An experimental study of the acoustic impedance characteristics of human hair

Abstract

Previous analytical and empirical studies of the human auditory system have shown that the cues used for localization are modified by the inclusion of nonrigid scattering surfaces (clothing, hair etc). This paper presents an investigation into the acoustic impedance properties of human hair. The legitimacy of a locally reactive surface assumption is investigated, and an appropriate boundary condition is formulated to account for the physiological composition of a human head with hair. This utilizes an equivalent impedance parameter to allow the scattering boundary to be defined at a reference plane coincident with the inner rigid surface of the head. Experimental examination of a representative synthetic hair material at oblique incidence is used to show that a locally reactive surface assumption is legitimate. Additional experimental analysis of a simple scattering problem illustrates that the equivalent impedance must be used in favor of the traditional surface impedance to yield physically correct pressure magnitudes. The equivalent acoustic impedance properties of a representative range of human hair samples are discussed, including trends with sample thickness, fiber diameter, bulk density, and mass.

The effect of hair on auditory localization cues

“…These were then repeated with the sphere hemispherically covered by a synthetic hair material. The equivalent impedance ͑impedance at a reference plane coincident with the inner rigid surface͒ and discussion of the acoustical properties of this material are given by Treeby et al ͑2007b͒. The hair material came attached to a thin fabric backing and the covering was constructed from several pieces of this sewn together to make the correct shape.…”

“…This pressure is calculated here using the analytical result described by Treeby et al ͑2007a͒ assuming a planar incident wave. The formulation assumes that the surface of the spherical scatterer is divided into two hemispheres, each with a uniformly distributed, locally reacting surface impedance ͓the validity of a locally reactive surface assumption for human hair is discussed by Treeby et al ͑2007b͔͒. If a unity source strength is assumed, at the appropriate surface locations, the complex pressure calculated by this formulation directly corresponds to the HRTF.…”

“…As discussed in detail by Treeby et al ͑2007b͒, the measured equivalent acoustic impedance characteristics of human hair are primarily dependent on the overall sample thickness and density. Increasing either the bulk thickness or density of the sample decreases the impedance magnitude, whilst an increase in thickness additionally produces a relative increase in the impedance phase angle.…”

“…For all pragmatic modifications, the equivalent impedance retains a stiffnesslike reactance, with the impedance phase angle on the order of 10°-50°. Figure 7 illustrates the change in HRTF due to a hemispherical hair covering utilizing three of the measured equivalent impedance properties discussed by Treeby et al ͑2007b͒. These correspond to human hair within a 20 mm sample holder at 40 kg/ m 3 ͓Fig.…”

“…The hair is modeled as a hemispherical covering on a spherical head utilizing a recent analytical solution to the corresponding scattering problem by Treeby et al ͑2007a͒. A locally reactive equivalent impedance parameter is used to encapsulate the acoustic properties of human hair as discussed by Treeby et al ͑2007b͒. Cue changes are discussed for several cases of measured hair impedance.…”