An Auditory Illusion of Proximity of the Source Induced by Sonic Crystals

Abstract

In this work we report an illusion of proximity of a sound source created by a sonic crystal placed between the source and a listener. This effect seems, at first, paradoxical to naïve listeners since the sonic crystal is an obstacle formed by almost densely packed cylindrical scatterers. Even when the singular acoustical properties of these periodic composite materials have been studied extensively (including band gaps, deaf bands, negative refraction, and birrefringence), the possible perceptual effects remain unexplored. The illusion reported here is studied through acoustical measurements and a psychophysical experiment. The results of the acoustical measurements showed that, for a certain frequency range and region in space where the focusing phenomenon takes place, the sonic crystal induces substantial increases in binaural intensity, direct-to-reverberant energy ratio and interaural cross-correlation values, all cues involved in the auditory perception of distance. Consistently, the results of the psychophysical experiment revealed that the presence of the sonic crystal between the sound source and the listener produces a significant reduction of the perceived relative distance to the sound source.

Fig 1. Experimental configuration employed in the binaural recordings and band diagram of the sonic crystal slab used on the experiments.

(a) Realistic 3D rendering of the sonic crystal slab, loudspeaker and one of the listener positions employed in the binaural recordings. (b) Schematic representation of the experimental setup and sound intensity map (for a noise band with central frequency 1.12 kHz, 1/3 octave bandwidth). The sound source position is shown by a loudspeaker icon on the top of the figure. For the recordings, the dummy head and the experimental subjects were placed on the black dots along the central line (a-d). The red and blue rays correspond to a geometric acoustics representation of the focusing by negative refraction. (c) Band diagram corresponding to the sonic crystal slab used in the experiments. The gray area on the band diagram delimitates a negative refraction band (central frequency 1.12 kHz, 1/3 octave bandwidth). The monaural intensity of this noise band was measured using a sound meter level and it is plotted as a colormap on panel (b). The insets is the first reduced Brillouin zone of the reciprocal space showing the points X, J and Γ that defines the directions of the wave vector in the reciprocal space (e.g. the Γ−X direction corresponds to the normal incidence in the direct space).

Fig 2. Binaural intensity BI (left), interaural cross-correlation IACC (center) and direct to reverberant ratio DRR (right) for one-third-octave noise bands.

The top plots corresponds to the recordings made with the sonic crystal slab between the source and the receiver (condition with-SC) and the bottom plots to the room response (condition without-SC). The results were obtained along the symmetry axis with a perpendicular distance to the slab (a-d). The results for the BI and DRR are expressed in dB, while the IACC is plotted in non-dimensional units. The dashed black frame delimits the focalization region defined in Eq 1.

Fig 3. Positive shifts for each stimuli set (1–5) as a function of frequency and position.

Proportion of positive shifts classified into three cases according to their confidence limits (α = 0.05) as a function of frequency, position and stimuli set for group A (top) and group B (bottom). The white region corresponds to statistically significant negative shifts; the gray region corresponds to ambiguous cases where no shift occurred; and the red region corresponds to statistically significant positive shifts, meaning that the source is consistently perceived farther for the without-SC condition.

Fig 4. Effect of focusing on the response.

Individual mean and standard errors of the effect of focusing on the response, separated by factors focusing and stimuli set for (a) group A and (b) group B. Responses under (non-) FOC refers to stimuli (not) belonging to the focusing region defined in Eq 1. The central dashed line indicates the chance level of the response.

Fig 5. Means of the effect of focusing on the response.

Means of the effect of the factor focusing across subjects separated by stimuli set for (a) group A and (b) group B.