• Sound Propagation in an Auditorium
• Direct Sound and Early Reflections
• Late Reflections
• Calculating Reverberation Time
• Air Absorption
• Criteria for Good Acoustics
• Background Noise
• Room Resonances

Auditorium Acoustics

The room in which we listen to sound has an important influence on what we hear. This section will identify some of the principal means currently available for judging the quality of an auditorium. While we have a variety of methods and criteria for the evaluation of an existing acoustic space, the design of such a space from a specified characteristic is still relatively difficult.

Sound Propagation in an Auditorium

• Sound waves travel at about 345 meters/second, so that the sound coming directly from a source within an auditorium will generally reach a listener after a time of anywhere from 0.01 to 0.2 seconds.

• Shortly after the arrival of the direct sound, a series of semi-distinct reflections from various reflecting surfaces (walls and ceiling) will reach the listener. These early reflections typically will occur within about 50 milliseconds.

• The reflections which reach the listener after the early reflections are typically of lower amplitude and very closely spaced in time. These reflections merge into what is called the reverberant sound or late reflections.

• If the source emits a continuous sound, the reverberant sound builds up until it reaches an equilibrium level. When the sound stops, the sound level decreases at a more or less constant rate until it reaches inaudibility.

• For impulsive sounds, the reverberant sound begins to decay immediately.

Direct Sound and Early Reflections

• Direct sound will decrease by 6 dB for each doubling of distance propagated.

• Our auditory system will determine the direction of a sound source from the direct sounds reaching the ear.

• Early reflections which arrive within about 35 milliseconds are not heard as separate from the direct sounds. Rather, they tend to reinforce the direct sound.

• The source is perceived to be in the direction from which the first sound arrives provided that (1) successive sounds arrive within about 35 milliseconds, (2) the successive sounds have spectra and time envelopes reasonably similar to the first sound, and (3) the successive sounds are not too much louder than the first. This is referred to as the precedence effect.

• From a study by Leo Beranek (1962), a concert hall is considered ``intimate'' if the delay time between the direct and first reflected sound is less than 20 milliseconds.

• First reflections usually arrive from the nearest side wall or from the ceiling for those seated in the center.

• Reflections from the ceiling or overhead reflectors are not as perceptually desireable as those from side walls.

Late Reflections

• During a continuous sound, the reverberant sound level is reached when the rate at which energy is supplied by the source is equal to the rate at which sound is absorbed by the room and its contents.

• Too much reverberant sound will result in loss of clarity.

• In a bare room, where all surfaces absorb the same fraction of the sound that reaches them, the theoretical reverberation time is proportional to the ratio of volume to surface area.

• Reverberation time is typically defined as the time required for the sound level to decrease by 60 dB (or $T_{60}$).

Calculating Reverberation Time

• When expressed in units of cubic and square meters, the reverberation time is given by RT = $0.161 V/A$, where $V$ is the volume of the room and $A$ is the effective ``total absorption'' area.

• The ``total absorption'' area is calculated as the sum of all surface areas in the room, each multiplied by its respective absorption coefficient.

Air Absorption

• Air contributes a substantial amount to the absorption of high frequency sound.

• Taking account of air absorption, RT = 0.161 $V/(A + mV)$, where $m$ is a constant which varies with air temperature, humidity, and frequency.

Criteria for Good Acoustics

• Optimum reverberation time is a compromise between clarity (requiring short reverberation time), sound intensity (requiring a high reverberant level), and liveness (requiring a long reverberation time).

• The optimum reverberation time of an auditorium is dependent on the use for which it is designed.

• Reflected sound arriving from the sides seems to be important to the overall reverberance of the room.

• Important subjective attributes of concert hall acoustics include intimacy, liveness, warmth, loudness of direct sound, reverberant sound level, definition or clarity, diffusion or uniformity, balance and blend, ensemble, and freedom from noise.

• In addition to the attributes above, spatial impression and early decay time are important. The spatial impression is dependent on contributions to the early reflections from above and especially from the sides. The initial rate of decay of reverberation is apparently more perceptually important than the total reverberation time.

• Echoes, flutter echoes, sound focusing, sound shadows, and background noise should be avoided in an auditorium design.

• The greater the early decay time (up to two seconds), the greater the preference for the concert hall. Above two seconds, the trend it reversed.

• Narrow halls are generally preferred to wide ones.

• Preference is shown for halls having a high ``binaural dissimilarity''.

• Less ``definition'' is preferred. Definition represents the ratio of energy in the first 50 milliseconds to the total energy.

Background Noise

• Concert halls should meet at least the NC-20 curve and preferably the NC-15 curve (see Figure 23.9 on pg. 471 of Rossing).

Room Resonances

• For very simple geometries, it is sometimes possible to obtain an analytic expression describing the resonance frequencies of a room.

• The resonances in a rectangular box with dimensions $a, b$, and $c$ and without damping are $f_{lmn} = \frac{v}{2} \sqrt{ (l/a)^{2} + (m/b)^{2} + (n/c)^{2}}$, where $v$ is the speed of sound and $l, m$, and $n$ are integers.