# Rayleigh's duplex theory

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The Duplex theory proposed by Lord Rayleigh (1907) provides an explanation for the ability of humans to localise sounds by time differences between the sounds reaching each ear (ITDs) and differences in sound level entering the ears (interaural level differences, ILDs).

The duplex theory states that ITDs are used to localise low frequency sounds, in particular, while ILDs are used in the localisation of high frequency sound inputs. A limitation of the duplex theory is that the theory does not completely explain directional hearing, as no explanation is given for the ability to distinguish between a sound source directly in front and behind. Also the theory only relates to localising sounds in the horizontal plane around the head. The theory also does not take into account the use of the pinna in localisation.(Gelfand, 2004)

Experiments conducted by Woodworth (1938) tested the duplex theory by using a solid sphere to model the shape of the head and measuring the ITDs as a function of azimuth for different frequencies. The model used had a distance between the 2 ears of approximately 22-23 cm. Initial measurements found that there was a maximum time delay of approximately 660μs when the sound source was placed at directly 90° azimuth to one ear. This time delay correlates to a sound input with a frequency of 1500Hz. The results concluded that when a sound played had a frequency less than 1500Hz the wavelength is greater than the time delay between the ears. Therefore there is a phase difference between the sound waves entering the ears providing acoustic localisation cues. With a sound input with a frequency closer to 1500Hz the wavelength of the sound wave is similar to the natural time delay. Therefore due to the size of the head and the distance between the ears there is a reduced phase difference so localisations errors start to be made. When a high frequency sound input is used with a frequency greater than 1500Hz, the wavelength is shorter than the distance between the 2 ears, a head shadow is produced and ILD provide cues for the localisation of this sound.

Feddersen et al. (1957) also conducted experiments taking measurements on how ITDs alter with changing the azimuth of the loudspeaker around the head at different frequencies. But unlike the Woodworth experiments human subjects were used rather than a model of the head. The experiment results agreed with the conclusion made by Woodworth about ITDs. The experiments also concluded that is there is no difference in ITDs when sounds are provided from directly in front or behind at 0° and 180° azimuth. The explanation for this is that the sound is equidistant from both ears. Interaural time differences alter as the loudspeaker is moved around the head. The maximum ITD of 660μs occurs when a sound source is positioned at 90° azimuth to one ear.