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Room Acoustics

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Visit https://alexisbaskind.net/teaching for a full interactive version of this course with sound and video material, as well as more courses and material.

Course series: Fundamentals of acoustics for sound engineers and music producers
Level: undergraduate (Bachelor)
Language: English
Revision: February 2020
To cite this course: Alexis Baskind, Room Acoustics
course material, license: Creative Commons BY-NC-SA.


Course content:
1. Time-Space perspective: Sound propagation in a room
Raytracing, example of a rectangular room, evolution from free field to diffuse field, initial time delay gap (ITDG), direct sound, first reflections, late reverberation, exponential decay of the pressure, definition of the reverberation time, T60, T30, T20, Schroeder curve, critical distance, flutter echoes, diffusion, effect of distance, effect of room size

2. Frequency-Space perspective: Room modes
Reminder: monodimensional standing waves, axial modes, tangential modes, oblique modes, eigenfrequencies, effect of room size on modal density, duration and bandwidth of modes, effect of absorption on modes, Schroeder Frequency

3. Time-Frequency perspective
Early reflections, modes and diffuse reverberation in an unified time-frequency perspective, waterfall view

4. Room acoustics design
prediction of the reverberation time, Sabine formula, frequency-dependent absorption, porous absorbers, effect of absorber’s thickness and air gap, resonant absorbers, membrane absorbers, Helmholtz absorbers

5. Room acoustics of listening rooms
importance of symmetry, need for a sufficient room size and controlled reverberation time, recommended reverberation time, need for controlling the early reflections, LEDE design, RFZ design

6. Spatial hearing in a room
perception of distance in a room, perception of the room size, clarity, apparent source width, envelopment, reverberation timbre

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Room Acoustics

  1. 1. Alexis Baskind Room Acoustics Alexis Baskind, https://alexisbaskind.net
  2. 2. Alexis Baskind Room Acoustics Course series Fundamentals of acoustics for sound engineers and music producers Level undergraduate (Bachelor) Language English Revision January 2020 To cite this course Alexis Baskind, Room Acoustics, course material, license: Creative Commons BY-NC- SA. Full interactive version of this course with sound and video material, as well as more courses and material on https://alexisbaskind.net/teaching. Except where otherwise noted, content of this course material is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. Room Acoustics
  3. 3. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  4. 4. Alexis Baskind Sound propagation in a room • The time evolution of the sound propagation in a room can be considered from the point of view of sound rays, reflection, absorption and diffusion surfaces • Most of room acoustics simulation softwares uses indeed among others raytracing algorithms (similar to 3D image rendering algorithms) • For this, let’s first consider a simple rectangular room, with a sound source and one listener Room Acoustics
  5. 5. Alexis Baskind Sound propagation in a room • The sound sources only emits a short impulse, for example a hand clapping, or a gunshot (gunshots were used a lot in the early ages to measure room acoustics) Room Acoustics Source: Charles Feilding
  6. 6. Alexis Baskind Direct Sound • The first information that reaches the listener is the direct sound • Without any further reflections, this would correspond to the so- called free-field (in an anechoic chamber) Room Acoustics Temporal representation Spatial representation Source: Charles Feilding
  7. 7. Alexis Baskind Early reflections • After a moment (called initial time-delay gap), the first reflected waves reach the listener, with less level because of absorption and the distance (inverse-square law) Room Acoustics Temporal representation Spatial representation In red: the initial time delay gap Source: Charles Feilding
  8. 8. Alexis Baskind Early reflections • The temporal density of reflections increases drastically with time Room Acoustics => =>Direct sound First-order reflections (i.e. reflected once) Second-order reflections (i.e. reflected twice) Source: Geoff Martin
  9. 9. Alexis Baskind Late Reverberation • After 20-100ms (depending on the room dimensions and on the diffusion – see below), the reflections become dense and come from every direction: the sound field becomes more and more diffuse => late reverberation Room Acoustics Temporal representation Spatial representation Source: Charles Feilding
  10. 10. Alexis Baskind Late Reverberation Without flutter echoes or other late reflections, the sound pressure decays on average exponentially with time during the late reverberation process Room Acoustics Soundpressure(linear) Room impulse response (schematic), linear representation
  11. 11. Alexis Baskind Late Reverberation Without flutter echoes or other late reflections, the sound pressure decays on average exponentially with respect to time during the late reverberation process Room Acoustics Sound pressure (Pa) Time (ms) in red: envelope of late reverberation decay Room impulse response (measured), linear representation
  12. 12. Alexis Baskind Late Reverberation Thus the sound pressure level (on a logarithmic scale) decays on average linearly with respect to time Same room impulse response (measured), logarithmic representationSound pressure level (dB SPL) time (ms) in red: envelope of late reverberation decay in blue: measurement noise Room Acoustics
  13. 13. Alexis Baskind Sound pressure level (dB SPL) Time (ms) Reverberation Time • The Reverberation Time (T60) is the time the sound pressure level needs for a 60 dB decrease • The reverberation time is the most well known measure to characterize a given reverberation 60 dB T60 = time corresponding to a 60 dB decrease Room Acoustics
  14. 14. Alexis Baskind Sound pressure level (dB SPL) Time (ms) Reverberation Time • In practice, the reverberation time is measured thanks to an estimation of the envelope (called „Schroeder-curve“), which is much smoother as the impulse response. In black: Schroeder-curve 60 dB T60 = time corresponding to a 60 dB decrease Room Acoustics
  15. 15. Alexis Baskind Sound pressure level (dB SPL) Time (ms) Reverberation Time • Since a dynamic range of 60 dB is almost impossible to achieve, the reverberation time is calculated based on a decay of 30 dB or 20 dB, and then doubled (for 20dB) or tripled (for 60dB), in order to stay coherent with T60 => Those estimations are called T20 and T30. • T30 is measured between -5 dB and -35 dB, and T20 between -5 dB and -25 dB with regards to the maximum of the curve T30 / 2 Max – 5dB Max – 35dB Room Acoustics
  16. 16. Alexis Baskind Sound pressure level (dB SPL) Time (ms) Reverberation Time • Since a dynamic range of 60 dB is almost impossible to achieve, the reverberation time is calculated based on a decay of 30 dB or 20 dB, and then doubled (for 20dB) or tripled (for 60dB), in order to stay coherent with T60 => Those estimations are called T20 and T30. • T30 is measured between -5 dB and -35 dB, and T20 between -5 dB and -25 dB with regards to the maximum of the curve T20 / 3 Max – 5dB Max – 25dB Room Acoustics
  17. 17. Alexis Baskind Free field / diffuse field • The time evolution of the sound propagation in a room can be considered as the evolution from a free field to a diffuse field – Direct sound = free field: the signals that reach the microphones/ears are highly correlated – Early reflections = the correlation between recorded signals drops more and more down as new reflections reach the microphones – Late reverberation = diffuse field: 1. The sound is coming from all directions with the same level 2. The correlation between sound pressures at different positions is close to zero 3. The diffuse field has the same characteristics at all positions of the room Room Acoustics
  18. 18. Alexis Baskind Critical Distance • The critical distance (or Room Radius) is defined as the distance to the source where the energy of the direct sound equals the energy of the reverberated sound Room Acoustics Distance from source • Below this distance, the energy mainly follows the inverse square law • Above this distance, the energy is roughly always constant whatever the position is, and corresponds to the level of the reverberant field
  19. 19. Alexis Baskind Diffusion • Late reflections, even attenuated by absorption, are often disturbing, since they may lead to audible echoes • The worst case is flutter echoes between parallel surfaces • Therefore, diffusive surfaces are often used as an alternative to reflective surfaces: they help to reduce late reflections without making the room dryer • The more diffusive surfaces, the earlier the transition to diffuse reverberation Room Acoustics
  20. 20. Alexis Baskind Diffusion Room Acoustics Without diffusion With diffusion Source: Takatoshi Yokota, Shinichi Sakamoto and Hideki Tachibana
  21. 21. Alexis Baskind Diffusion Room Acoustics Source: Takatoshi Yokota, Shinichi Sakamoto and Hideki Tachibana
  22. 22. Alexis Baskind The effect of Distance • How is the reverberation changed when the source gets farther ? Room Acoustics timetime The source is farThe source is close
  23. 23. Alexis Baskind Effect of Distance With increasing distance: 1. The direct sound and the early reflections come later 2. The initial time delay gap is smaller 3. The early reflections come less from the sides and more from the front. According to the cocktail-party effect, they are preceptually less easy to distinguish from the direct sound => Coloration 4. The level of the direct sound decreases, but the level of the diffuse reverberation remains more or less identical => the relative part of reverberation increases Room Acoustics
  24. 24. Alexis Baskind The effect of Room Size • How does the reverberation depend on the size of the room ? Room Acoustics The room is bigThe room is small timetime
  25. 25. Alexis Baskind The effect of Room Size If the room is bigger: 1. The overall sound level decreases 2. The early reflections come later 3. The reverberation time is longer This means that a relatively long reverberation time can be achieved: – In a small room which walls, ceiling and floor are not good absorbers (like small echo chambers used in studios) – In a very large room which walls, ceiling and floor are good absorbers => the main difference between those two cases is that early reflections come earlier in a small room (which is used by perception to recognize if a room is small or big) Room Acoustics
  26. 26. Alexis Baskind Limits of the geometrical model • The geometrical model makes only sense if the wavelengths are short enough, so that reflections can occur. • This is a requirement in order to consider the reverberant field as diffuse • At low frequencies, surfaces and distances between them are too small compared to the wavelength: the geometrical model does not work any more, and must be replaced with a modal model (i.e. standing waves) Room Acoustics
  27. 27. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  28. 28. Alexis Baskind Room resonances • Reminder: monodimensional standing waves between two walls Room Acoustics Wall 1 Wall 2 distance between walls wavelength
  29. 29. Alexis Baskind Axial modes only depend on 1 dimension Tangential modes depend on 2 dimensions Room resonances • In 3 dimensions, more complex combinations are possible: Room Acoustics Oblique modes (also called diagonal) depend on 3 dimensions Image sources: mcsquared.com
  30. 30. Alexis Baskind Room resonances • In 3 dimensions, more complex combinations are possible: Room Acoustics Image source: gikacoustics.com
  31. 31. Alexis Baskind Frequency distribution of modes • Because modes are 3-dimensional, their frequencies (called eigenfrequencies) are not distributed regularly (on a harmonic series), contrary to the 1-D case Room Acoustics Example: simulated eigenfrequencies for a rectangular room with dimensions: 4.6m x 3.75m x 2.34m Hz frequency
  32. 32. Alexis Baskind Frequency distribution of modes • The frequency distribution depends on the size of the room: the bigger the room, the bigger the modal density (i.e. the number of modes per frequency) • The higher the frequency, the bigger the modal density Room Acoustics Example: simulated eigenfrequencies for a rectangular room with dimensions: 9.2mx 7.5m x 4m Hz frequency
  33. 33. Alexis Baskind Modes: Duration and Bandwidth • The duration and the bandwidth of single modes, like for every resonances (or like band-pass filters), are inversely proportional with each other: the longer it lasts, the narrower it is in the frequency spectrum • Therefore: – Modes in a room without any absorbing material are long, thus very narrow in the frequency spectrum (= a high quality factor) => very clear resonances, holes between two modes – Modes in a room with a proper acoustic treatment (i.e. enough absorption at low frequencies) are short, thus wider in the frequency spectrum (= a low quality factor) => the spectrum is more flat, less obvious resonances Room Acoustics
  34. 34. Alexis Baskind Modes: Duration and Bandwidth -0.10 0.00 0.10 Volts/Volts 0 100 200 300 400 500 Time (ms) Impulse Response -0.10 0.00 0.10 Volts/Volts 0 100 200 300 400 500 Time (ms) Impulse Response -0.10 0.00 0.10 Volts/Volts 0 100 200 300 400 500 Time (ms) Impulse Response Frequency Response Impulse Response (time) lessresonant (=lowQ-Factor) moreresonant (=highQ-Factor) Room Acoustics Behavior of a single mode with respect to frequency and time, depending on damping
  35. 35. Alexis Baskind Modes: Duration and Bandwidth Example: empty room (no treatment) Source : Ethan Winer Time Frequency Level Room Acoustics
  36. 36. Alexis Baskind Modes: Duration and Bandwidth ... With 12 thin absorbers: 703-FRK from Owens Corning Source : Ethan Winer Time Frequency Level Room Acoustics
  37. 37. Alexis Baskind Modes: Duration and Bandwidth ... With 12 thin absorbers: 705-FRK from Owens Corning Source: Ethan Winer Time Frequency Level Room Acoustics
  38. 38. Alexis Baskind Modes and frequency response The overall frequency spectrum at low frequencies consists in the overlapping of all modes. Example: calculated modes and frequency response in a rectangular room (left: single modes, right overlapping = estimated frequency response) Room Acoustics Image sources: BBC Research Department Report, Low-Frequency Room Responses
  39. 39. Alexis Baskind Modes and frequency response Room Acoustics Caution: the overlapping of modes leads not only to constructive interferences, but also sometimes destructive Holes in the frequency spectrum Example (Simulation of room modes in the Software “Room EQ Wizard”): • The eigenfrequencies of the room modes are shown als colored lines • There are holes at ca. 44Hz and 52 Hz, that result from the big frequency distance between the closest modes as well as from destructive interferences between them. • There is also a hole at 62 Hz although the closest mode (63 Hz) is quite strong at this position. This hole can only be explained with destructive interferences
  40. 40. Alexis Baskind Example of the frequency response of real room Room Acoustics
  41. 41. Alexis Baskind Example of the frequency response of real room Room Acoustics Low-frequency Modes
  42. 42. Alexis Baskind The problem with room modes When the modal density is too small at low frequencies (i.e. for small rooms), the sound pressure level present strong variations as a function of the position of the source and of the listener. Room Acoustics Source: Thomas Görne, “Tontechnik” Simulated position-dependent sound field in a rectangular room 3m x 3.40m x 2.40m (Reverberation time ca. 0.5 s); sound pressure on the horizontal plane 1,2m above the floor at 80 Hz, 93 Hz, 109 Hz, 127 Hz; the level varies up to 40 dB as a fonction of position
  43. 43. Alexis Baskind Modes and Modal Density: Summary • Modes can also interfere in a destructive way • The position of the loudspeakers and the listening position are extremely important for the linearity of reproduction at low frequency So there are 3 possible causes for amplitude dips at low frequencies: 1. The loudspeaker or the listening point is at a node of a room mode 2. The frequency lies between 2 modes with a big frequency distance between their eigenfrequencies 3. The frequency lies between 2 modes with a small distancebetween their eigenfrequencies, but the two modes interfere in a destructive way at the listening position Room Acoustics
  44. 44. Alexis Baskind Modes and Modal Density: Summary • If the modal density is too small: 1. There will be amplitude dips between the eigenfrequencies 2. The amplitude varies a lot for a given position with respect to position • If the modal density is big enough: 1. The distance between the modes is smaller 2. The amplitude for a given frequency depends on several modes => less influence of position, less destructive interferences, the room sound field is more diffuse The bigger the modal density, the better • Room modes are especially problematic in small rooms, for which the modal density is often too small at low frequencies Room Acoustics
  45. 45. Alexis Baskind Schroeder-Frequency • The Schroeder-Frequency provides an order of magnitude of the frequency region above which the modal density is big enough (>=3) to consider the room sound field as diffuse • It can be calculated as follows: • This means: – The bigger the room, the smaller the Schroeder-Frequency – The drier the room , the smaller the Schroeder-Frequency Small listening rooms must be dry in order to minimize linear distortions at low frequencies Room Acoustics Fs» 2000 T60 V (T60 is the reverberation time in this frequency region, V is the room volume)
  46. 46. Alexis Baskind Acoustics of Listening Rooms The ITU-R BS.1116-1 recommendation suggests that: • The average reverberation time, measured over the frequency range 200 Hz to 4 kHz, should be: … where V is the volume of the room in m3 RTm = 0.25 V 100 3 (s) Room Acoustics
  47. 47. Alexis Baskind Acoustics of Listening Rooms The ITU-R BS.1116-1 recommendation suggests that: • The reverberation time stays in the given limits: RTm Room Acoustics
  48. 48. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  49. 49. Alexis Baskind Time-frequency model of a reverberation • Time and frequency approaches can be grouped in a single model: Room Acoustics Frequency (Hz) Time (s) Modes Early reflections Diffuse reverberation
  50. 50. Alexis Baskind Waterfall View • The Waterfall view is a time-frequency representation of a measured room response: Room Acoustics Frequency (Hz) Time (ms) Level (dB)
  51. 51. Alexis Baskind Waterfall View • The Waterfall view shows very well the frequency dependence of the late decay (see later) • On small rooms, the low-frequency modes are also quite visible • It gives in general more information as the frequency response (since it also shows thetime evolution of the spectrum) • But: the time resolution is very low. Among others, it does not reveal the early reflections Room Acoustics
  52. 52. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  53. 53. Alexis Baskind Room acoustics design • The first step and requirement for the acoustic design of a room is the stipulation of the desired reverberation time • The required reverberation time depends on the usage of the room (recording room, listening room, concert hall, teaching room etc.). There are specific recommandation for each kind of room: for instance, a listening room is designed to be typically drier as a recording room • Based on the reverberation time, the room dimensions and the construction materials (concrete, dry wall, wood...), a selection of absorbing, diffusive and reflective surfaces is being made in order to reach the required reverberation time and optimize the acoustics Room Acoustics
  54. 54. Alexis Baskind Prediction of the Reverberation Time • Several (partly empirical) formulas provide an estimation of the reverberation time. The most well known are from Sabine (1898) and Eyring (1920) => Sabine Formula (for low absorptions coefficients): the surfaces are categorized by their material, thus their absorption properties: … with: V = Room volume in m3 αi is the absorption coefficient for the surface Si The product αi.Si is called equivalent absorption area (unit = Sabins). • Since the absorption coefficient depends on frequency, the reverberation time also depends on frequency Room Acoustics 𝑇60 ≈ 0.161 𝑉 𝛼𝑖 𝑆𝑖𝑖
  55. 55. Alexis Baskind Absorption Coefficient of various materials Room Acoustics
  56. 56. Alexis Baskind Frequency-dependent absorption • Reverberation time is typically bigger at low frequencies, since most absorbers are not efficient for big wavelengths: Room Acoustics Example: Reverberation time as a function of frequency for 3 concert halls
  57. 57. Alexis Baskind Sound Absorbers • Absorbers are usually classified in 3 categories Room Acoustics . Porous absorber (=velocity-based absorber) => Used as wideband absorbers if they are thick enough 1/ Resonant absorbers (=pressure-based absorbers) . Membrane absorbers . Helmholtz-Absorber: with holes or slots 2/ „Tube traps“ (3/ active bass traps) Absorptioncoefficient High-frequency absorber mid-frequency absorber low-frequency absorber Frequency
  58. 58. Alexis Baskind Porous Absorbers • Porous Absorber are velocity-based absorbers: they reach a maximum of efficiency at positions where the sound velocity is maximum • The sound velocity is maximum at zeros of the sound pressure (=nodes) Room Acoustics • This means for standing waves, that the maximum of efficiency is reached for a distance to the wall of λ/4, 3λ/4, 5λ/4, etc. blue: sound pressure red: sound velocity
  59. 59. Alexis Baskind Porous Absorbers This means: the lower cutoff frequency of absorption depends on the thickness of the absorber Room Acoustics red: sound velocity for standing waves with various wavelengths gray: porous absorber high frequencies: several maxima of the sound velocity in the absorber => maximum efficiency Lower cutoff frequency: the first maximum of sound velocity is at the limit between absorber and air Low frequencies: maxima of the sound velocity are outside the absorber => lower efficiency
  60. 60. Alexis Baskind Porous Absorbers This means: the lower cutoff frequency of absorption depends on the thickness of the absorber Room Acoustics Example: simulated absorption coefficient for two different thicknesses (source: www.acousticmodelling.com)
  61. 61. Alexis Baskind Porous Absorbers Room Acoustics High-frequency absorber High-frequency absorber with increased absorption surface Corner absorbers: often sold as als „bass traps“, but typically efficient above 100-200 Hz and almost useless at lowest frequencies
  62. 62. Alexis Baskind Porous Absorbers A possibility to increase the efficiency at low frequencies is to place the absorber at a certain distance with the reflecting surface => for instance usefull for ceiling absorbers Room Acoustics red: sound velocity for standing waves with various wavelengths gray: porous absorber High frequency Frequenzen: several maxima of the sound velocity in the absorber => maximum efficiency (although bigger dependence on the wavelength) smaller (but not zero-) efficiency Again good efficiency, since the first maximum of the sound velocity is within the absorbing material Air gap
  63. 63. Alexis Baskind Porous Absorbers Room Acoustics Example: simulated absorption coefficient with and without air gap (source: www.acousticmodelling.com) Porous Absorber with air gap with reflecting surface
  64. 64. Alexis Baskind Resonant Absorbers • Resonant absorber are pressure-based absorbers: they reach a maximum of efficiency at positions where the sound pressure is maximum: this means against the walls and room corners • Resonant absorbers are harmonic oscillators and work like spring-mass systems. This means: – The absorption is achieved thanks to friction. Without friction, the energy may actually be amplified instead of absorbed – The resonance frequency: • Increases with the spring constant (stiffness) • Decreases with increasing mass • Decreases with increasing friction – The bandwidth increases with friction Room Acoustics
  65. 65. Alexis Baskind Membrane absorbers Room Acoustics Source: Heinrich Kuttruff, “Room Acoustics” • Membrane absorbers consist in a thin oscillating rigid or soft membrane (typically wooden) clamped with a spacing to the ceiling or wall. The enclosure is airtight and partly filled with absorbing (porous) material • The mass is the masse of the membrane • The stiffness depends on the volume of air and absorbing material in the enclosure, and partly also on the elasticity of the membrane and clamping • Friction takes place partly in the wood but mostly in the absorbing material
  66. 66. Alexis Baskind Perforated plates, slat absorbers Room Acoustics Source: Heinrich Kuttruff, “Room Acoustics” • Perforated plates and slit absorbers work as Helmholtz resonators: the panel does not vibrate, but the air in the openings (holes or slots) • The resonance frequency depends on the geometry (thickness and width of the openings), width of the air volume. Source: topakustik.ch
  67. 67. Alexis Baskind Perforated plates, slat absorbers Room Acoustics Perforated Panel with Porous Absorber Properties of panel Display options Panel thickness (tp) 6,0 mm 0,236 in Start graph at 62,5 Hz Eq 6.8 Repeat distance (D) 25,0 mm 0,984 in To see the graph in the standard Hole radius (a) 10,0 mm 0,394 in analysis frequencies, select Open Area ( ) 50,27% Show subdivisions of "Whole Octaves" and set the Properties of cavity starting frequency to 62.5Hz Cavity depth (d) 100,0 mm 3,937 in Absorber thickness (ta) 10,0 mm 0,394 in Air space in cavity (d - ta) 90,0 mm 3,543 in This is ignored for the "No Air Gap" plot. Cavity assumed to be filled with absorber. Absorber flow resisitivity 10 000 rayls/m This plot is a simplification of reality because it is only calculated for normal incident sound. 2 f 2 / Eq 5.19 Eq 5.20 Eq 5.11 Eq 5.9 Eq 5.10 Eq 5.26 Eq 5.27 Eq 6.15 Eq 6.26 Eq 1.22 Eq 1.25 Eq 6.22 Eq 6.23 Eq 6.24 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00 62,5 70 79 88 99 111 125 140 157 177 198 223 250 281 315 354 397 445 500 561 630 707 794 891 1000 1122 1260 1414 1587 1782 2000 2245 2520 2828 3175 3564 4000 4490 5040 5657 6350 7127 8000 8980 10079 11314 12699 14254 16000 Absorption Frequency (Hz) Normal incidence absorption Absorber against panel Absorber against backing No Air Gap a/ b/ c/ • The absorption properties depend also on the position and thickness of the material
  68. 68. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  69. 69. Alexis Baskind Acoustics of Listening Rooms Room dimensions • Most important: a listening room (and the position of the loudspeakers) should have a symmetry axis! • It should be big – Room modes are lower in frequency and the modal density is bigger – Reflections do not arrive too early (to avoid a “boxy” sound) 100 m3 (it would correspond for example to 6m x 6m x 3m if it were rectangular) is the reference volume in the ITU-R BS.1116-1 recommendation Room Acoustics
  70. 70. Alexis Baskind Acoustics of Listening Rooms • A listening room should not be too dry – Unnatural sound – Tendency to add too much artificial reverberation in the mix – Need for a certain amount of short reverberation (typically 0.25 – 0.3 s) – Need for envelopment => late reflections • But it should not be too live as well – Lack of precision – Spectral effects (because of early reflections) Room Acoustics
  71. 71. Alexis Baskind Acoustics of Listening Rooms The ITU-R BS.1116-1 recommendation suggests that: • The reverberation time stays in the given limits: Room Acoustics RTm
  72. 72. Alexis Baskind Acoustics of Listening Rooms For mid and high frequencies (> 200 Hz) • There should not be flutter echoes => no parallel walls (otherwise put absorbers or diffusors) • The ceiling and the floor as well can create flutter echoes => ceiling should not be horizontal (otherwise put absorbers or diffusors) Room Acoustics
  73. 73. Alexis Baskind Acoustics of Listening Rooms • Too loud early reflections (< 15ms) entail comb- filtering and alteration of the stereo image • The ITU-R BS.1116-1 recommendation suggests that: “Early reflections caused by the boundary surfaces of the listening room, which reach the listening area during a time interval up to 15 ms after the direct sound, should be attenuated in the range 1-8 kHz by at least 10 dB relative to the direct sound.” Room Acoustics
  74. 74. Alexis Baskind Acoustics of Listening Rooms The fluctuations of the frequency responses are mostly determined by the early reflections (comb-filtering) Room Acoustics Influence of the early reflections Example: measurement of a listening room, frequency response for the direct sound only
  75. 75. Alexis Baskind Acoustics of Listening Rooms The fluctuations of the frequency responses are mostly determined by the early reflections (comb-filtering) Room Acoustics Influence of the early reflections Example: measurement of a listening room, frequency response for the first 1.3 ms
  76. 76. Alexis Baskind Acoustics of Listening Rooms The fluctuations of the frequency responses are mostly determined by the early reflections (comb-filtering) Room Acoustics Influence of the early reflections Example: measurement of a listening room, frequency response of the whole room response
  77. 77. Alexis Baskind Acoustics of Listening Rooms The ITU-R BS.1116-1 recommendation suggests that the frequency response stays in the given limits: Room Acoustics Frequency response
  78. 78. Alexis Baskind Example 1: LEDE • LEDE-design (“Live-End-Dead-End”), proposed in 1979, aims at reducing the early reflections while keeping enough late diffusion (for the envelopment) Room Acoustics (Source: F. Rumsey, Spatial Audio)
  79. 79. Alexis Baskind Example 2: RFZ • With RFZ-design („Reflection-free zone“), proposed in 1984, early reflections are not any more strongly absorbed but deviated from the zone around the sweet spot • Like with LEDE, the back wall is diffusive (and not absorbing), so that the room does not become to dry Room Acoustics
  80. 80. Alexis Baskind Outline 1. Time-Space perspective: Sound propagation in a room 2. Frequency-Space perspective: Room modes 3. Time-Frequency perspective 4. Room acoustics design 5. Room acoustics of listening rooms 6. Spatial hearing in a room Room Acoustics
  81. 81. Alexis Baskind Perception of distance • As explained above, the perceived distance to the sound source depends on: – The direct-to-reverberant ratio: the softer the direct sound with respect to reverberation, the farther the source is localized – The initial time delay gap: the smaller the ITDG, the farther the source is localized – The lateralness of the early reflections: the source is localized farther if the early reflections come from the front as if they come from the sides Room Acoustics
  82. 82. Alexis Baskind Perception of the room size • Human Hearing uses two cues to judge the size of a room: – The reverberation time is the major parameter – The time distribution of the early reflections are considered to provide extra cues, but only in extreme cases Room Acoustics A reverberant chamber is a small but very reverberant room. It’s meant to simulate big halls, and it works somehow well, even if the early reflections are “too” early
  83. 83. Alexis Baskind Clarity • The Clarity of a room for a given seat is the ability to understand the message (usually speech) driven by the source • Clarity is known to depend on three factors: – The quantity of early reflections after the echo threshold (typically 20-30 ms for percussions, 50-60 ms for speech, 80-100 ms for signals without clear transients): early echoes can heavily damage the clarity of the sound ! – The direct-to-reverberant ratio: reverberation can partly mask the direct sound and reduce clarity – Reflections in the direction of the source damage the clarity more than lateral reflections (see cocktail-party effect and comb filtering) Room Acoustics
  84. 84. Alexis Baskind Clarity • Examples (from David Griesinger) Room Acoustics • Dry speech – Note the sound is uncomfortably close • Mix of dry with early reflections at -5dB. – The mix has distance (depth), and is not muddy! – Note there is no apparent reverberation, just depth. • Same but with the reflections delayed 20ms at -5dB. – Note also that with the additional delay the reflections begin to be heard as discrete echos. • But the apparent distance remains the same. • Same but with the reflections delayed 50ms at -3dB – Now the sound is becoming garbled. These reflections are undesirable! – If the speech were faster it would be difficult to understand. • Same but with reflections delayed 150ms at -12dB – I also added a few reflections between 20 and 80ms at a level of -8dB to smooth the decay. – Note the strong hall sense, and the lack of muddiness.
  85. 85. Alexis Baskind Apparent Source Width • The Apparent Source width corresponds to the perceived size of the source • A point source in a non reverberant room will be perceived as very narrow (equivalent of a monophonic pan-potted sound) • The presence of early lateral reflections (before 80- 120ms) blurs the time and intensity cues and creates a (often pleasant) widening of the perceived source • The reflections have to be lateral to create this effect. Frontal reflections only modify the tone color Room Acoustics
  86. 86. Alexis Baskind Envelopment • Envelopment is the sensation of being surrounded by the diffuse field • This sensation corresponds to the proportion of late lateral reflections (after 100-150ms) Room Acoustics until ca. 100 ms: widening ca. 100-200 ms: Envelopment Perception of the room Time Perception of the source Soundpressure Direct sound Early reflections Late reverberation
  87. 87. Alexis Baskind Reverberation Timbre • The timbre of the reverberation („dark hall“, „warm room“, „bright stage“, etc.) depends on the ratio between reverberation times at low, mid and high frequencies: – For a „dark“ room, the reverberation time is relatively longer at low frequencies – For a „warm“ room, the reverberation time is relatively longer at low-mids than at low and high frequencies – A „bright“ room has similar reverberation times at low and high frequencies Room Acoustics

Visit https://alexisbaskind.net/teaching for a full interactive version of this course with sound and video material, as well as more courses and material. Course series: Fundamentals of acoustics for sound engineers and music producers Level: undergraduate (Bachelor) Language: English Revision: February 2020 To cite this course: Alexis Baskind, Room Acoustics course material, license: Creative Commons BY-NC-SA. Course content: 1. Time-Space perspective: Sound propagation in a room Raytracing, example of a rectangular room, evolution from free field to diffuse field, initial time delay gap (ITDG), direct sound, first reflections, late reverberation, exponential decay of the pressure, definition of the reverberation time, T60, T30, T20, Schroeder curve, critical distance, flutter echoes, diffusion, effect of distance, effect of room size 2. Frequency-Space perspective: Room modes Reminder: monodimensional standing waves, axial modes, tangential modes, oblique modes, eigenfrequencies, effect of room size on modal density, duration and bandwidth of modes, effect of absorption on modes, Schroeder Frequency 3. Time-Frequency perspective Early reflections, modes and diffuse reverberation in an unified time-frequency perspective, waterfall view 4. Room acoustics design prediction of the reverberation time, Sabine formula, frequency-dependent absorption, porous absorbers, effect of absorber’s thickness and air gap, resonant absorbers, membrane absorbers, Helmholtz absorbers 5. Room acoustics of listening rooms importance of symmetry, need for a sufficient room size and controlled reverberation time, recommended reverberation time, need for controlling the early reflections, LEDE design, RFZ design 6. Spatial hearing in a room perception of distance in a room, perception of the room size, clarity, apparent source width, envelopment, reverberation timbre

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