Fundamentals In Acoustics & Architectural Design

1. Fundamental Physical Acoustics

Examples:
Frequency = 113 Hz ý Wavelength = 10 ft = 3.048 m
Frequency = 11'300 Hz ý Wavelength = 0.1 ft = 3.048 cm
Sound Waves travel approx. 1 ft (30 cm) in 1 Millisecond

2. Modal Response - Internal Room Acoustics without Electroacoustical Equipment

Every longitudinal room dimension supports a specific wavelength and therefore a specific frequency. This phenomena is called "standing wave", "eigentones" or "axial mode".

In a three-dimensional rectangular room, three fundamental eigenton frequencies will be present, with each of the fundamental frequencies also generating even harmonics (multiples of the fundamental frequency). An acoustical design goal must be the correct distribution of these fundamental and harmonic frequencies over the frequency spectrum. Certain room ratio values (proportion of length to width to height) are less preferrable than others.

An ideal room ratio value will

1. distribute the axial mode frequencies evenly over the spectrum and therefore prevent a buildup at certain frequencies, and
2. result in a constantly increasing number of axial modes per frequency band with increasing frequency (in contrast to a decreasing number of axial modes per frequency band with increasing frequency).
   

3. Speaker Boundary Interference Response - Internal Room Acoustics with Electroacoustical Equipment

At low frequencies every speaker radiates its acoustical energy in an omnidirectional pattern, that means: to all sides, even towards the back. The radiated acoustical energy will be reflected from the side- and backwalls, ceiling and floor and eventually combine with the direct sound. The reflected sound has a longer travel path and therefore arrives at the listening position slightly later in time as the direct sound. This results in frequency-dependent additive or subtractive interference, which is audible as comb-filtering effects (basically the elimination of certain frequencies). An acoustical design goal must be the correct placement of the speaker systems in respect to the surrounding walls to prevent excessive interference effects.

Two design approaches have been proven to give acceptable results:

1. careful calculation and/or computer simulation of the speaker boundary interferences to determine optimal speaker placement, or
2. flush-mounting the speaker cabinets against a wall, which results in approx. zero travel path difference between direct sound and reflected sound.

4. Reflections and RT60 Reverberation Time

It has been shown that the subjective listening experience, the sonic quality and the speech intelligibility are heavily dependent on the reverberation characteristics in a room. Reverberation consists of many direct reflections off the room's boundaries and objects and a diffuse reverberation field where the reflections are so dense that they are no longer audible as separate elements.

The commonly used parameter "RT60 Decay Time" measures the time necessary for a 60 dB decay in sound pressure level and is often expressed as a function of frequency. Scientific research has defined optimal Decay Times for certain room volumes and purposes. Making the room's RT60 Decay Time conform to the recommended values must be an acoustical design goal. Of equal importance is a uniformity of the RT60 values throughout various octave bands, e.g. ± 15% octave to octave comparative differences.

5. Example

Surround Sound Listening Room, "Good" Room Dimensions:
Length x: 5.13 m = 16.83 ft
Width y: 4.14 m = 13.58 ft
Height z: 2.59 m = 8.5 ft

Fundamental Room Modes 3D Graph:
(dark areas: high pressure, light areas: low pressure)

 

Distribution of Eigentones Graph:

Speaker Position Iteration Graph
for optimized Speaker Boundary Interference Response:

 

Raytrace Simulation
with increasing number of displayed reflections:

 

(All graphs in paragraph 5 are created using Acoustic-X Software by Pilchner-Schoustal, Canada)