Background on hearing¶

Auditory localisation¶

The auditory system is able, even in the absence of visual cues to derive a representation of the world thanks to its two sensors, the ears. The location of a sound source relative to the listener’s head can be described in terms of azimuth, elevation and distance.

Localisation in azimuth is mainly attributed to a binaural processing of acoustic cues based on time and intensity differences between the ears. Localisation in elevation is explained by the use of monaural cues although these cues also play a role in azimuth localisation. Localisation in distance can be determined from various acoustic cues related to the transmission of sound over distance, such as intensity and spectral content, and to the effects of acoustic reflections, such as interaural coherence and reverberant tails.

Localisation in azimuth¶

The duplex theory¶

[Ray76] attempted to account for localisation in azimuth in terms of interaural difference cues. He appreciated that when a sound is presented from the side, the listener’s head interrupts the path from the source to the opposite ear. The result is a difference in pressure between the closest ear (ipsilateral) and the farthest ear (contralateral) known as ILD. The relative difference will increase with frequency. However, for sources below $1000$ Hz, because the sound wavelength will be several times larger than the head, the head does not present a significant obstacle. Rayleigh pointed out that at these low frequencies, the ILD between the two ears would consequently be too small to be perceptible. [Ray07] demonstrated that humans are also sensitive to the ITD of low frequency pure tones. ITD reflect the difference in path distance to each ear when sound source is located to one side (see Fig. 1). However Rayleigh pointed out that, for a pure tone, the azimuth corresponding to a given ITD is ambiguous if the tone’s wavelength is less than the width of the of the head. For pure tones, therefore, ITD are effective for frequencies whose wavelengths are well below about $20~cm$, whereas, ILD are effective for frequencies whose wavelengths are well above $20~cm$. This two-mechanism account of sound localisation in azimuth became known as the duplex theory.

Fig. 2 Representation of the binaural cues ITD and ILD (After [Dan11]). Representation of Interaural time and intensity differences for a monochromatic sound sound.

The duplex theory was supported by several studies such as [SN36], who found a minimum in accuracy for pure-tone localisation at around $3000~Hz$ ($\sim{11}~cm$). [STFJ55] found a minimum around $1500~Hz$ ($\sim{23}~cm$). These results suggest that there is a range between $1500$ and $3000 Hz$ where the wavelength is too high to provide adequate ILD. At low frequencies, where the wavelength is important compared to the radius head, the sound wave is reflected to a negligible degree, meaning that the ILD will be close to $0$. It should be noted, however, that this is only true for a source beyond about $1~m$ where the wave can be treated as planar. Close to the head, the wave front will be spherical and thus subject to the inverse-square relationship between sound intensity and distance, which will have the same effect at all frequencies. The difference in path distance to each ear can thus result in a significant difference in intensity between the two ears, even if no head shadowing occurs [SCSK00].

Limitation of the binaural cues¶

ITD and ILD depend on both frequency and elevation. [Wal39] described a form of geometrical locus which has the shape of a cone centred on the interaural axis and corresponding to an infinite number of positions for which the ITD and ILD are roughly constant. This locus id known as the “cone of confusion” [WS54] (see Fig. 3). Because many positions on these cones surfaces can correspond to the same pairing of ITD and ILD, ambiguities in localisation occur, even within the horizontal plane, resulting in front/back errors. [You31] showed that head movement can compensate for the lack of pinnae in localisation. This was confirmed later on by [FF68] who used a broadband noise pulse and subjects were asked the position of the source according to several conditions such as head restrained of free and with their own pinnae, an artificial pinnae or no pinnae. His finding was that head movements brought in all conditions a very good disambiguation of the source position. [Wal40] introduced a general description of the nature of head movements during localisation tasks and pointed out the need for dynamic cues for localisation disambiguation. This was confirmed by [Bur58] who compared front/back errors with clamped or free head and with or without covering one or two ears using a noise (per octave band). His conclusions were that disambiguation was almost complete when the head was free. The disambiguation slightly decreased when using noise between $800$ and $2400~Hz$ and decreased dramatically at higher frequencies (above $2400~Hz$) when both ears are coveredfootnote{The ear away from the loudspeaker was covered with an earphone, which was fed with a wide band random noise in order to mask it at all frequencies.}.

Fig. 3 The cone of confusion. Identical values of ILD and ITD of two opposite points anywhere on the surface of the cone represented by the hyperbolia in two dimensions (After [Bla83]).

Localisation in elevation¶

The presented localisation cues, based on interaural differences are not sufficient to explain discrimination within the cones of confusion when the head is stationary. [Ray76] suggested that spectral cues may play a role. He later confirmed that distorting the acoustics of the pinna (by adding “little reflective flaps”) could adversely affect accuracy of front/back judgements ([Ray07]). Monaural cues (or spectral cues) can be used to explain discrimination of elevation because the sound is spectrally distorted by reflections and diffractions around the torso, shoulders, head and pinnae before reaching the ear in a way that is dependent on elevation. The resulting colorations for each ear of the source spectra, depending on both direction and frequency, provide a localisation cue. [LB02] showed that spectral cue has an impact in localisation in high frequencies and especially, by testing narrow band noises, they suggested that up-down localisation depend upon frequencies between $4$ and $16~kHz$ and front-back localisation on frequencies between $8$ and $16~kHz$. In case of remaining confusion about a source position, [WK99] showed that head movements will solve these ambiguities and support the Wallach’s theory ([Wal40][TR67]).

Fig. 4 Representation of main auditory cues used for localisation according to the frequency.

Localisation in distance¶

According to [Rum12], there is mainly $4$ cues in localisation in distance:

the inverse-square law of intensity.
direct to reverberant ratio.
small path differences between direct sound and reflections.
high frequencies attenuation.

Intensity¶

In the earliest studies, intensity was considered the primary acoustic cue to distance ([Tho92]). [Edw55] in two experiments using a metronome and the ticking of a clock. He measured that the JND in distance was about $20~\%$ of overall distance. For a stationary sound source in acoustic free field and emitting uniform spherical waves, the sound source intensity is related to distance from the sound source by an inverse square law. The intensity is related the distance $R$, from the source to the listener by a factor $\frac{1}{R^{2}}$. Since sound pressure is proportional to the square root of intensity, pressure obeys a $\frac{1}{R}$ relation.

Reverberation¶

In any environments with sound reflecting surfaces, the ratio of energy reaching a listener directly to energy reaching a listener after reflecting the surface contact varies systematically with distance. This cue is called the direct-to-reverberant energy ratio and decreases as distance between the listener and source increases. In rooms, change in direct-to-reverberant energy ratio is primarily due to the effect of the inverse-square law on the direct sound because the energy in the later part (all the reflection of an order $n > 0$) is relatively constant for varying source distance [Bla83].

Spectral shape¶

Under certain circumstances, sound source spectrum varies as a function of distance. At greater distance (above $15~m$ [Bla83]), the sound absorbing properties of air significantly modify the higher frequencies of the source. Moreover, these properties depend on environmental factors such as relative humidity or the temperature. [Ing53] suggested that at $40~\%$ of humidity, the attenuation peak was at $4000$~Hz and was about $6~dB$ every $100~m$. Some studies suggested that humans take advantage of binaural cues in their distance judgement. [Col68] showed that perceived distance varies when you cut off the high frequencies of an click stimulus. He tested several distances (from $2.5$ to $8.5~m$) and observed that for closer source the perceived distance increases when you remove high frequencies (above $7680~Hz$). For further sources, the perceived distance is roughly accurate. But these results are challenged by several other studies such as [Koe00][CTS68]

Todo

These last two articles need to be read more deeply.

Other factors in distance perception¶

Vision

is known to affect percept of auditory space, including perceived distance.

Familiarity

and prior information about the characteristics of a sound can significantly influence the auditory distance perception.

Dynamic cues¶

As we briefly explain above, localisation can be improved or remove disambiguation through head movements and hence dynamic cues changes either by a source movement or a listener’s movement.

For localisation of sound source in space, a listener naturally seeks to orientate his head toward this one and face it. It is in that position that sounds are localise the most accurately. However, [PN97a] suggested that an improvement of localisation accuracy in azimuth can be obtained by dynamic cues even if the sound is too short for the listener to face it. This result showed that localisation cues called “dynamic” introduced by head movements contribute in themselves to the localisation percept of a source. According to [Mac09], head movements from $5^\circ$ (at $50^\circ/s$) generate usable dynamic cues. This is why head movements are beneficial even for short sound as described by [PN97a] comparing a localization performances of a low-pass noise stimulus lasting $3$ or $0.5$ seconds with or without slight head movements. The front/back ambiguities are reduced by analysing the dynamic changes of ITD and ILD. For example, for a source in front of the listener. If the listener turn his head to the right along the horizontal plan, the sound source will be perceived closer to the left ear. If he turn his head to the left, the sound source will be perceived closer to the right ear. If the source is behind the listener’s head, the effect will be the opposite

Todo

create a figure explaining that.

[PN97b] studied the effect of dynamic cues in the elevation plan and suggested that head movement in this plan are beneficial for sources really high or low ($\pm30^\circ$). [Wal39][Wal40] explained this by the fact that in these conditions the amplitude of dynamic variations of interaural cues lead by the head rotations are lower than sources closer of the horizontal plane. By using a low-pass noise, [PN97b] suggested that ITD changes are more reliable than ILD.