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Introduction to Alternating Binary Frequency diffusers

In modern studio design acoustic diffusers are used to control wall reflections and create a smoothed sound environment to make it easier for the mixing engineer to judge the true sound of a recording. A common method to define the size of the wells is the QRD-Algorithm leading to a so called Schröder-diffuser. Here a different method is used.

ABD - Sound Treatment

While most known diffuser designs focus one particular frequency we use in fact four of them in our first approach. Starting with a value of 80cm for both width and depth of the diffuser the basic frequency thus results in 682 Hz. The next 3 octaves are used too and are superimposed with alternating sign. This leads to the following wave shape consisting of 16 wells:

-1 -1 -1 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 +1 +1 +1 (80)
+1 +1 +1 +1 -1 -1 -1 -1 +1 +1 +1 +1 -1 -1 -1 -1 (40)
-1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 (20)
+1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 (10)

The values of the frequencies are summed up using the corresponding depth of 80cm (low), 40cm, 20cm, 10cm (high) and by adding 85 to achieve suitable lengths:

 -40 -40 -40 -40 -40 -40 -40 -40 40 40 40 40 40 40 40 40 20 20 20 20 -20 -20 -20 -20 20 20 20 20 -20 -20 -20 -20 -10 -10 10 10 -10 -10 10 10 -10 -10 10 10 -10 -10 10 10 5 -5 5 -5 5 -5 5 -5 5 -5 5 -5 5 -5 5 -5 -25 -35 -5 -15 -65 -75 -45 -55 55 45 75 65 15 5 35 25 60 50 80 70 20 10 40 30 140 130 160 150 100 90 120 110

A 1D acoustic diffuser using ABF-method for 682Hz (80 cm)

To clarify the function of the ABF-diffuser, a detailed look at the frequencies is necessary. The optical shape represents the acoustic effect which can be expected from waves with frequency significantly higher than the highest design frequency. The subsequent image gives an impression, how the diffuser appears for the highest design frequency. The shape of the effective diffuser which is smoothed is shown as the summed value in violet. The resulting residue period is shown yellow giving an impression of the scattering direction when disregarding corner effects. From the view of the high frequency, the scattering works in +/-45 degrees for a 90 degrees wave, because of the wells' size which perfectly meet the period.

Effective shape for the double frequency:

Effective shape for the 3rd (lowest) frequency:

Design

Conclusion and Summary

Binary numbers with alternating signs can be used to obtain an alternative kind of sound diffusers.

See the former article about APV-diffusers