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Acoustics Flashcards
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- 1SoundSound:
Vibrations that travel through the air or another medium and can be heard when they reach the ear - 2Point of EquilibriumPoint of Equilibrium:
The point of rest - 3DisplacementDisplacement:
A movement away from P.O.E. - 4AmplitudeAmplitude:
maximum displacement, farthest distance away from P.O.E. - For every positive amplitude exertion there is an equal and opposite negative exertion - 5CycleCycle:
a complete rotation of the sine wave. A complete event starting with a rise from zero energy to maximum amplitude, it’s return to zero, it’s fall to max in the opposite direction, and finally it;s return to zero. - 6FrequencyFrequency:
cycles per second, measured in Hz. - 7WavelengthWavelength:
The physical length of one cycle, ie. The total distance required to complete one cycle. - 8PeriodPeriod:
time it takes one cycle (time is seconds) - 9Damping ResistanceDamping Resistance:
forces which remove energy from the system and act to stop vibration - 10Decay EnvelopeDecay Envelope:
time it takes for a system to stop vibrating, losing amplitude not frequency - 11Resonant FrequencyResonant Frequency:
the frequency a system wants to naturally vibrate at - 12Human range of hearingHuman range of hearing: 20 Hz - 20kHz
- 13Wave equation:Wave equation: = V = f λ
Where v = velocity, Speed of sound (m/s, ft/s) - 14inverse square lawinverse square law = sound intensity is directly proportional to the distance from the source - squared.
Example: when energy is twice as far from the source, it’s spread over 4x the area, so it is 1/4 as intense.
When energy is three times as far away from the source, it is spread over 9x the area, so it is 1/9th as intense. - 15NodeNode:
the point of zero or minimum amplitude - 16AntinodeAntinode:
the point of maximum amplitude - 17Phase AnglePhase Angle:
physical point on a wave form measured in degrees. - 18Phase Shift:Phase Shift:
always a comparison*** if two waves have matching phase angles they are said to be “in phase” / if their phase angles don’t match, they are out of phase. - 19SuperpositionSuperposition:
two waves travelling on the same medium in opposite directions pass through each other without being disturbed and net displacement is the sum of each of their amplitudes.
Example: a wave with amp +1, -1 passes through another wave amp +1, -1, will result in a third wave amp +2, -2 - 20Constructive interferenceConstructive interference:
two waves featuring amplitudes with similar signs (either both positive or both negative) will sum together to form a wave with a larger amplitude. - 21Destructive interference:Destructive interference:
two waves with amplitudes of opposite signs (one positive, one negative) will subtract together to form a wave with lower amplitude. - 22Fouriers TheormFouriers Theorm:
any complex waveform can be broke down into X number of sine waves, each of different frequencies, amplitudes and phase. - 23Transverse WavesTransverse Waves:
particles moving up/down perpendicular (90 degrees) to the wave moving left-right. Think: Sine Wave - 24Longitudinal wavesLongitudinal waves:
when particle motion is parallel to wave motion. Think: Slinkly being let go from left to right. - 25Attack DeviceAttack Device:
initiates the vibration. - 26Vibrating ElementVibrating Element:
does the actual vibrating - 27Resonator:Resonator:
usually coupled to the vibrating element. Amplifies / projects the vibration - 28Explain modes of vibrationmodes of vibration: aka Degrees of Freedom -
a term used to characterize how many ‘way’s a vibrating element can physically vibrate. Each mode results in different partials and harmonics. - 29Fundamental FrequencyFundamental Frequency:
the lowest and loudest frequency a vibrating element can vibrate at - 30Harmonic modes of vibrationHarmonic modes of vibration:
modes of vibration with frequencies that are whole number multiples of the fundamental. Ex. 100Hz, 200Hz, 300Hz - 31Inharmonic modes of vibrationInharmonic modes of vibration:
modes of vibration that are not whole number multiples of the fundamental. - 32ChordaphoneChordaphone:
any instrument that uses a stretch string as it’s vibrating element Ex: Guitar, voice, violin - 33MembranaphoneMembranaphone:
instruments that use stretch membrane as their vibrating element. Ex: Drums - 34IdiophoneIdiophone:
instruments conducted of naturally sonic material. Ex: wood block - 35AerophoneAerophone:
instruments that use air chamber (vibrating column) as vibrating element. Ex: Saxophone, Flute - 36Beat frequenciesBeat frequencies:
constructive and destructive interference between two sound waves will result in the formed sound wave beating at the frequency equal to the absolute difference between the two original frequencies. —-> F beat = | F2 - F1 |
- the closer the frequency of the waves, the slower the beat frequency - 37Amplitude Envelope (ADSR)Amplitude Envelope (ADSR) :
used to describe the behaviour of a sound - 38Attack:Attack:
from 0-Max Amplitude, result of attack device - 39DecayDecay:
from Max Amplitude to sustain level - 40SustainSustain:
created by the resonator - 41ReleaseRelease:
the fall from sustain to P.O.E. - 42Specular ReflectionSpecular Reflection:
when sound encounters a boundary, it will reflect or bounce off that boundary in the the form that it encountered it. - 43DiffusionDiffusion:
the type of reflection that occurs when sound encounters a medium that isn’t flat. Think ——> Basketball bouncing off the ground, exploding into 1000 ping pong balls - 44Refraction:Refraction:
a change in direction due to a change in speed. A wave travelling through a medium who’s properties change, or from one medium to another will encounter a change in speed, therefore wavelength will change. Think —-> class holding hands running across sand onto pavement. First part of the class that meets the pavement will speed up essentially resulting in change of waveform - 45DiffractionDiffraction:
when a wave encounters an obstacle and is able to bend around it. Think low frequencies - 46Transmission:Transmission:
when sound encounters a boundary and is able to pass through it. Think in a home studio when sound leaks out of the room. - 47AbsorptionAbsorption:
when sound comes into contact with a boundary and is diminished - 48WavefrontWavefront:
how LF propagates. Bubble Expanding. Lines of constant pressure forming a continuous surface which moves with time, in which every point is the same phase. - 49RaysRays:
how HF propagates. Think arrow shot from bow. A point travelling in a straight line over time, in the direction of wave motion - 50Doppler ShiftDoppler Shift:
as sound gets closer to the source, perceived frequency increases, as sound moves further from the source, perceived frequency decreases. Think: sound becoming louder the closer you get to a speaker - 51Standing WavesStanding Waves
Phenomena caused by reflection and superposition with wavefronts
a sound wave bounces back and forth between surfaces, amplifying itself
creates a wave which appears to be static, nodes and antinodes remain in the same - 52Room Resonant ModesRoom Resonant Modes
Standing waves which occur within a room have specific frequencies
these frequencies “stand out” and are “louder” than others in the room
Largest contributor to the “sound” of a space. - they colour/create peaks in the frequency response of the room
caused by reflection of LF - most problematic in rooms with rigid walls which reflect LF, for example: Basements - 533 Kinds of Resonant Modes3 Kinds of Resonant Modes
(determined by the way they bounce around)
Axial Modes - exist between 1 pair of surfaces
Tangential Modes - exist between 2 pairs of surfaces (4 walls)
(Wave coming out of speaker, bouncing off left wall —-> to the front wall, bouncing off the front wall ——> to the right side wall, bounces off the right side wall ——> to the back wall, bounces from the back wall —-> to the left wall)
Oblique Modes - exist between 3 pairs of surfaces
(Wave coming out of speaker bouncing off 6 walls) - 54Resonant Modes - Modal FrequenciesResonant Modes
Modal frequencies are predictable and are determined by room dimension
the frequencies that have wavelengths which fit into dimensions will overlap themselves in phase, hence they will stand
exist at fundamental as well as harmonics
For example: if mode occurs at 100Hz, there will be modes at 200Hz, 300Hz, etc. - 55Axial ModesAxial Modes
are the loudest - least distance traveled, fewest # of surfaces contacted, therefore the most energy
largest contributor to room coloration
usually lower frequencies than tangential and oblique.
Axial = twice as loud (twice) the energy of tangential
Tangential = twice as loud (twice the energy) of oblique - 56Axial Mode CalculationsAxial Mode Calculations
if the dimensions are known, modal response can be calculated
modal frequency = Velocity of sound / 2xDimension
modalities frequency = 1130 / 2xD = 565/D where D is the dimension in Ft. - 57What resonant modes will exist in a room which is 10ft wide?What resonant modes will exist in a room which is 10ft wide?
F = 565/D = 565/10 = 56.5Hz
Modes exist at fundamental and harmonics (whole number multiples), therefore there will also be modes at 113Hz, 169.5Hz, 226Hz etc. - 58Integers p, q, r - The Labeling system (Nomenclature) used for modes1, 0, 0 - one whole number denotes an axial mode
1, 1, 0 - 2 whole numbers denotes a tangential mode
1, 1, 1, - 3 whole numbers denotes an oblique mode
Integers with a value of 1 indicate fundamental,
value of 2 indicate harmonic 2x the fundamental
value of 3 = 3x fundamental, etc.
what position indicates what surfaces are involved:
1st position (p) indicates mode occurs in the length
2nd position (q) = mode occurs in width
3rd position (r) = mode occurs in the height - 59Zero Spaced Modes:Zero Spaced Modes:
- modes which occur at the same frequency, and amplify each other. Example: full class standing shoulder to shoulder would be looked at as normal, where as majority of class standing shoulder to shoulder with one student standing on another students shoulder is a prime example of zero spaced mode. - 60Coincident modes:Coincident modes:
- modes which are separated by less than 5Hz from each other. Example: full class standing shoulder to shoulder would be looked at as normal, where as majority of class standing shoulder to shoulder with two students off to the side hugging would be an example of a coincident mode. - 61Acoustically isolated modesAcoustically isolated modes:
- a mode separated from both neighbouring modes by more than 20Hz, will “stand out”. - 62Room ratios - whats not acceptable?Whats bad:
Obviously “cube” rooms with ratios of 1:1:1 are bad because same modes = tripling of acoustic intensity.
- any two equal dimensions are bad. Eg: 1:1:3, same modes occur in two dimensions = doubling of acoustic intensity
any ratio which has integer related dimensions Eg: 1:2:3, 1:4:8 will also result in an undesirable modal distribution
modes occur at fundamental and harmonics (whole number multiples) if room ratio consists of dimensions which are whole number multiples, dimensions will produce equal modal frequencies. - 63Room ratios - whats acceptable?Avoid regular geometry i.e.. cubes, rectangles with integer related dimensions
- work with an acceptable room ratio (google search) which yields optimal distribution
- modes exist in any enclosed space, including rooms that aren't rectangular (parallel surfaces)
- in non- rectangular rooms, modes will develop based on the mean distance between walls - 64RT60RT60
- Time it takes for reverberant signal to decay by 60dB
measured in seconds
the decay envelope for the room itself
60dB represents a change in sound intensity of 1 million, from loud to inaudible as far as human perception is concerned
- An important Psycho-acoustic factor in the sound of a room:
if RT 60 too short, sound dies away to quick, we perceive the room as “dead” (think perfectly treated recording booths)
if RT 60 too long, too many reflections destroy intelligibility, increase amplitude in a room (think high school gym during a speech, awful acoustics with a lot of background noise)
- reflected waves can significantly colour direct signal - superposition! - 65What does the ideal RT60 depend on?the ideal RT60 depends on circumstance.
Opera, Classical music = long RT60
Speech = Short RT60 to preserve intelligibility
Ideal RT60 for most average sized recording studios is around 400ms
Generally we prefer a 40% increase in RT60 of LF over RT60 of midrange
creates “warmth” helps increased perceived levels of LF - 66ReverberationReverberation
1. Direct sound reaches observer first —> dependant on distance from source
2. Early reflections from major boundaries arrive next —> dependant on distance from boundaries (walls)
3. Random reflections with less energy, longer bounce paths follow next
Our brain sums all of these together so we perceive them all relatively at the same time - 67RT60 and Room ModesRT60 and Room Modes
RT 60 varies with frequency, HF should decay faster than LF.
Modal Frequencies take longer to decay than other frequencies in the room.
Ideally all LF’S should decay at the same rate - 68Modal BandwidthModal Bandwidth
Each mode has a bandwidth (a range of frequencies affected by a boost or cut)
the bandwidth is the distance, in Hz, measured at the 3dB down point - 69Modal Bandwidth and RT60Modal Bandwidth and RT60
Modal Bandwidth is determined by and inversely proportional to RT60
Bandwidth (Hz) = 2.2 / RT60
Short RT60 = Wide Modal bandwidth
Long RT60 = Narrow modal bandwidth - 70RT60 and Room VolumeRT60 and Room Volume
Length x Width x Height
the larger the volume, the further apart the walls. The further apart the walls, the longer the path of the reflections, the longer they take to reach listener, the longer RT 60.
RT60 is inversely proportional to rooms volume.
also vey affected by surface materials - 71RT60 and Surface MaterialsRT60 and Surface Materials
RT 60 is caused by reflections off the the surfaces in the room
the energy of these reflections is determined by the absorption properties of the materials on the surfaces
high absorption = really short RT60
low absorption = long RT60 - 72Absorption CoefficientAbsorption Coefficient
Measurement of the absorption properties of a material
tells us whether or not we’re getting absorbed, how much if so
symbol = a, when a = 1, 100% of the energy at that frequency will be absorbed. When a = 0.3, 30% absorbed
extent of absorption varies with frequency, therefore a is given across selected octave divisions. - 73Calculation of RT60Calculation of RT60
Sabine Equation
As stated previously RT 60 depends on room volume and absorption, to calculate RT60 must take into account both factors
Sabine Equation :
RT60 = 0.049v / Sa
Where 0.049 = constant (if Volume = m cubed use 0.161)
V = volume in feet cubed
Sa - total Sabin (Sabines) of absorption - 74LF Absorption: Classification of AbsorbersLF Absorption: Classification of Absorbers
Absorbers can be broken down into 2 Categories
Passive: Porous absorbers: foam, fiberglass, fabric, etc.
also called: Velocity Absorbers: because action of absorption is triggered by the velocity component of the wave.
Resonators: use vibrating membrane, panel, or volume of air
also called Pressure Absorbers: because they’re activated by the pressure component of the wave. They need a push, work by converting friction to heat. - 75Passive AbsorbersPassive Absorbers
- action of absorption is triggered by the velocity component of the wave.
Passive absorption follows the 1/4 wavelength rule: only absorb frequencies that have a 1/4 wavelength equal or less than thickness of absorber. So, there is a direct correlation between the thickness of the absorber and the wavelength of the signal we’re trying to absorb
e.g.: 100Hz wavelength = 12 ft. To absorb 100Hz we would need a passive absorber at least 3 ft thick. Not practical, also problematic because a 3ft thick absorber will absorb all frequencies above 100Hz.
Why the 1/4 wavelength rule?
- at a wall surface sound pressure is at a maximum, particle velocity is at a minimum. Because the boundary creates a situation where the particles can’t move
at 1/4 wavelength from the wall sound pressure is minimum, but particle velocity is maximum.
placing absorption at the area where particle velocity is max. = max friction = max energy dissipation - 761/4 wavelength ruleUsed in passive absorption.
1/4 wavelength rule: only absorb frequencies that have a 1/4 wavelength equal or less than thickness of absorber.
Why the 1/4 wavelength rule?
- at a wall surface sound pressure is at a maximum, particle velocity is at a minimum. Because the boundary creates a situation where the particles can’t move
at 1/4 wavelength from the wall sound pressure is minimum, but particle velocity is maximum.
placing absorption at the area where particle velocity is max. = max friction = max energy dissipation - 77Practical Use of Passive AbsorptionPractical Use of Passive Absorption
Simple to build, are just rigid mineral finer or fibreglass panels placed at a distance from a wall
rigid mineral fibre is denser than regular fibreglass. The more dense = more absorption.
Greater the distance from the wall, the lower the frequency absorbed
Most commercial available “bass traps” are this type. For example: Real Traps, Tube Traps, Attack Wall, Auralex - 78ResonatorsResonators:
work by sound pressure
each active absorber has a resonant frequency which they vibrate at. The resonant frequency is the frequency which they will absorb
Resonators typically have a very narrow bandwidth of absorption.
Can be designed to absorb very low frequencies - more practical for very low frequencies than passive absorbers, resonators not governed by 1/4 wavelength rule.
Resonators work by sound pressure not particle velocity. So they are most effective when placed in areas of greatest sound pressure (antinodes)
pressure from room modes is usually greatest in corners of room, or against any wall - 79Helmholtz Resonators:Helmholtz Resonators:
an enclosed volume of air coupled to the room by an aperture (opening).
- As we know, volume of air has a resonant frequency. Larger the volume of air, or the smaller the opening (aperture), the lower the resonant frequency.
Porous absorption is placed inside the cavity to add damping resistance and prevent “acoustics capacitor” effect (ringing.
—> Helmholtz Resonators: creating a very localized high velocity area for the frequency we are trying to absorb - 80Panel Absorber:Panel Absorber:
constructed of a “Panel” over an air space. “Membranophone”
Sound pressure causes the panel to flex like a membrane. (basically building a type of drum)
Resonant frequency = volume of space behind the panel, mass/density of the panel
more volume, more mass = lower resonant frequency
placing porous absorption behind panel adds damping resistance and increases bandwidth. - 81Variations of Panel AbsorbersVariations:
Perforated Panel Absorber: panel with holes in it (perf” board”) over an air space
- creates a panel absorber with Helmholtz resonance capabilities
- greater the volume of air behind the panel, smaller the holes in panel, the fewer the number of holes, greater the mass = lower resonant frequency.
Poly-cylindrical Panel Absorbers: semi circular curved panels over an air space.
- Shape results in diffusion characteristics as well as absorption
- greater the mass of panel, larger the air space, the lower the resonant frequency. - 82Reflection Control:Reflection Control:
Acousticians can utilize three aspects of sound behaviour to control reflected energy in a room
- Reflection
- Absorption
- Diffusion - 83Diffusion Gratings:Diffusion Gratings:
devices constructed to have predictable diffusion characteristics across desired frequency bandwidths. A series of “wells/grooves” of fixed width and varying depth. An equation is used to calculate the sequence of depths and widths to obtain complete diffusion
Diffusers: work by altering phase of reflected waves. - Wave encounters grooved surface, enters the wells then reflects out of them - Wells vary in depth, so some waves take longer to reflect back out than others - Time difference = Phase difference - 84Phase Gradient Diffusers or RPG’s (Reflection Phase Gradients)Phase Gradient Diffusers or RPG’s (Reflection Phase Gradients)
Interference occurs between waves arriving at surface and waves reflecting out of grooves. - Results in numerous low energy reflections spread throughout the room in a predictable pattern
known as Phase Gradient Diffusers or RPG’s (Reflection Phase Gradients) - 85What does diffusion do to a room?What does diffusion do to a room?
reduces amplitude and spreads the energy
Diffusion doesn’t take energy out of the room, it spreads it out so therefore does not drastically affect the RT60. - 86Advantages / Disadvantages of DiffusersAdvantages of Diffusers
- Spreads wave energy equally throughout the room
- resultant reflections have less energy, less amplitude. Absorbed easier because of less interference with direct signal
- “smoothes out” the reverberant field or makes the sound not as harsh/more musical
- reasonable sizes
Disadvantages of Diffusers
- Can be difficult/time consuming/expensive to design and build. - Uses mathematical equations to derivable depth series
- as a result of above they are expensive to buy commercially ($650 for a 2x4ft panel) - 87QRDQRD =
Quadratic Residue Diffuser, uses a quadratic residue equation to calculate groove depth sequence - 88PRDPRD =
prime root diffuser, AKA “Skylines use Prime toot equation. - 2D diffusion - 89Building a QRDBuilding a QRD
calculate well depth and width based on the frequency range you want diffused
determine “size” which is the number of grooves
to follow a quadratic sequence, number of grooves must be a prime number + 1, prime number = 3, 5, 7, 11, 13, 17, etc.
E.g. a “prime 7” QRD will have 8 wells numbered 0-7, a “prime 13” QRD will have 14 wells, numbered 0-13.
The higher the prime number used, the more “even” the diffusion pattern
the better suppression of specular reflection
the higher the prime number, the larger the diffuser becomes
FYI
Use the formula: depth = n squared modulo p
where n = groove number
p = prime number used
to determine the well depth proportionality sequence
modulo: a mathematical term which means that the “p” is repeatedly subtracted from “n squared” until a positive remainder is achieved between 0 and p. The remainder is the answer - 90—
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