Golden Ratio Concept in Acoustic Design

The "golden ratio" of the slot centers in the described acoustic paneling plays a critical role in optimizing frequency dispersion, reducing echo, and balancing sound reflections. Here's a detailed understanding:

Golden Ratio Concept in Slot Design

• The "golden ratio" refers to a mathematical proportion often found in nature, art, and architecture, approximated as 1.618.
• In the context of the acoustic paneling:
• The slot centers follow the proportions of the cube root of 2 (≈ 1.26, 1.59, 2.00).
• This results in irregularly spaced slots, which avoid the resonance and interference issues associated with regularly spaced slots (as seen in earlier designs like Devatone panels).

What the Slot Centers Provide

1. Frequency Dispersion Across a Broad Spectrum:

   • The slot spacing ensures that sound waves of various frequencies encounter different reflective and absorptive properties.

   • Specific frequencies interact differently with the slots, minimizing the chance of standing waves or resonances.

   • Calculated slot centers correspond to key frequencies:

     • 53,66 and 84 mm centers relate to sound wavelengths based on the speed of sound ( c = 344 m/s ). Using the wavelength formula λ = f c​, we find the following:

     Slot Center (mm)	Approximate Frequency (Hz)
     53	6.49 kHz
     66	5.21 kHz
     84	4.10 kHz

     These frequencies correspond to critical ranges for speech intelligibility and high-frequency noise like children’s chatter.

   • Flutter Echo Reduction:

     • Irregular slot spacing breaks up parallel soundwave paths, dispersing energy rather than allowing repetitive reflection between parallel surfaces.
     • Reducing flutter echoes enhances clarity and avoids harsh sound reflections.

   • Scattering of High-Frequency Sounds:

     • High frequencies (shorter wavelengths) are scattered effectively by the slot depth of 15 mm.
     • A 15 mm slot depth approximates a quarter-wavelength interaction at λ/4=60mm, corresponding to 5.5kHz, ensuring effective dispersion at this and higher frequencies

   • Retention of Mid-Frequencies for Room Liveliness:

     • The slots allow partial reflections of mid-frequency sounds (300–500 Hz), important for preserving the natural sound characteristics of singing and speech.
     • This balance prevents the room from sounding too “dead.”

   • Randomized Scattering:

     • By avoiding uniform slot placement, the panels scatter sound in multiple directions, creating a more even sound field within the room.
     • This is crucial for minimizing “hot spots” of amplified sound or dead zones.

Benefits of Using the Golden Ratio in Panel Design

1. Improved Acoustic Balance:
   • The golden ratio spacing avoids periodicity, which would otherwise amplify certain frequencies and attenuate others.
   • This leads to a smoother frequency response in the room.
2. Aesthetic and Functional Harmony:
   • The irregular slot spacing not only contributes to acoustics but also provides a visually pleasing, non-repetitive design.
3. Compatibility with Speech and Singing:
   • High-frequency noise from children or equipment is scattered, while mid-range frequencies critical for speech and singing are retained, supporting both clarity and "liveliness."

Conclusion

The use of golden ratio slot spacing in the paneling design is an intelligent acoustic solution that diffuses sound effectively across a range of frequencies. It avoids the pitfalls of earlier designs by minimizing standing waves and flutter echoes, dispersing high frequencies, and maintaining mid-frequency reflections for a balanced acoustic environment. This approach creates a harmonious blend of absorption and reflection, making the space acoustically optimized for both speech and singing.