Understanding how sound propagates in different environments is crucial for optimizing audio quality, particularly in rectangular rooms. According to the principles outlined in Everest, sound waves behave differently based on their frequencies and the physical dimensions of the room. This article explores the division of the audio spectrum into distinct regions based on sound propagation characteristics in parallelepiped-shaped environments.
Room Dimensions and Frequency Characteristics
In a parallelepiped room, sound waves interact with three pairs of parallel walls. The room can be defined using three axes:
- X-axis: Length (the longest axis)
- Y-axis: Width (the intermediate axis)
- Z-axis: Height (the shortest axis)
For example, let’s consider a room with dimensions:
- Length (X) = 5 m
- Width (Y) = 4 m
- Height (Z) = 3 m
The audio spectrum can be divided into various frequency regions:
- Sub-bass Frequencies: Below 34 Hz
- Bass Frequencies: Omnidirectional frequencies centered around 187.5 Hz
- Mid Frequencies: Hybrid frequencies that fall within a specific range
- High Frequencies: Directional frequencies that can be reflected or diffused
Where ( c ) is the speed of sound (approximately 340 m/s) and ( L ) is the maximum room dimension. For a room with the longest axis being 5 m:
This frequency represents the lowest resonant frequency in the room due to the longest open tube (X-axis).
Avoiding Undesirable Resonances
To avoid undesirable resonance patterns (denoted as Region A) where certain frequencies cannot resonate due to excessive wavelength, we impose the condition:
Thus, to support the entire audio spectrum from 16 Hz upwards, the longest axis (X) should exceed 10 m.
To ensure even distribution of standing waves without creating harmonics that overlap across all three axes, it is advisable to:
- Avoid equal or multiple dimensions.
- Avoid excessively different dimensions.
- Consult pre-calculated proportionality triplets.
- Use tools such as the AMK acoustics calculator to determine ideal room dimensions.
Regions of Resonance
sub low (omni) mid (omni/direct) High (direct)
- Region B: This includes ambient resonances of the room, represented by standing waves that are omnidirectional. In this region, sound waves can be perceived more prominently at antinodes (areas of maximum amplitude) such as walls and less at nodes (areas of minimal amplitude). Proper placement of sources, listeners, and traps is crucial, with sources and listeners positioned away from antinodes and traps placed at those locations for optimal absorption.
- Region C: This covers mid frequencies (two octaves) which are hybrid in nature. These frequencies do not adhere to a specific physical model, instead displaying characteristics of both standing waves and direct sound propagation. The first octave tends to show stronger resonances at antinodes, while the second octave exhibits more directionality.
- Region D: This region encompasses high frequencies with wavelengths significantly smaller than the room dimensions. These frequencies propagate directionally and are influenced by geometric acoustics principles, including reflection, diffusion, refraction, and diffraction.
Reverberation Time and Room Volume
The reverberation time (RT60), defined as the time taken for sound to decay by 60 dB, is given by the formula:
The upper frequency boundary of Region B is inversely proportional to the room volume ( V ) and directly proportional to the reverberation time ( RT60 ).
Conclusion
In conclusion, understanding the division of the audio spectrum and its interaction with room dimensions is essential for achieving optimal sound quality. By carefully considering the physical properties of a space and the placement of sound sources, listeners, and acoustic treatments, one can create an environment conducive to balanced sound reproduction.
For more detailed guidelines on ideal reverberation times and room dimensions, resources like Everest and tools such as the AMK acoustics calculator are invaluable.