The overall result of this diffraction grating technique is that the single sharp hard wall reflection is splintered into a set of 3 to 4 lower level reflections whose strength is about 10dB down. The splintered reflections are distributed out in time at 1/3 ms intervals and are within 3dB of each other. A balance has been struck in the dispersion of sound between the higher frequency, diffracting edge effects distributed absorption.

As a basis for comparison, recall the strength of a reflection off a 2” high density fiberglass. About 28dB of cut compared to the hard surface reflection is produced by this ever-so-common flat wall “acoustic treatment” for sound rooms.

The overall strength (Ld) of a multiple reflection signal is determined by the mean signal level (Lo), the number of signals level (Ln) and the fraction of time signal level (Lt).

Ld = Lo + Ln + Lt where Ln = 10LogN and Lt = 10Log (L1 + L2 + . . . ) / T

The perpendicular reflection off a hard surface was split into three reflections (N=3) each some 12dB below the single hard surface reflection strength (Lo= -12). The time width of each reflection was 0.15ms, 0.2ms, and 0.15ms over a (T=1.2ms) period. The perceived strength of this composite is calculated:

Ld = - 12 + 10Log3 + 10Log((0.15 + 0.2 + 0.15) / 1.2) = - 12 + 4.2 – 3 = - 10.8dB

The diffraction grating reflection is 10.8dB down from the hardwall bounce. It is spread out in time by a factor of 10.

The oblique reflection off the grating produced 4 spikes each down 9dB and spread over a 1.8ms time smear. The discrete reflections are 0.2, 0.1, 0.1 and 0.15ms long. The resulting splintered reflection has a calculated level:

Ld = - 9 + 10Log4 + 10Log(0.2 + 0.1 + 0.15) / 1.8 = - 9 + 6 – 5.1 = - 8.1dB

The oblique, angled reflection off the absorption grating is down 8.1dB compared to the hard wall bounce and is spread out over time by a factor of 15.

The most general diffraction grating is the Fresnel which allows for a spherical wavefront, the source being near the grating. A subclass is the Fraunhoffer diffraction, which requires parallel wave fronts. The absorptive diffraction gratings presented here are of the complex, Fresnel type. The sound source in small rooms is necessarily close to the diffraction grating and Fresnel diffraction occurs.

5.0A shows test positions for a 4 x 8 sheet of plywood in the open, with and without a grid of the 1/2 round sound traps. The speaker is at 8 feet and mic positions are every 5.6 degrees on a 5 foot radius about the center of the panel (14).

5.1A and 5.1B (see below) show the ETC and EFC (Energy Frequency Curve) of the flat panel for perpendicular reflection. The ETC is 6dB per division with a 30ms window. The reflection is 12 feet behind the direct signal and down 15dB, due of course to the expansion of the wavefront (the mic faces the panel, giving the reflection a small directional boost). The frequency scale (B) is linear, to see comb effects. An unimpressive, but realistic speaker frequency response is seen.

5.1C and 5.1D (see below) show the diffraction grating effect. Notice the early double peak return off the reflectors of the center trap and the pair aside. The 1.1ms time difference between the first reflection and the surface reflection produces a 1/1.1 sec or 900Hz comb effect, characteristic of diffraction gratings.

5.1E and 5.1F (see below) are the 32 frequency sweeps at 5.6 degree intervals that compare the smooth, specular reflection (E) with the very irregular, diffraction grid reflection (F), similar to that of 5.1D. The frequency sweep is 200 to 8K, linear scale. Throughout the angles measured, dramatic diffraction grating effects are obvious.

The following is a set of polar plots taken at 5.6 degree intervals at specific frequencies. Data compares specular reflection to diffraction grating reflection of a spherical wavefront. Each plot is normalized to the strength of the reflection, perpendicular to the panel. Absolute levels are not displayed. The lobing near the 90 degree axis is erroneous, due to the direct signal leaking into the time window that is centered on the reflection.

Conclusion

We have illustrated methods by which a specific type of acoustic signature can be developed. It is characterized by the direct signal being immediately followed by a dense group of signals that rapidly decay out in time. This timewise signature is objectively distinct but that alone provides insufficient basis upon which to draw conclusions. The content of the trailing signal group remains to be resolved and its impact on the direct signal established.

The direct signal is a voice which can be colored by lower level signals that are both derived from the direct signal and received by the listener within 10ms following the direct signal. Reflected sound is obviously a signal derived from the incident sounds, correlation between the two is very high. The reflected signal may not have the same spectral content as the incident sound, depending on the absorption characteristics of the reflecting surface. The direct signal can be colored by spectral characteristics of its nearby reflections.

An instrument has directional properties in the sound field it produces. Its total sound is desired to be presented to the mic. Acoustical containment resulting in multiple reflections is a means by which the divergent components of the instrument’s sound field become redirected to pass by and be captured by the recording mic. In order for the multiple reflections to compliment and develop the voice of the instrument, they must fill the first 10ms time window. A small room is in order as the reflections are too time delayed in larger rooms.

There are two very different types of sound dispersive reflecting surfaces. The absorptive reflection method is signal coherent while the resonance reflection systems are signal incoherent. By definition the resonant reflection panels available today ought not to be able to faithfully develop the voice of an instrument. Both reflecting systems can produce comparable ETC records that look healthy but the quality of coherence or incoherence in the diffuse reflections is the issue. Incoherent diffuse early reflections should create distracting room ambience effects that mask the presence of the instrument’s voice. Collection of instrumental ambience requires retention of coherent, diffuse reflections that have good correlation to the direct signal. There remains both subjective and objective exploratory work to be done in the area of coherent vs. incoherent diffuse early reflections.

Epilogue

There once was a great singer who was accompanied by an excellent local choir. They were quite successful and hired an agent to schedule a world tour. This fella was very creative and decided the choir needed a more worldly air. He proceeded to thank, then discharge each of the local choir members. He replaced them with singers from many foreign countries. Each was to sing in their own native tongue. With this complete, the great singer and his newly formed entourage left on tour. They were know as the “Choir of Babbel” and were never heard of again.