a barrier there is an acoustic shadow (absence of sound)
·         With apertures, large openings allow sound to pass through (with shadows on either side)
o   Small openings reject most incoming sound – the rest passes through, and appears to emanate from a point source at the opening
·         For slits, not surprisingly, if sound arrives at strange angles, it attenuates
·         Zone plates (a bunch of concentric circles) can focus sound on the other side
·         Human heads block 1k-6k
·         Speaker cabinets also diffract sound and create comb-filtering

X.	Chapter 10: Comb-Filter Effects
	A.	Intro
		1.	Effect of delayed reflection on frequency response of 						signal
		2.	Steady- state phenomena and only effects steady state 					periods of speech and music
	B.	Superposition of Sound
		1.	Net effect of two wavefronts is the combination of both ripple 					patterns.
		2.	This creates both constructive and destructive interference
		3. 	Superposition: Movement of a particle is the sum of various 					disturbances.
		4. 	Motion of particle is the vector sum of its disturbances.
	C.	Tonal Signals and Comb Filters
		1.	If two signals are 180 degrees out of phase they will completely 					cancel each other out.
		2.	Two two signals are in phase, the signals reinforce each other
		3.	Microphones responds to vector sum of various air pressure 					fluctuations.
		4.	A tonal signal will fluctuate many times between positive and 					negative every second.
		5.	One cycle of a wave is equal to 360 degrees, and delays of time 					less than that of the wave cycle are measured in degree amounts 					from 0 to 360.
		6.	Adding direct and delayed sine waves of the same frequency 					results in a sine wave with the same frequency.  
		7.	Adding direct and delayed sine waves of different frequencies 					gives periodic waves of irregular wave shape.  
		8.	Adding direct and delayed sine waves cannot create comb 						filtering.
		9.	Comb filtering requires signals having distributed energy (speech, 					music, pink noise)
	D.	Combing of Music and Speech Signals
		1.	When adding two identical segments of music that are slightly 					delayed, the result will have different spectral content than the 					original.
		2.	There are peaks and nulls in the frequency response which, when 					plotted on a linear frequency scale, has a pattern that looks like a 					comb.
	E.	Combing of Direct and Reflected Sound
		1.	Delay can result from reflection off a wall or object
		2.	Combining direct and reflected sounds creates a comb filter in 					frequency response.  
		3.	Nulls happen when two signals are out of phase (one half 						wavelength apart in time)
		4.	The nulls and peaks are determined by the amount of delay
		5.	First null is frequency with period twice delay time (f=1/(2t))
		6.	Successive nulls occur at odd multiples (f=n/(2t), n=1,3,5,7…)
		7.	First peak at f=1/t, successive peaks at f=n/t, n=1,2,3,4,5
		8.	Space between peaks is 1/t.
		9.	Delays of about 0.1 msec may occur from having the source or 					listener very close to a reflective surface
		10.	Increasing delay increase the number of peaks and nulls 						proportionally.
		11.	As the spacing between peaks and nulls decreases, the effect 					becomes less noticeable  
		12.	Small reflection times are more normal in small rooms, with large 					rooms creating larger delay times
		13.	Therefore comb filtering is more associated with small rooms
		14.	Concert halls and auditoriums usually don't have comb filtering 					problems.  
	F.	Comb Filters and Critical Bands
		1.	Audibility of comb-filtering depends on critical bands of human ear
		2.	Width of a comb peak must be compared to the width of a critical 					band of the human ear at the given frequency to determine if it is 					audible
		3.	Critical bands are more narrow at low frequencies, comb filtering 					is more audible at these frequencies
		4.	Critical band table:
			Center frequency - > width of band
			100 - > 38
			200 - > 47
			500 - > 77
			1000 - > 128
			2000 - > 240
			5000 - > 650
		5.	40 sec is usually too long a delay to perceive peaks and nulls
		6.	0.5 sec shift at 1K would create a perceptible change in timbre
	G.	Comb Filters in Multichannel Playback
		1.	Signals coming from two speakers are displaced in time with 					respect to one another due to spacing, creating comb filters
		2.	Body ignores these changes in timbre, called binaural 						suppression
		3.	 The comb filtering is barely audible in the first place
	H.	Reflections and Spaciousness
		1.	Perception of a reflected component is always different from the 					direct component
		2.	Absorption of air varies by frequency, changing timbre of sound at 					greater distances.
		3.	Weakly correlated input signals to the ears contribute to 						impression of spaciousness
		4.	There have to be reflections for there to be feeling of 						spaciousness.  
	I.	Comb Filters in Microphone Placement
		1.	Spaced microphones have comb filtering problems due to slight 					delays between the two signals.  
		2.	Sometimes this combing is perceived as ambience and some find 					it pleasing.  
	J.	Comb-Filter Effects in Practice
		1.	Example 1: Reflection between microphone and floor
		2.	Example 2: Two spaced microphones feeding into same amplifier
		3.	Example 3: Adjacent singers with microphones who's voices are 					picked up in each others microphones.
		4.	Example 4: Two spaced loudspeakers towards audience
		5.	Example 5: 3 way loudspeaker experiencing comb filtering 						between drivers.
		6.	Example 6: Flush mounting microphone with a surface
	K.	Estimating Comb-Filter Response
		1.	Spacing between peaks and nulls: 1/t Hz
		2.	Adding two sine waves in phase doubles amplitude (6dB)
		3.	For a  1 msec delay, first null is 500 Hz, important component of 					speech.

XI.	Reverberation
	A.	Intro
		1.	Audio from a loudspeaker reaches steady state when the energy 					radiated is great enough to overcome losses in the air and at walls
		2.	When a speaker turns off, there is a period of time for level in room 				to decay, this is reverberation and it is based on quality of room.
	B.	Growth of Sound in a Room
		1.	Sound has to build to final level in room, based on rate of growth
		2.	Direct sound arrives at listener and sound pressure at listener 					doesn't increase until reflections begin to arrive
		3.	Sound pressure will increase stepwise as more reflections arrive
		4.	Sound pressure takes a while to increase because length 						reflected components travels varies
		5.	In practice sound growth is fast enough to be perceived as 						instantaneous to the listener
	C.	Decay of Sound in a Room
		1.	Stability stops when source is turned off 
		2.	Reflected components continuously lose energy at hard surfaces 					and through the air.
		3.	Rate of decay is exponential
D.	Idealized Growth and Decay of Sound: While growth and decay are stepwise in theory, there are so many reflections that there is an idealized shape for growth and decay
	E.	Calculating Reverberation Time
		1.	Measure of rate of decay in sound, time it takes for sound intensity 				to drop 60 dB from original level.
		2.	This measurement is called RT60
		3.	Calculating RT60 is difficult if background noise is above 30 dB
		4.	First 20 or 30 dB decay is most important to human ear
	F.	Sabine Equation
		1.	Reverberation time depends on room volume and level of 						absorption.
		2.	Greater absorption, less reverb time, greater volume, longer 					reverb time.
		3.	4V/S describes average distance sound travels between 						reflections (V=volume, S=surface area)
		4.	Sabine equation: RT60 = 0.049V/A (V=volume, a=absorption)
		5.	Absorption found by multiplying square footage of each material 					by its absorptive coefficient and summing the results.
		6.	Absorption coefficients for most materials vary by frequency, total 					absorption must be calculated at various frequencies
		7.	Sabine equation assumes sound in a room is diffuse, and works 					best for coefficients less than 0.25
	G.	Eyring-Norris Equation
		1.	Used for more absorptive rooms
		2.	RT60 = 0.49/-Sln(1-alpha), V=room volume, S=surface area 					alpha=average absorption coefficient
	H.	Air Absorption
		1.	Only significant about 2 kHz and large rooms
		2.	RT60 = 0.049/A + 4mV (Sabine) 0.049/-Sln(1-alpha)+4mV
	I.	Measuring Reverberation Time
		1.	Impulse Sources
			a.	Impulse has to be loud enough so decay is significantly 						greater than noise floor
			b.	Includes spark discharge, pistols, balloons
			c.	More diffuse sound fields have smoother decay response
		2.	Steady-State Sources
			a.	Sine waves have very irregular decays
			b.	Warbling tones are better but random noise is the best
			c.	Measures growth as well as decay
		3.	Measuring Equipment
			a.	Pink noise amplified with loudspeaker with switch
			b.	Speaker aimed towards corner
			c.	Omnidirectional mic placed at ear height
		4.	Measurement Procedure
			a.	Room filled with pink noise, mic picks up decay when signal 					stops.
			b.	Signal to noise ratio determines length of decay to study
	J.	Reverberation and Normal Modes
		1.	Frequencies at which sound energy in rooms is accentuated
		2.	These are the reason more than one equation is needed to 						describe rooms.
		3.	When an oscillator is played in a room, it will be louder at certain 					frequencies.  
		4.	Decay times vary by frequency as well
		5.	Reverberation time is difficult for small rooms because of large 					variations in decay time by frequency
	K.	Analysis of Decay Traces
		1.	Axial, tangential, and oblique modes are all very close to each 					other in frequency.
		2.	Modes alternate between high and low levels of agitation
	L.	Mode Decay Variation
		1.	Decays in the same room with the same frequency will vary 					slightly due to the nature of random noise
		2.	Variations occur mostly from beats between closely spaced modes
		3.	Five decays for octave per microphone are recommended
		4.	The more modes a band has, the less irregularities it will have
	M.	Frequency Effect
		1.	Lower frequency decays will have more fluctuations due to less 					bands
		2.	Higher frequency bands with more modes will have statistical 					smoothing.
	N.	Reverberation Characteristic
		1.	Amount of absorption varies with frequency
		2.	Long reverb at high frequencies, short at low creates "thin" or 					"harsh" sound
		3.	Reverberation characteristic graph plots reverb time against 					frequency
		4.	Equalization cannot fix reverb time of certain frequencies, the 					characteristics of the room have to be changed.
		5.	Measured by playing pink noise band passed to certain octave 					bands and calculating RT60.
		6.	Rooms with smooth response and somewhat higher response in 					low frequencies are preferred.
O.	Reverberation Time Variation with Position: There is enough variation to 		justify taking RT60 at multiple positions.
	P.	Decay Rate and the Reverberant Field
		1.	Because small room conditions are not ideal enough due to mode 					effects, the measurement is called decay rate and not reverb time.
		2.	In a dead enough room, only the decay rate of normal modes can 					be found.
		3.	Axial modes decay rates determined by absorbance of walls and 					their spacing
		4.	Tangential and oblique modes decay based on distance traveled, 					surfaces involved, absorption coefficients, and angle of incidence
	Q.	Acoustically Coupled Spacs
		1.	Double slope reverberation may occur if there are openings to a 					more acoustically live room close to the listener
		2.	An example is being in an acoustically dead auditorium but having 					the door open to a hall with hard surface
		3.	After the source room's reverb decays, the coupled room's reverb 					dominates
		4.	Electroacoustically Coupled Spaces
			a.	When recorded music is played in a room, the combined 						reverb time of the recorded room's characteristics and the 						room the track is played in are greater than either alone
			b.	Combined reverb is closer longer decay time, decay isn't a 					straight line
	R.	Eliminating Decay Fluctuations
		1.	Equivalent of the average of many decays can be done by using 					one decay
		2.	Process:
			a.	Record decay of impulse
			b.	Play back decay reversed
			c.	Square voltage of reversed decay
			d.	Integrate squared signal
			e.	Record integrated signal and then reverse
	S.	Reverberation on Speech	
		1.	Lower level consonants can be masked by excessive 						reverberation.
		2.	Usually these lower level consonants are at the end of words
		3.	Speech is more intelligible in rooms with lower reverb
		4.	However, in a dead room or outdoors, speech may not be heard.
		5.	The reverb in live rooms adds acoustic power to the source, 					making them more audible.
		6.	There must be a balance between gain and intelligibility
	T.	Influence of Reverberation on Music
		1.	Optimal reverberation time varies on genre and is subjective
		2.	Both the reverberation time and echo pattern of a room are 						important to how they are perceived.  
		3.	Normal modes are active in concert halls as well, oftentimes 					shifting the pitches during decay in highly reverberant churches
	U.	Optimum Reverberation Time
		1.	Optimal value depends on who is judging, and type of sound 					considered
		2.	Spaces for space require shorter reverb times than for music for 					clarity.
		3.	Music in dead spaces may effect loudness and balance
		4.	Slow melodic music is suited best for longer reverb times
		5.	Quick rhythmic music requires shorter reverb times
		6.	Recording studios must be dead for acoustic separation between 					tracks.
		7.	Speech and recording venues have similar reverb times
		8.	Bass Rise of Reverberation Time
			a.	Goal in voice studios is reverb that is same throughout 						spectrum.
			b.	THis is difficult for low frequencies
			c.	Bass absorbers are much more difficult to install than high 						frequency absorbers
			d.	Rises of up to 80% at 63 Hz and 20% at 125Hz in RT are 						tolerable to the listener though
			e.	In performance halls, bass rise adds sonority and warmth 						and is acceptable for classical music
		9.	Initial Time-Delay Gap
			a.	Direct sound arrives first followed by reverberated sound
			b.	Gap between this is Initial Time Delay Gap
			c.	Gap of less than 40 sec, direct and reverberant sound are 						heard at same time.
			d.	This gap gives ear information about size of the hall
		10.	Listening Room Reverberation Time
			a.	Monitoring room of studio should have same RT similar to 						that of typical listening room
			b.	Living room RT varies greatly from house to house
	V.	Artificial Reverberation
		1.	Standard practice to add to recordings in dry recording studios
		2.	Challenge is mimicking response of music halls without 						introducing frequency distortion to signal
		3.	Reverberation rooms where recordings are played and re-						recorded used to be used
		4.	Digital reverb implemented by delaying a portion of a signal and 					feeding it back.
		5.	1000 echoes per second needed to sound natural
		6.	Reverberators in parallel needed for that number
		7.	Feeding delay into itself and into other delays helps create density

Chapter 8 - refraction

	refraction is the change in the direction of travel of sound because of differences in the velocity of propagation.
	
	refraction of sounds in solids- rays of sound are always perpendicular to sound wavefronts
	refraction of sound in the atmosphere- sound travels faster in warm air than cool air. wind can also carry sound.
	enclosed spaces- less significant indoors.
	ocean- 4.3 times faster than air. Vertical refraction is prominent, less so than horizontal refraction. as temperature drops, the speed decreases, but around 4200 feet, the greater pressure takes over and the speed picks back up again.

 Chapter 9 - Diffusion

	Perfectly diffuse sound field
	-frequency and spatial irregularities - negligible
	-beats in decay must be negligible
	-decay is perfectly exponential
	- Reverb Time is equal at all points in the room
	-decay is equal for all frequencies
	-decay is independent of direction characteristics of measuring mic
	Decay Beats- smoothness of decay increases as frequency increases
	Exponential Decay- dual exponential decay - 2 slopes
				non exponential decay -> true difuse conditions do not prevail
	spatial uniformity of RT- spatial variations in RY are related partially to the degree of diffusion in the space
	geometrical irregularities- must be 1/7 of a wavelength for effect to be felt.
					rectangular shaped diffusers provide greatest effect
	absorbent in patterns- better to have absorptive materials in patches (MuE Classroom)
	concave surfaces- avoid because they focus sound
	convex surfaces-polycylindrical diffuser- effective @ wideband diffusion. Diffusing elements should be random- otherwise certain frequencies come through.
	-plane surfaces are inferior