Fundamentals of Sound


Perceptual attributes of acoustic waves


Perceptual criteria for room acoustics
Acoustical and room construction / layout correlates
Architectural Acoustics

 Reflection / Reverberation / Diffusion Criteria:
    "Liveness;"  Warmth;  Brilliance;  Clarity;
     Intimacy;  Uniformity;  Smoothness
 Multidimensional Criteria
Spaciousness;  Freedom from noise;  Performer satisfaction
 Small Room Acoustics






Page based mainly on information from the following resources, which you are expected to visit


  • Concert Hall Acoustics
    Site produced by: Jessica Hall; Advisor: Prof. Lily Wang. University of Nebraska, Lincoln. (page currently under re-construction)

  • Concert Hall Acoustics
    Part of, an acoustics website by M Skålevik of Brekke & Strand Akustikk, Norway.

  • Auditorium Acoustics and Architectural Design (2nd ed.) (book .pdf)
    Barron, M. (2009). Auditorium Acoustics and Architectural Design (2nd Ed.). Spon Press (Routledge). Oxfordshire, UK. On-line (.pdf) version of Barron's book, exploring the acoustical characteristics of music performance spaces. Supported by over 40 detailed case studies and architectural drawings of 75 auditoria at a scale of 1:500, the survey of each auditorium type is completed with a discussion of current best practice to achieve optimum acoustics.



The environment in which sound waves are produced (e.g. rooms and other enclosed spaces) modifies the sounds that are heard or recorded.  Different types of rooms will impose different types of modifications, with no single room-type being able to provide appropriate listening context to all types of stimuli and listening. Watch: How architecture impacts music

The most important sound-modifying parameters of a sound environment are:

•  Overall room size and shape
•  Shape/texture of the reflecting surfaces
•  Location of critical reflecting surfaces relative to a sound source and the listeners, and
•  Absorption characteristics of the reflecting surface materials

Let us consider the example of the path, within a room, of a short percussive sound signal: 

Direct Sound
The shortest possible path from source to listener (or microphone) is a straight line, and the direct sound-wave traveling this path arrives first. 

It is followed shortly by several reflected waves from walls or ceiling.  The distance traveled for each reflecting path determines the delay
a) between reflections and the original/direct sound and b) among reflections. 

First and Early Reflections
Reflections arriving within approximately 50-100 ms after the direct sound-wave qualify as early reflections.  If they follow closely enough after/before one another, they are perceived as a unified acoustical event.
Early reflections with delays <~50ms (<~17m/56ft path difference between direct sound and early reflections) contribute to the overall perceived loudness and sense of spaciousness. If their level is comparable to the level of the direct sound they may "muddy/blur" the perception of the direct sound's attack portion, particularly for impulse signals.
Early reflections with delays >~50ms (>~17m/56ft path difference) may be perceived as distinct echoes (if their level is within 10dB from the direct sound) and are to be avoided in listening environments designed for musical performances.

Late/Diffused Reflections - Reverberation
After this event, we continue to receive sound waves from more and more different multiple-reflection paths.  Each individual contribution gets weaker as the number of reflections increases and they all arrive at slightly different times, merging together in a continuously decaying reverberant sound perceived as a stretching out and gradual decay of the original acoustic event.

For a sustained note (e.g. bowed string), the contribution of reflections builds up for some time after the arrival of the direct sound wave. Only after a time sufficient for many reflected waves to arrive and die out does the total sound approach a steady intensity level. 
When energy stops being supplied to the instrument, the direct sound stops first. For the reverberant sound to die out, it takes approximately as long as it did for it to build up.

Before continuing, see this table summarizing the relationship between spectral variables and verbal descriptors of timbre. The table addresses source signals and complements the discussion on reflection, reverberation, and diffraction that follows. [Vassilakis, P. (2009); Unpublished work]



Reflection / Reverberation / Diffusion Criteria
"Liveness;" Warmth; Brilliance; Clarity; Intimacy; Uniformity; Smoothness


1. Liveness - Loudness - Warmth vs. Brilliance

Reverberation is the perceptual manifestation of the way sound energy reflects and decays within an enclosed space.  Reverberation must have appropriate loudness relative to the original sound and smooth rates of attack (build-up) and decay (dying-out).

Reverberation is controlled by the size of the room and by the absorption/reflection characteristics of the walls, ceiling, and floor.
Strong reflections at low frequencies are responsible for warmth, and at high frequencies for brilliance.  Although it is hard to influence the reflection of low frequencies it is possible to decrease that of high frequencies and thus change the balance between ‘warmth’ and ‘brilliance’ (see also below). Placing carpets (or other soft materials) on the floor, ceiling, and/or walls, as well as filling up a room with people (or anything that increases the total surface and irregularity of a room) increases the absorption and diffused spread of high frequencies more than that of low frequencies.

The absorption coefficient, α, of a surface material is defined as the ratio of absorbed intensity over incident intensity.
Absorption unit: 1 Sabine (named after Wallace Sabine, widely recognized as the founder of the field of Architectural Acoustics).
1 Sabine provides the absorption of a 1m2 surface of a perfectly absorbing material (i.e. a=1 and placing this material on a wall would be equivalent to creating an opening of the same size).

Absorption coefficients - α - for some common materials can be found in the two tables below. What is the main difference between them? 
(see under the tables for the answer)

Material α

Plaster walls 0.01 - 0.03
Unpainted brickwork 0.02 - 0.05
Painted brickwork 0.01 - 0.02
3 mm plywood panel 0.01 - 0.02
6 mm cork sheet 0.1 - 0.2
6 mm porous rubber sheet 0.1 - 0.2
12 mm fiberboard on battens 0.3 - 0.4
25 mm wood wool cement on battens 0.6 - 0.07
50 mm slag wool or glass silk 0.8 - 0.9
12 mm acoustic belt 0.5 - 0.5
Hardwood 0.3
25 mm sprayed asbestos 0.6 - 0.7

The table to the right is more accurate. It better captures the fact that the absorption coefficient of a given material is different at different frequencies (standard absorption ratings provide coefficients for the frequencies, above).
It also reveals that for some materials, absorption increases with frequency while for others it decreases. In general (see here):
a) porous materials are high-frequency absorbers
b) flat, smooth, non porous materials and membranes are low frequency absorbers (depending on the combination of their mass, thickness, and elasticity)
c) cavities (e.g. Helmholtz resonators) can function as narrow-band absorbers, depending on their dimension/shape/materials.

A room's liveness or reverberance is characterized by the reverberation time of primarily the high and middle frequency ranges and is mainly determined by a room's volume and effective surface area.  Reverberance can be altered by changing the area and nature of absorbing materials that cover a room's surfaces, and its suitability depends on the nature of sound/music in the room.
A room with too short a reverb time may be classified as "dry" or "dead"  for a particular type of music, while one that is too "alive" or has too long a reverb time may be called "muddy" or "watery" for another.

Reverberation clearly increases the overall loudness of a sound.  The contribution of reverberation to loudness may be objectively measured in terms of the sound pressure level at a position in the hall, relative to the sound level of the same source in a free field (measured usually at a distance of 10m).  Similarly to absorption, the contribution of reverberation to loudness is frequency dependent, with the contribution at middle frequencies being the most important (why?).  Reverberation-related loudness is inversely proportional to total surface-area absorption in a space.

As discussed above, the reverb time of the low frequencies relative to that of the middle and high frequencies determines the degree of warmth or brilliance of the sound within a room.  For a nearly constant reverb time as a function of frequency, a room will be classified as "bright" or "brilliant". Long reverbs with excessive high frequency energy may be classified overly bright or "screetchy."
Increasing the relative reverb time of lower frequencies (< ~ 500Hz) increases the sense of warmth.  However, too long low-frequency reverb times are perceived as "muddiness".  In general, the reverb time is usually a little longer for frequencies below rather than above 500Hz, and most highly-regarded concert halls are classified as warm.

2. Clarity (often contrasted to 'fullness') & Intimacy

Each note should arrive to the listeners cleanly, crisply, and unobstructed, unless ‘obstruction’ is desirable (as, for example, in recording a musical event where room contributions or audience reactions are important to the resulting sound).  The clarity criterion is especially important if a room is used for speech as well as music, because the intelligibility of words depends directly on clarity of articulation. 
Clarity is sacrificed in a room with a lot of diffused reflections (e.g. a "muddy" room), a result that may be desirable for certain types of music (e.g. it may enhance slow passages of music from the romantic era).

Clarity is measured in terms of direct-to-reflected (reverberant) sound intensity ratio and can therefore be increased by increasing the level of the direct sound and/or decreasing the level of the reverberant sound.
Strong and unobstructed direct sound can be achieved by
a) getting all listeners (including microphones) as close to the stage as possible,
b) raising the stage, which may also be racked, and
c) placing the audience on a sloped surface or in balconies.
If every listener has a good unobstructed sight line, the acoustical clarity will, likely, also be good.

The greatest clarity can only be achieved by sacrificing reverberation. High reverberation results in rooms being perceived as "full" but, in the case of spoken word or fast, highly articulated musical passages, being perceived as unclear or "undefined."

Related to the perceptual criterion of clarity is the sense of intimacy portrayed when listeners are located closely to the sound source. The time between the arrival of the direct sound and the first reflection determines the listeners' perceived proximity to the performers.  An intimate feeling occurs when the time delay between direct sound and first reflections is 5-20ms.

3. Uniformity (Balance & Blend)

Listeners in all parts of a room should hear as nearly the same sound as possible; there should be no dead spots (i.e. no areas where no or almost no sound arrives) or areas with distinct spectral and therefore timbral coloring.  Instead, there should be uniform spatial distribution of both direct and reflected sound energy throughout the audience.

Uniformity in the direct sound corresponds to minimization of differences between the direct sound arriving at different places in a room. It can be enhanced by minimizing the distance between first and last rows in an auditorium (e.g., by using a shallow hall with several balconies).

Uniformity and diffusion of the reflected sound energy depend on the size and shape of a room's reflective surfaces. 
Concave walls are undesirable since they tend to focus sound rather than diffuse it. 
Rectangular rooms with plain flat walls are also undesirable because they make it possible for sound to bounce back and forth repeatedly over the same path, creating standing waves.  If standing waves are built-up in a room there will be some areas where the sound will be very soft (dead spots) and other areas where it will be very loud. 
Dead spots or sonic "shadows" may also be caused by physical obstructions or balcony openings and can be remedied through the use of fill-in loudspeakers.

Sound is more thoroughly mixed and distributed over rooms that have irregular shape, nonparallel walls, convex surfaces, and many protruding edges.  There should be small-, medium-, and large-scale structures, each one helping diffuse sounds with wavelengths comparable to the structures' size.

Sound coming from different locations on the stage should have balanced intensities and be well blended
Balance and blend problems are common for seats close to a wide stage and may be partially corrected by a low, irregularly shaped ceiling and appropriate onstage reflecting surfaces.

4. Smoothness (Freedom from echo)

Even though there will be repeated sound reflections off walls, under normal circumstances none of these should be perceived as a separate echo; all reflections must blend together smoothly and must die away smoothly with time.

A poorly placed concave surface or even a large, flat, hard surface may provide a particularly strong reflection more than 100ms after the direct sound (depending on room size).  This will be perceived as a distinct echo, which is usually undesirable.  If the reflected sound level is strong enough, even a delay of around 30 or 40ms can result in an unpleasant, rough perception.  To ensure that reflections blend together smoothly, successive time gaps between reflections must be kept under 30ms (time gaps between ~ 5 and 15ms contribute to a feeling of intimacy).
Since sound travels at ~0.34 m/ms, the above limit means that the first reflection path for every seat in a room should be < ~11m (~35 feet) longer than the direct path.  This may require careful placement of reflecting panels toward the front of an auditorium and the inclusion of sound diffusers of different sizes.



Multidimensional Criteria
Spaciousness; Freedom from noise; Performer satisfaction


1. Spaciousness (Listener envelopment and auditory source width)

Auditory impressions of space have two perceptual dimensions: Listener Envelopment (LE) and Auditory Source Width (ASW).

LE refers to the impression of being ‘bathed’ in sound from all sides, rather than feeling separated from the source. 
ASW describes how wide the sound source appears to the listener.

For effective LE and large ASW, early reflections should arrive not just from the front or back walls, but also from the ceiling and especially the sidewalls. Preferably, the sides and ceiling should not be completely leveled but should include enough level variation to provide several different early reflections, surrounding the listener with sound. The distinction between ASW and LE depends on the arrival time of lateral reflections. Early lateral reflections (within 80 ms of the direct sound) seem to affect ASW, while late lateral reflections (after 80 ms of the direct sound) seem to affect LE. In general, early reflections should arrive from all directions in order to give the listener a sense of envelopment.

Not all types of music require the same degree of LE. For example, organ music requires an extreme sense of envelopment, assisted by (occasionally inactive) pipes being placed above, behind, or to the side of the audience to mask the origin of the sound source. For other types of music, too much envelopment may be undesirable, as it can blur the aural image of the stage.

2. Freedom from background noise

Soft passages in the music should not be disturbed by noise outside or inside the auditorium (unless, again, such ‘noise’ is desirable).
Background noise may stem from many possible sources such as the heating, ventilation, and air-conditioning (HVAC) systems, other equipment in the room, the audience, exterior sources such as traffic or airplane noise, or neighboring spaces.
Calculation of background noise can be based on one of many available noise criteria methods and involves first measuring the sound noise levels in octave bands across a certain frequency range and comparing them to a series of 'accepted' noise level curves.

Substantial construction, double doors, and felt stripping for doors or windows are important in keeping unwanted sounds from entering a performance space.  Total background noise exceeding 45dB (with no audience present) makes a room unsatisfactory for musical performances that explore a relatively wide dynamic range.  Noise levels of ~ 30dB are considered acceptable.  Any standard less than ~ 20dB is difficult to achieve and of little noticeable benefit.

3. Performer satisfaction

The stage must be free from distracting echoes and at the same time provide enough enclosure for performers in a group to feel that they are in good communication with one another.

A single strong echo from the wall behind the performers is in general undesirable.  A blend of many reflections should return to the stage strongly enough and with uniform, short decay (shorter than the shortest distance between notes), to give the performer some sense of what the audience is listening.  A good stage usually has a more-or-less shell-type shape to enable the members of a group to hear one another as well as to help project the sound out to the audience. 
The stage should not have hard parallel sidewalls, which may cause flutter echo (the sound of a sharp percussive tone bouncing back and forth repeatedly).  Flutter echo also indicates that part of the sound energy is trapped on stage not reaching its intended audience.
Ensembles in which members are separated by more than approximately 5 meters may easily lose synchronicity and usually need visual cues (e.g. a conductor) to remain playing in time.


The majority of the above criteria are most important when we rely on the natural acoustics of an auditorium.  Many musical and other sonic events depend on powerful electronic amplification to create their characteristic sound in a wide variety of rooms that would be entirely unsatisfactory for non-amplified sound.  Nevertheless, the discussed issues of reflection, absorption, and diffusion remain.

The above criteria also represent general guidelines. Specific goals may be quite different depending on the kind of sound/music to be listened to and/or recorded.  One example is the desired mix of direct sound, early reflections, and reverberation.  Speech is at one extreme; clarity is the overriding criterion and very little reverberation is desired.  At the other extreme, certain pieces for pipe organ call for a sound so full that the reverberation may even outweigh the direct sound and with one sonic event often bleeding into the next.

The majority of enclosed spaces in which we find ourselves recording do not meet most of the criteria discussed.  This means that the position of listeners or microphones relative to the sound sources greatly influences the quality of the experienced/recorded sound.



Small Room Acoustics


Slides Decks
(large files with embedded videos)

1) Wave Behavior Refresher
(reflection, diffraction, etc.)

2) Reverberation / Sound Fields

3) Room Modes

4) Studio Acoustics

5) [Optional] Architectural Acoustics




Loyola Marymount University - School of Film & Television