Abstract: In this paper, we discuss the propagation of sound in the narrow pathways of an occluded-ear simulator typically used for the measurement of insert-type earphones. The simulator has a standardized frequency response conforming to the international standard (IEC60318-4). In narrow pathways, the speed and phase of sound waves are modified by viscous air damping. In our previous paper, we proposed a new finite element method (FEM) to consider the effects of air viscosity in this type of audio equipment. In this study, we will compare the results from the ear simulator FEM model, and those from a three dimensional human ear canal FEM model made from computed tomography images, with the measured frequency response data from the ear canals of 18 people.
Abstract: To focus on the vibration mode of a cone loudspeaker,
which acts as an electroacoustic transducer, excitation experiments
were performed using two types of loudspeaker units: one employing
an impulse hammer and the other a sweep signal. The on-axis sound
pressure frequency properties of the loudspeaker were evaluated, and
the characteristic properties of the loudspeakers were successfully
determined in both excitation experiments. Moreover, under
conditions identical to the experiment conditions, a coupled analysis of
the vibration-acoustics of the cone loudspeaker was performed using
an acoustic analysis software program that considers the impact of
damping caused by air viscosity. The result of sound pressure
frequency properties with the numerical analysis are the most closely
match that measured in the excitation experiments over a wide range
of frequency bands.
Abstract: This paper discusses the propagation of sound waves in
air, specifically in narrow rectangular pathways of an occluded-ear
simulator for acoustic measurements. In narrow pathways, both the
speed of sound and the phase of the sound waves are affected by the
damping of the air viscosity. Herein, we propose a new finite-element
method (FEM) that considers the effects of the air viscosity. The
method was developed as an extension of existing FEMs for porous,
sound-absorbing materials. The results of a numerical calculation for a
three-dimensional ear-simulator model using the proposed FEM were
validated by comparing with theoretical lumped-parameter modeling
analysis and standard values.
Abstract: Earphones and headphones, which are compact electro-acoustic transducers, tend to have a lot of acoustic absorption materials and porous materials known as dampers, which often have a large number of extremely small holes and narrow slits to inhibit the resonance of the vibrating system, because the air viscosity significantly affects the acoustic characteristics in such acoustic paths. In order to perform simulations using the finite element method (FEM), it is necessary to be aware of material characteristics such as the impedance and propagation constants of sound absorbing materials and porous materials. The transfer function is widely known as a measurement method for an acoustic tube with such physical properties, but literature describing the measurements at the upper limits of the audible range is yet to be found. The acoustic tube, which is a measurement instrument, must be made narrow, and the distance between the two sets of microphones must be shortened in order to take measurements of acoustic characteristics at higher frequencies. When such a tube is made narrow, however, the characteristic impedance has been observed to become lower than the impedance of air. This paper considers the cause of this phenomenon to be the effect of the air viscosity and describes an FEM analysis of an acoustic tube considering air viscosity to compare to the theoretical formula by including the effect of air viscosity in the theoretical formula for an acoustic tube.
Abstract: Headphones and earphones have many extremely small
holes or narrow slits; they use sound-absorbing or porous material (i.e.,
dampers) to suppress vibratory system resonance. The air viscosity in
these acoustic paths greatly affects the acoustic properties. Simulation
analyses such as the finite element method (FEM) therefore require
knowledge of the material properties of sound-absorbing or porous
materials, such as the characteristic impedance and propagation
constant. The transfer function method using acoustic tubes is a widely
known measuring method, but there is no literature on taking
measurements up to the audible range. To measure the acoustic
properties at high-range frequencies, the acoustic tubes that form the
measuring device need to be narrowed, and the distance between the
two microphones needs to be reduced. However, when the tubes are
narrowed, the characteristic impedance drops below the air impedance.
In this study, we considered the effect of air viscosity in an acoustical
tube, introduced a theoretical formula for this effect in the form of
complex density and complex sonic velocity, and verified the
theoretical formula. We also conducted an experiment and observed
the effect from air viscosity in the actual measurements.
Abstract: Sound pathways in the enclosures of small earphones
are very narrow. In such narrow pathways, the speed of sound
propagation and the phase of sound waves change because of the air
viscosity. We have developed a new finite element method that
includes the effects of damping due to air viscosity for modeling the
sound pathway. This method is developed as an extension of the
existing finite element method for porous sound-absorbing materials.
The numerical calculation results using the proposed finite element
method are validated against the existing calculation methods.
Abstract: In very narrow pathways, the speed of sound propagation and the phase of sound waves change due to the air viscosity. We have developed a new finite element method (FEM) that includes the effects of air viscosity for modeling a narrow sound pathway. This method is developed as an extension of the existing FEM for porous sound-absorbing materials. The numerical calculation results for several three-dimensional slit models using the proposed FEM are validated against existing calculation methods.
Abstract: This paper describes vibration analysis using the finite
element method for a small earphone, especially for the diaphragm
shape with a low-rigidity. The viscoelastic diaphragm is supported by
multiple nonlinear concentrated springs with linear hysteresis
damping. The restoring forces of the nonlinear springs have cubic
nonlinearity. The finite elements for the nonlinear springs with
hysteresis are expressed and are connected to the diaphragm that is
modeled by linear solid finite elements in consideration of a complex
modulus of elasticity. Further, the discretized equations in physical
coordinates are transformed into the nonlinear ordinary coupled
equations using normal coordinates corresponding to the linear natural
modes. We computed the nonlinear stationary and non-stationary
responses due to the internal resonance between modes with large
amplitude in the nonlinear springs and elastic modes in the diaphragm.
The non-stationary motions are confirmed as the chaos due to the
maximum Lyapunov exponents with a positive number. From the time
histories of the deformation distribution in the chaotic vibration, we
identified nonlinear modal couplings.