Physics of outer ear
Principle
The auricle
(pinna) and auditory canal (meatus externus) together form the outer ear. The
pinna's most important function is the reflection and channeling of the
incoming pressure-waves to the opening of the auditory canal. In humans,
channeling is a minor factor, but for certain animals (e.g. rabbits, owls) it
contributes significantly to hearing. This channeling is of major
importance for improvement of directional
hearing in vertical directions. The most important
auditory effect of the hearing canal is the increase in sensitivity around 3½
kHz
Pinna and source elevation
Audiograms
are preferably measured in anechoic chambers with loudspeakers on a large
distance of the head. Remaining reflections, despite the absorbing structures,
can be cancelled by electronic-acoustic
feedback. This is an imitation of the free field measurement (no
vegetation). However, routinely the measurements are performed with headphones
or with earphones. It has been proven that these measurements give little
difference with the measurements with loudspeakers. I.e. for the sensitivity of
pure tones (or 1/8 octaves tones) the presence of a pinna is without function. However,
this does not apply to source
localization (direction and distance).
Fig. 1 Transfer of the pinna as a function of frequency. Upper
panel: the lines give the angle of the elevation in the median plane of -40,
-35,…, +55 degrees. The line thickness increases with the angle. Lower panel:
the same data, but now in the elevation/frequency plane. More blackening
represents a larger gain as a result of the pinna-acoustics. (From Hofman, 2000)
Source
location is a complicated cerebral process since for pre-processing only the
tonotopic organization of both basilar membranes is available. For localization
in the horizontal plane the interaural phase difference (IPD) becomes available
as a result of the difference in time of arrival caused by the interaural
distance difference with regard to the source. This applies up to 1500 Hz. In
addition, the difference in interaural intensity (IID) is of importance, for
example caused by a distance difference or by head shade. This applies above
1500 Hz, because waves of lower frequencies deflect around the head what
reduces the IID. IID’s amounts many dB’s, up to a maximum of 35 dB. IPD and IID
can concern a pure tone (as in a clinical test or laboratory experiment), but
also a complete spectrum. The later applies in daily practice.
For
source localization in the vertical plane, the pinnae are of importance. The
signal impinging upon the tympanum is the sum of the sound which comes straight
forward from the source, and the signal which reaches the tympanum by means of
reflections of the ear flap. Generally these signals reinforce each other, but
can also (partly) cancel each other. The ear flap adds an acoustic “pinna
image” which is dependent on the direction (elevation and azimuth) of the sound
source. For the azimuth this is not relevant since then IID’s and IPD’s are the
cues for localization, except for the case to solve the in front – behind (180o)
ambiguity (symmetrical front – behind locations of solving give the same IPD
and IID). Below 4 kHz the transfer characteristic of the auricle is little
dependent on the elevation, although it can differ 15 dB from frequency to
frequency. Without pinna there is an average loss of 10 dB. Above 4 kHz the
contribution of the auricle is strongly elevation dependent, up to 20 dB, and
moreover more frequency-dependent than below 4 kHz (Fig. 1). Besides the
contribution of the pinna, the head and the shoulder contribute to some extent.
The ear canal (meatus)
Sound
travels down through the (external) meatus and sound pressure wave causes the
tympanum to vibrate. Frequencies will resonate when they can perform standing
wave behaviour. The auditory canal can be considered as a vibrating cavity with
the pinna as open end (ventral segment) and the tympanum as a closed end (node),
analogue to the open organ pipe. Resonance occurs when ¼λ has the length
(L) of the meatus, with λ the wavelength of the frequency. The average ear
has a meatus of
Application
The physics of the ear
canal has been examined thoroughly for development of audiological equipment (such
as an earphone, see More Info) and
hearing aids.
More Info
There
are more frequencies which fulfil the condition of having a node at the
tympanum and a ventral segment at the pinna. Their wavelengths and frequencies
are:
λ = 4L/(2n+1) and f = c(2n+1)/(4L). (1)
Consequently,
the next resonance frequency (for n=1) is 3x3.4 ≈ 10 kHz. Its effect is generally
too small (depending on the experimental technique) to be revealed in the
threshold audiogram.
The amplitude variation in transversal direction caused by a
planar wave at the entrance of the meatus is irrelevant up to 4 kHz and beyond
it slowly increases to almost 5 dB at 15 kHz. In practice it will be something
more (no planar wave). The transfer in the canal can be calculated along the
central axis, given the length along the curved central axis and the variation
in diameters along this axis. More precise calculations have been done with a
numerical 3D computer model (Stinson and Daigle, 2005).
Acoustic coupling
between an earphone and the tympanum
The model of the
acoustic coupling between the eardrum and
the eardrum is based on a funnel-shaped device. The air in the small tube on
one end (the ear canal) of the coupler is treated as a lumped mass. A force Mtat
(with a the acceleration) is exerted on this mass (M) by the pressure at the
earphone and the pressure at the eardrum. The air in the conical cavity is
treated as a spring which couples the air in the tube with the diaphragm of the
eardrum. Damping is included to represent losses in the conical cavity and the
tube.
Hofman P. On the role of spectral pinna cues in human
sound localization. Ph.D. thesis,
Stinson MR,
Daigle GA. Comparison of an analytic horn equation approach and a
boundary element method for the calculation of sound fields in the human ear
canal. J Acoust Soc Am. 2005;118:2405-11.