# Influence of geometric structure, convection, and eddy on sound propagation
in acoustic metamaterial with turbulent flow

Myong Chol Pak111Associate Professor, Department of Physics,
<EMAIL_ADDRESS>Kim Il Sung University, Taesong District, 136,
Pyongyang, Democratic People’s Republic of Korea  Kwang-Il Kim222Associate
Professor, Department of Physics<EMAIL_ADDRESS>Kim Il Sung
University, Taesong District, 136, Pyongyang, Democratic People’s Republic of
Korea  Hak Chol Pak333Professor, Department of Physics<EMAIL_ADDRESS>Kim Il Sung University, Taesong District, 136, Pyongyang, Democratic People’s
Republic of Korea  and Kwon Ryong Hong444Research fellow, Institute of Natural
Sciences<EMAIL_ADDRESS>Kim Il Sung University, Taesong
District, 136, Pyongyang, Democratic People’s Republic of Korea

###### Abstract

The problem of reducing noise in the transportation is an important research
field to prevent accidents and to provide a civilized environment for people.
A material that has recently attracted attention in research to reduce noise
is acoustic metamaterial, and most of the research projects so far have been
limited to the case of static media without flow. We have studied the sound
transmission properties of acoustic metamaterial with turbulent flow to
develop acoustic metamaterial that be used in transportation. In this paper,
the effect of geometrical structure, the convective effect, and the eddy
effect on sound propagation in acoustic metamaterial with turbulent flow are
investigated, and the relationships between them are analyzed. The convective
effect and the eddy effect both reduce the resonant strength of sound
transmission loss resulting from the unique geometry of the acoustic crystal,
but shift the resonant frequencies in opposite directions. In addition, when
the convective effect and the eddy effect of the airflow, as well as the
intrinsic interaction effect generated from the unique geometrical structure
of the acoustic metamaterial cannot be ignored, they exhibit competition
phenomena with each other, resulting in a widening of the resonance peak. As a
result, these three effects cause the shift of the resonance frequency of the
sound transmission loss and the widening of the resonance peak. The results of
this study show that even in the case of turbulent flow, acoustic metamaterial
can be used for transportation by properly controlling the geometric size and
shape of the acoustic metamaterial.

## Nomenclature

BLI = | boundary-layer ingestion
---|---
CFD = | computational field dynamics
$c_{0}$ = | Speed of sound, m/s
$k$ = | turbulent kinetic energy, m${}^{2}/$s2
$k_{0}$ = | wave number of incident acoustic wave, m-1
LBM = | lattice Boltzmann method
Ma = | Mach number
$L_{p}$ = | sound pressure level, dB
PML = | Perfectly Matched Layer
$p_{rms}$ = | root mean square pressure, Pa
$p_{ref}$ = | reference pressure for zero level corresponding to 0dB, Pa
RANS = | Reynolds-averaged Navier-Stokes
$r_{a}$ = | radius of annular cavity, m
$r_{d}$ = | radius of circular duct, m
SPL = | sound pressure level
SST = | Shear Stress Transport
$t_{a}$ = | height of annular cavity, m
$t_{d}$ = | half of the height of neck in circular duct, m
TL = | transmission loss, dB
$t_{s}$ = | height of acoustic source, m
$t_{p}$ = | height of PML, m
$\alpha_{p}$ = | coefficient of thermal expansion, K-1
$\beta_{T}$ = | isothermal compressibility, Pa-1
$\varepsilon$ = | turbulent dissipation rate, m${}^{2}/$s3
$\eta$ = | Kolmogorov’s scale, m
$\mu$ = | dynamic viscosity, Pa$\cdot$s
$\mu_{B}$ = | bulk viscosity, Pa$\cdot$s
$\mu_{T}$ = | turbulent dynamic viscosity, Pa$\cdot$s
$\nu$ = | fluid kinematic viscosity, m2/s
$\nu_{T}$ = | turbulent kinematic viscosity, m2/s
$\tau$ = | viscous stress tensor, Pa
$\tau_{T}$ = | turbulence time scale, s
$\omega$ = | specific dissipation rate, s-1
$\omega_{0}$ = | angular frequency of incident acoustic wave, s-1

##  1 Introduction

With the recent development of technology, attentions been focused on the
improvement of human environment, and interests in noise reduction are
increasing. Among them, acoustic metamaterial are widely applied because they
can reduce noise by controlling the density and the bulk modulus of the
material.

Studies have been discussed using acoustic metamaterial to control sound
transmission by absorbing low-frequency sound in linear and nonlinear regions
[1, 2] and doping impurities inside zero-index metamaterial [3]. Also, the
method for minimizing indoor sound energy by using an acoustic metamaterial
with a flat panel structure [4] and the method for detecting an acoustic image
by constructing an acoustic superlens using membrane-based a two-dimensional
metamaterial having a negative density were reported [5]. In addition, a non-
resonant metasurface design for broadband elastic wave mode division that be
used for elastic communication and biomedical diagnostic evaluation has also
been proposed [6]. Lu K. et al. showed through simulation that acoustic
metamaterial with honeycomb structure effectively cause acoustic transmission
loss in the low frequency range [7] and Fan L. et al. proved that the plates
with circular holes blocked by membranes are effective in sound insulation at
low frequencies by using numerical analysis [8]. Wang X.et al. proposed that a
sound insulation effect can be obtained in the low frequency range by
controlling the shape, stiffness and position of a thin film-type acoustic
metamaterial with a stick fixed in the middle of the frame [9]. Acoustic
metamaterial used to block broadband noise including low-frequency regions in
air can be applied to water as well as air. Bok E.et al. proposed a way to use
the acoustic metasurface consisting of a membrane and an air cavity filled
with meta atoms in order to increase the acoustic sensitivity in water [10].

As the practical applicability of acoustic metamaterial increases, research
projects on acoustic metamaterial panels that can increase the noise reduction
function while passing through a fluid are actively taking place [11, 12, 13].
In Ref. [14], they designed an acoustic metamaterial panel that does not
interfere with the flow of fluid while reducing the noise in a broadband in
the audible frequency range. The proposed acoustic metamaterial panel allows
the fluid to pass through the straight hole, but serves to block broadband
noise by periodic annular cavities surrounding the hole. However, in these
papers, the effect of the flow velocity of the fluid passing through the
acoustic metamaterial on the sound wave is not discussed.

Meanwhile, research projects to control sound wave propagation in laminar and
turbulent flows of fluids are also attracting attention. Yang Z. et al.
proposed the idea that sound waves can propagate in one direction along the
surface regardless of the presence of defects or obstacles in the acoustic
structure with laminar circulation flow [15]. Research projects for
investigating sound propagation properties in turbulent flow rather than
laminar flow are attracting a lot of attention because they have a lot to do
with practical applications. Turbulence effect of the fuselage on the fan
noise of the BLI (Boundary-Layer Ingestion) configuration [16], the
relationship between the structural flexibility of the elastic trailing-edge
and the aeroacoustic response [17], prediction of broadband sound generated in
a low Mach number turbulent boundary layer by lattice Boltzmann method (LBM)
[18], simulation of indoor noise generated by indoor window vibration [19],
and acoustic source model to reduce aerodynamic noise generated from wind
turbine blades [20] have been discussed. Most of the interest, such as the
reduction of aerofoil interaction noise by new serration profile group [21,
22], the noise generation mechanism of controlled diffusion aerofoil and their
dependence on Mach number [23], and the role of the porous material placed on
the tail edge of the 3D chamber airfoil [24], focuses on the reduction of
noise caused by the interaction between aerofoil and turbulent flow.

Most of the researchers are only interested in sound wave control and noise
generation in turbulent flows, but there are few studies on the effect of
geometric structure, convective, and eddy effect on sound propagation in
acoustic metamaterial with turbulent flow. Therefore, we discuss the
convective and eddy effects on acoustic propagation as turbulence flows into
the acoustic metamaterial consisting of straight holes and periodic annular
cavities surrounding the hole. Also, in this case, the change in broadband
acoustic wave blocking characteristics according to the geometric size and the
number of annular cavities is investigated. This paper is organized as
follows. Section 2 describes the theoretical basis for aeroacoustic properties
in turbulent flows. In Section 3, numerical results for sound transmission
loss and sound pressure level of acoustic metamaterial are shown and analyzed
in both cases of no flow and turbulent flow. In particular, the turbulence
flowing in the acoustic metamaterial is analyzed by CFD (computational fluid
dynamics), and based on the results, the convective effect and the eddy effect
on sound transmission are discussed. Also, the sound transmission properties
according to the geometric size of acoustic crystals and the number of ring-
shaped cavities are also considered. Finally, in Section 4, the influence of
geometric structure, convection, and eddy on sound propagation in acoustic
metamaterial with turbulent flows are concluded, and future application
prospects are described.

##  2 Theoretical Background

Using the linearized Navier-Stokes equation, we study the propagation
properties of sound waves in a fluid. This equation consists of the
continuity, momentum, and energy equations [25].

$\frac{{\partial{\rho_{t}}}}{{\partial
t}}+\nabla\cdot({\rho_{0}}{{\bf{u}}_{t}}+{\rho_{t}}{{\bf{u}}_{0}})=M$ (1)
${\rho_{0}}[\frac{{\partial{{\bf{u}}_{t}}}}{{\partial
t}}+({{\bf{u}}_{t}}\cdot\nabla){{\bf{u}}_{0}}+({{\bf{u}}_{0}}\cdot\nabla){{\bf{u}}_{t}}]+{\rho_{t}}({{\bf{u}}_{0}}\cdot\nabla){{\bf{u}}_{0}}=\nabla\cdot{\bf{\sigma}}+{\bf{F}}-{{\bf{u}}_{0}}M$
(2) $\begin{array}[]{l}{\rho_{0}}{C_{p}}[\frac{{\partial{T_{t}}}}{{\partial
t}}+({{\bf{u}}_{t}}\cdot\nabla){T_{0}}+({{\bf{u}}_{0}}\cdot\nabla){T_{t}}]+{\rho_{t}}{C_{p}}({{\bf{u}}_{0}}\cdot\nabla){T_{0}}\\\
-{\alpha_{p}}{T_{0}}[\frac{{\partial{p_{t}}}}{{\partial
t}}+({{\bf{u}}_{t}}\cdot\nabla){p_{0}}+({{\bf{u}}_{0}}\cdot\nabla){p_{t}}]-{\alpha_{p}}{T_{t}}({{\bf{u}}_{0}}\cdot\nabla){p_{0}}=\nabla\cdot(\kappa\nabla{T_{t}})+\Phi+Q\end{array}$
(3)

where ${p_{t}}$, ${{\bf{u}}_{t}}$, ${T_{t}}$, and ${\rho_{t}}$ are the
acoustic perturbations to the pressure, the velocity, the temperature, and the
density, respectively. ${p_{t}}$, ${{\bf{u}}_{t}}$, and ${T_{t}}$ are equal to
the sum of the physical quantities in the background acoustic field and the
scattered field.

${p_{t}}=p+{p_{b}},\;{{\bf{u}}_{t}}={\bf{u}}+{{\bf{u}}_{b}},\;{T_{t}}=T+{T_{b}}$
(4)

Also, $M$, ${\bf{F}}$, $Q$, $C_{p}$, $\alpha_{p}$, and $\kappa$ are the mass
source, the volume force source, the volumetric heat source, the heat capacity
at constant pressure, the coefficient of thermal expansion, and the thermal
conductivity, respectively. Additionally, the stress tensor, the linearized
equation of state and the linearized viscous dissipation function are defined
as,

${\bf{\sigma}}=-{p_{t}}{\bf{I}}+\mu(\nabla{{\bf{u}}_{t}}+{(\nabla{{\bf{u}}_{t}})^{T}})+({\mu_{B}}-2\mu/3)(\nabla\cdot{{\bf{u}}_{t}}){\bf{{\rm
I}}}$ (5) ${\rho_{t}}={\rho_{0}}({\beta_{T}}{p_{t}}-{\alpha_{p}}{T_{t}})$ (6)
$\Phi=\nabla{{\bf{u}}_{t}}:{\bf{\tau}}({{\bf{u}}_{0}})+\nabla{{\bf{u}}_{0}}:{\bf{\tau}}({{\bf{u}}_{t}})$
(7)
${\bf{\tau}}({{\bf{u}}_{t}})=\mu[\nabla{{\bf{u}}_{t}}+{(\nabla{{\bf{u}}_{t}})^{T}}]+({\mu_{B}}-2\mu/3)(\nabla\cdot{{\bf{u}}_{t}}){\bf{{\rm
I}}}$ (8)
${\bf{\tau}}({{\bf{u}}_{0}})=\mu[\nabla{{\bf{u}}_{0}}+{(\nabla{{\bf{u}}_{0}})^{T}}]+({\mu_{B}}-2\mu/3)(\nabla\cdot{{\bf{u}}_{0}}){\bf{{\rm
I}}}$ (9)

where $\bf{\tau}$, $\beta_{T}$, $\mu$, and $\mu_{B}$ are the viscous stress
tensor, the isothermal compressibility, the dynamic viscosity and the bulk
viscosity, respectively. In the linearized Navier-Stokes equation, $p_{0}$,
${\bf{u}}_{0}$, $T_{0}$, and $\rho_{0}$ are absolute pressure, velocity,
temperature, and density of the background mean flow used to account for the
effect of the background mean flow on the sound wave. This is calculated by
using the CFD study of the fluid.

When sound waves propagate into a turbulent flow, the flow properties are
evaluated by Reynolds-averaged Navier-Stokes (RANS) model [26]. The Reynolds-
averaged representation of turbulent flows divides the flow quantities into a
time-averaged part and a fluctuating part.

${{\bf{u}}_{0}}={{\bf{\bar{u}}}_{0}}+{{\bf{u^{\prime}}}_{0}},\,{\rho_{0}}={\bar{\rho}_{0}}+{\rho^{\prime}_{0}},\;{p_{0}}={\bar{p}_{0}}+{p^{\prime}_{0}}$
(10)

In order to discuss the turbulent flow, the SST (Shear Stress Transport)
turbulent method is used among various RANS models [25]. The advantage of this
method is that it can describe the flow characteristics well close to the wall
and the dependence on the initial parameters of the main free stream flow is
not very large.

The basic equation governed is as follows.

$\frac{{\partial{{\bar{\rho}}_{0}}}}{{\partial
t}}+\nabla\cdot({\bar{\rho}_{0}}{{\bf{\bar{u}}}_{0}})=0$ (11)
$\begin{array}[]{l}{{\bar{\rho}}_{0}}\frac{{\partial{{{\bf{\bar{u}}}}_{0}}}}{{\partial
t}}+{{\bar{\rho}}_{0}}({{{\bf{\bar{u}}}}_{0}}\cdot\nabla){{{\bf{\bar{u}}}}_{0}}=\nabla\cdot\\{-{{\bar{p}}_{0}}{\bf{I}}+(\mu+{\mu_{T}})[\nabla{{{\bf{\bar{u}}}}_{0}}+{(\nabla{{{\bf{\bar{u}}}}_{0}})^{T}}]\\\
\;\;\;\;\;\;\;\;\;\;\;\;\;-\frac{2}{3}(\mu+{\mu_{T}})(\nabla\cdot{{{\bf{\bar{u}}}}_{0}}){\bf{I}}-\frac{2}{3}{{\bar{\rho}}_{0}}k{\bf{I}}\\}+{\bf{F}}\end{array}$
(12)

The model equations are formulated in the averaged turbulent kinetic energy
$k$ and the turbulent frequency $\omega$,

${\bar{\rho}_{0}}\frac{{\partial k}}{{\partial
t}}+{\bar{\rho}_{0}}({{\bf{\bar{u}}}_{0}}\cdot\nabla)k=\nabla\cdot[(\mu+{\mu_{T}}{\sigma_{k}})\nabla
k]+P-{\bar{\rho}_{0}}\beta_{0}^{*}k\omega$ (13)
${\bar{\rho}_{0}}\frac{{\partial\omega}}{{\partial
t}}+{\bar{\rho}_{0}}({{\bf{\bar{u}}}_{0}}\cdot\nabla)\omega=\frac{{{{\bar{\rho}}_{0}}\gamma}}{{{\mu_{T}}}}P-{\bar{\rho}_{0}}\beta{\omega^{2}}+\nabla\cdot[(\mu+{\mu_{T}}{\sigma_{\omega}})\nabla\omega]+2(1-{f_{v1}})\frac{{{{\bar{\rho}}_{0}}{\sigma_{\omega
2}}}}{\omega}\nabla\omega\cdot\nabla k$ (14)

where,

$P=\min({P_{k}},\;10{\bar{\rho}_{0}}\beta_{0}^{*}k\omega)$ (15)
${P_{k}}={\mu_{T}}\\{\nabla{{\bf{\bar{u}}}_{0}}:[\nabla{{\bf{\bar{u}}}_{0}}+{(\nabla{{\bf{\bar{u}}}_{0}})^{T}}]-\frac{2}{3}{(\nabla\cdot{{\bf{\bar{u}}}_{0}})^{2}}\\}-\frac{2}{3}{\bar{\rho}_{0}}k\nabla\cdot{{\bf{\bar{u}}}_{0}}$
(16)

In this case, the turbulent eddy viscosity is,

${\mu_{T}}=\frac{{{{\bar{\rho}}_{0}}{\alpha_{1}}k}}{{\max({\alpha_{1}}\omega,S{f_{v2}})}}$
(17)

where $S$ is the characteristic magnitude of the mean velocity gradients,

$S=\sqrt{2S_{ij}S_{ij}}$ (18)

and $S_{ij}$ is the mean strain-rate tensor,

${S_{ij}}=\frac{1}{2}(\frac{{\partial{{\bar{u}}_{0i}}}}{{\partial{x_{j}}}}+\frac{{\partial{{\bar{u}}_{0j}}}}{{\partial{x_{i}}}})$
(19)

The constants $\beta$, $\gamma$, $\sigma_{k}$, and $\sigma_{\omega}$ are
interpolated values between inner and outer values.

$\left\\{\begin{array}[]{l}\beta={f_{v1}}{\beta_{1}}+(1-{f_{v1}}){\beta_{2}}\\\
\gamma={f_{v1}}{\gamma_{1}}+(1-{f_{v1}}){\gamma_{2}}\\\
{\sigma_{k}}={f_{v1}}{\sigma_{k1}}+(1-{f_{v1}}){\sigma_{k2}}\\\
{\sigma_{\omega}}={f_{v1}}{\sigma_{\omega 1}}+(1-{f_{v1}}){\sigma_{\omega
2}}\end{array}\right.$ (20)

The interpolation functions $f_{v1}$ and $f_{v2}$ are

${f_{v1}}=\tanh(\theta_{1}^{4})$ (21)

and,

${f_{v2}}=\tanh(\theta_{2}^{2}).$ (22)

In this case,

${\theta_{1}}=\min[\max(\frac{{\sqrt{k}}}{{\beta_{0}^{*}\omega{l_{\omega}}}},\;\frac{{500\mu}}{{{{\bar{\rho}}_{0}}\omega
l_{\omega}^{2}}}),\,\frac{{4{{\bar{\rho}}_{0}}{\sigma_{\omega
2}}k}}{{C{D_{k\omega}}l_{\omega}^{2}}}],$ (23)
$C{D_{k\omega}}=\max(\frac{{2{{\bar{\rho}}_{0}}{\sigma_{\omega
2}}}}{\omega}\nabla\omega\cdot\nabla k,\;{10^{-10}}),$ (24)
${\theta_{2}}=\max(\frac{{2\sqrt{k}}}{{\beta_{0}^{*}\omega{l_{\omega}}}},\;\frac{{500\mu}}{{{{\bar{\rho}}_{0}}\omega
l_{\omega}^{2}}}).$ (25)

where $\beta_{1}=0.075$, $\beta_{2}=0.0828$, $\gamma_{1}=5/9$,
$\gamma_{2}=0.44$, $\sigma_{k1}=0.85$, $\sigma_{k2}=1$,
$\sigma_{\omega_{1}}=0.5$, $\sigma_{\omega_{2}}=0.856$, $\alpha_{1}=0.31$,
$\beta_{0}^{*}=0.09$, and $l_{\omega}$ is the distance to the closest wall.

##  3 Results and Analysis

In this section, we first describe the simulation parameters and acoustic
characteristic parameters of the acoustic metamaterial to be considered. Also,
in order to investigate the effect of the geometrical structure on sound
transmission, sound pressure level characteristic values and transmission loss
results are calculated and analyzed using finite element simulation in the
case of no flow. Next, when there is turbulent flow, the CFD analysis of the
flow is performed, and sound transmission properties are investigated for the
flow velocity, and the convective effect and the eddy effect are compared with
each other. Finally, while changing the geometric structure parameter, we
observe the change of sound pressure level and sound transmission loss values.

###  3.1 Simulation parameters

Fig. 1 is a design diagram of an acoustic metamaterial consisting of a
straight hole through which a fluid can pass and periodic annular cavities
surrounding the hole.

Figure 1: A design diagram of the acoustic metamaterial to be discussed.

In Fig.1, $r_{a}$ is the radius of annular cavity, $r_{d}$ is the radius of
circular duct, $t_{a}$ is the height of annular cavity, $t_{d}$ is a half of
the height of neck in circular duct, $t_{s}$ is the height of acoustic source,
and $t_{p}$ is the height of PML(Perfectly Matched Layer). Table 1 shows the
remaining geometric structure parameter values excluding $r_{a}$ because the
calculation is performed while changing the size of the radius $r_{a}$.

Table 2:  Geometric structure parameters $r_{d}$(mm) |  $t_{a}$(mm) |  $t_{d}$(mm) |  $t_{s}$(mm) |  $t_{p}$(mm)
---|---|---|---|---
8 | 5 | 5 | 1 | 2

As shown in Fig. 1, the discussed acoustic wave is a plane wave, and its
incident surface is perpendicular to the rotation axis direction of the
acoustic metamaterial. The finite element simulation was performed with the
commercial software COMSOL Multiphysics 5.5. In this case, the boundary
condition of the numerical simulation is assumed to be no slip and the sound
velocity is ${c_{0}}=343\;{\rm{m/s}}$. PML is applied at the inlet and outlet,
which acts to absorb acoustic waves by simulating an open boundary. We
calculated the sound pressure in the frequency range of 2000 to 6000 Hz and
evaluated the transmission loss and sound pressure level based on it. In this
case, the transmission loss of the system is defined as,

$TL=20{\log_{10}}(\left|{\frac{{{p_{in}}}}{{{p_{out}}}}}\right|)$ (26)

where $p_{in}$ and $p_{out}$ are the average pressure at the inlet and outlet,
respectively [27, 28]. And when the sound pressure $p$ changes harmonically
with time, the sound pressure level (SPL) $L_{p}$ is expressed by the root
mean square (rms) pressure $p_{rms}$ of the fluid, such as

${L_{p}}=20{\log_{10}}(\frac{{{p_{rms}}}}{{{p_{ref}}}})\;,\;\;{p_{rms}}=\sqrt{p{p^{*}}/2}$
(27)

where $p_{ref}$ is the reference pressure for the zero level corresponding to
0dB [29]. The zero level corresponding to this dB scale depends on the type of
fluid. For example, the reference pressure for air is 20$\mu$Pa and the
reference pressure for water is 1$\mu$Pa .

###  3.2 Calculation results of sound pressure level in case of no flow

We first investigate the acoustic pressure of the acoustic metamaterial in
case of no flow in order to evaluate the effect of the geometry on the sound
transmission of the acoustic metamaterial with turbulent flow. In this case,
an incident acoustic plane wave with an amplitude of 1Pa is incident in a
direction perpendicular to the axis of rotation of the acoustic metamaterial
in the area marked in red in Fig. 1. Since the properties of the sound
pressure vary according to the geometric size, we investigated the change in
the sound pressure level corresponding to the radius of annular cavity and the
number of annular cavities.

Fig. 2(a) shows the sound pressure level values versus the frequencies of the
sound wave when there is no flow (Ma=0) and the radius of annular cavity is
22.5mm. As shown in Fig. 2(a), as the frequency increases initially, the sound
pressure level values decrease rapidly, have a minimum value at a specific
frequency (4529.1 Hz in the case of N=5), and then rise again. In other words,
it has a resonant property, which can be treated as the result of the
interaction between the particle vibration in the direction of sound
propagation in the circular duct and the particle vibration perpendicular to
the direction of sound propagation in the annular cavity [14].

(a) $r_{a}$=22.5mm, Ma=0

(b) $r_{a}$=25.0mm, Ma=0

(c) $r_{a}$=27.5mm, Ma=0

(d) $r_{a}$=30.0mm, Ma=0

Figure 2:  In the case of no flow, the change in sound pressure level
according to the change in the radius of annular cavity and number of annular
cavities.

This property appears regardless of the number of annular cavities. However,
as the number increases, the magnitude of these minima becomes obviously
smaller and the resonance strength becomes stronger. This is because, as the
number of annular cavities increases, the cross-region between the particle
vibration in the sound propagation direction in the circular duct and the
particle vibration perpendicular to the sound propagation direction in the
annular cavity increases, and as a result, the interaction becomes stronger.
In the case of N=1, another peak appears at 3293.8Hz. Its peak intensity is
smaller than the peak discussed earlier, and it gets weaker as the number of
annular cavities increases. This is a peak related to the length of the
circular duct. In the case of N=1, this peak cannot be ignored because the
resonance related to the interaction is not very large. However, as the number
of annular cavities increases, the interaction between the particle vibration
in the direction of sound propagation in the circular duct and the particle
vibration perpendicular to the direction of sound propagation in the annular
cavity increases, and the intensity of this peak disappears.

Even when $r_{a}$ are 25.0mm, 27.5mm, and 30.0mm, the resonance properties
analyzed above still appear (Fig. 2(b), 2(c), 2(d)). Table 2 shows the
resonant frequency values corresponding to the annular cavity radii when N=5.
Note in Fig. 2 and Table 2 that the resonant frequency decreases as the radius
of the annular cavity increases. This is analyzed with particle vibrations
perpendicular to the direction of sound propagation in the annular cavity. As
the radius of the annular cavity increases, the wavelength of the stationary
wave in the cavity increases, and thus the resonance frequency decreases. As a
result, the resonance frequency of the sound propagation is also lowered due
to the interaction between the particle vibration in the sound propagation
direction in the circular duct and the particle vibration perpendicular to the
sound propagation direction in the annular cavity. This proves once again that
this resonance property is closely related to the particle vibration in the
annular cavity.

Table 3:  Resonant frequency values corresponding to the radii of annular cavity in case of N=5 $r_{a}$(mm) | 22.5 | 25.0 | 27.5 | 30.0
---|---|---|---|---
$f^{res}$(Hz) | 4529.1 | 3804.8 | 3267.6 | 2862.3

###  3.3 CFD analysis for turbulent flow

In order to investigate the sound propagation properties of acoustic
metamaterial with turbulent flow, CFD analysis of turbulence in airflow is
performed using the SST model mentioned above. The velocity of turbulent flow
is evaluated with the Mach number Ma, and the properties of the case where Ma
is 0.02, 0.05, 0.10, 0.15, 0.17, 0.20, 0.22 are discussed. In this case, the
kinematic viscosity of air is
$\nu={\rm{1}}{\rm{.50}}\times{\rm{1}}{{\rm{0}}^{{\rm{-5}}}}\;{{\rm{m}}^{\rm{2}}}{\rm{/s}}$.

To investigate turbulent flow, the turbulent kinetic energy $k$, specific
dissipation rate $\omega$, turbulent dissipation rate $\varepsilon$, turbulent
dynamic viscosity $\mu_{T}$, turbulent kinematic viscosity $\nu_{T}$, and
turbulence time scale $\tau_{T}$ should be evaluated and analyzed. Table 3
shows the turbulent flow parameters obtained at the outlet of the acoustic
metamaterial by simulating while changing the velocity of the turbulent flow.
As Ma increases, turbulent kinetic energy, specific dissipation rate,
turbulent dissipation rate, turbulent dynamic viscosity, and turbulent
kinematic viscosity increase. However, the turbulence time scale decreases as
Ma increases, which is in good agreement with the fact that $\tau_{T}$ is
inversely proportional to the specific dissipation rate $\omega$. Fig. 3 shows
a quarter cross section of turbulent dynamic viscosity $\mu_{T}$ in the case
of Ma = 0.15. It is evident that the turbulent dynamic viscosity is not zero
in the annular cavity region of Fig.3, and this fact intuitively shows that
the annular cavity region has a great influence on the airflow flowing through
the circular duct.

Table 4:  Turbulent flow parameters at the outlet of acoustic metamaterial Ma | 0.02 | 0.05 | 0.10 | 0.15 | 0.17 | 0.20 | 0.22
---|---|---|---|---|---|---|---
$k\;({{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{s}}^{\rm{2}}})$ | 0.00538 | 0.225 | 3.86 | 14.6 | 21.1 | 33.3 | 43.0
$\omega\;({10^{5}}{{\rm{s}}^{-1}})$ | 8.92 | 8.94 | 9.25 | 10.1 | 10.5 | 11.3 | 11.9
$\varepsilon({10^{4}}{{\rm{m}}^{\rm{2}}}{\rm{/}}{{\rm{s}}^{\rm{3}}})$ | 0.0432 | 1.81 | 32.1 | 132 | 199 | 338 | 461
${\mu_{T}}({10^{-7}}{\rm{Pa}}\cdot{\rm{s}})$ | 0.0727 | 3.03 | 50.2 | 175 | 242 | 355 | 436
${\nu_{T}}({10^{-7}}{{\rm{m}}^{\rm{2}}}{\rm{/s}})$ | 0.0603 | 2.52 | 41.7 | 145 | 201 | 294 | 361
${\tau_{T}}({10^{-5}}{\rm{s}})$ | 1.25 | 1.24 | 1.20 | 1.11 | 1.06 | 0.983 | 0.933
Figure 3:  Quarter cross section of the turbulent dynamic viscosity in the
case of Ma=0.15.

It is important to evaluate the property of the turbulent dissipation rate
$\varepsilon$ well in investigating the turbulent flow of a fluid. The
turbulent dissipation rate $\varepsilon$ does not depend on the kinematic
viscosity $\nu$, but instead is determined by the nature of the largest eddy
that extracts energy from the mean flow [30]. A scale that well reflects the
balance between the inertia effect and the viscous effect of eddy is
Kolmogorov’s scale, defined as,

$\eta={({\nu^{3}}/\varepsilon)^{1/4}}$ (28)

Therefore, it is necessary to consider this scale carefully to evaluate the
properties of turbulent flow and to analyze the sound transmission result
accurately in turbulent flow. Thus, we investigated the Kolmogorov’s scale
versus the velocity of air (Fig. 4). As shown in Fig. 4, as Ma increases,
Kolmogorov’s scale gradually decreases. That is, the faster the velocity, the
smaller the effect of eddy. In Fig. 4, the scale change was also investigated
while changing the number of annular cavities, but there is no significant
change depending on the number.

Figure 4:  Kolmogorov’s scale versus the velocity of airflow.

###  3.4 Sound transmission in turbulent flow

We investigated the transmission properties of sound waves in turbulent flow
with the linearized Navier-Stokes Model discussed in Section 2, based on
determining the pressure, velocity, temperature, and density of turbulent flow
in acoustic metamaterial. In this case, the incident acoustic plane wave of
${p_{b}}={p_{0}}{e^{-i{k_{0}}z}}$ is incident on the area marked in red in
Fig. 1 in a direction perpendicular to the rotation axis of the acoustic
metamaterial, where ${p_{0}}=1{\rm{Pa}}$,
${k_{0}}={\omega_{0}}/[{c_{0}}{\rm{(Ma}}+1)]$, and $\omega_{0}$ is the angular
frequencies of the incident acoustic wave.

Figure 5:  A quarter cross section of the acoustic pressure in the case of
$f$=5700Hz, Ma=0.15, and $r_{a}$=25mm.

Fig. 5 shows a quarter cross section of the acoustic pressure obtained as a
simulation result for $f$=5700Hz, Ma=0.15, and $r_{a}$=25mm. This figure shows
that even in turbulent flow, sound transmission can be relatively blocked due
to the geometry of the acoustic metamaterial. Thus, we investigated the sound
transmission loss while increasing the flow velocity.

(a) Ma=0.02, N=5

(b) Ma=0.05, N=5

(c) Ma=0.10, N=5

(d) Ma=0.15, N=5

Figure 6:  Sound transmission loss corresponding to the size of Ma and the
number of annular cavities with $r_{a}$=25mm in the case of Ma=0.02, 0.05,
0.10, and 0.15.

(a) Ma=0.17, N=5

(b) Ma=0.20, N=5

(c) Ma=0.22, N=5

(d) Ma=0.15, N=7

Figure 7:  Sound transmission loss corresponding to the size of Ma and the
number of annular cavities with $r_{a}$=25mm in the case of Ma=0.17, 0.20, and
0.22. (* (d) Transmission loss graph investigated while changing the number of
annular cavities from 1 to 7 when Ma = 0.15)

Fig. 6 and Fig. 7 show the sound transmission loss results calculated while
changing the size of Ma and the number of annular cavities in the case of
$r_{a}$=25mm. In order to evaluate the sound transmission loss corresponding
to the flow velocity and the number of annular cavities in detail, in Fig.
6(a)-6(d) and Fig. 7(a)-7(c), the number of annular cavities was changed from
1 to 5 and the size of Ma was changed from 0.02 to 0.22. Also, in Fig. 7(d), a
detailed calculation of the transmission loss graph is shown while changing
the number of annular cavities from 1 to 7 when the flow velocity is Ma =
0.15.

In the case of Ma=0 and $r_{a}$=25mm, the resonant frequency is 3804.8Hz. If
you analyze Fig. 6(a) in detail, you can see that the resonance frequency is
rather lower than in the case of no flow. In this case, since Ma=0.02, the
convective velocity is small, on the contrary, the Kolomogorov’s scale is very
large (see Fig. 4). Therefore, the effect of eddy is greater than the effect
of convective velocity on sound transmission. The fact that the resonance
frequency in the case of N=1,2,3,4 in Fig. 6(a) is lower than that in the case
of no flow shows that the effect of eddy shifts the resonance frequency to a
lower frequency. The figure also reflects the fact that as N increases, the
intrinsic interaction of acoustic metamaterial becomes stronger, and the peak
intensity gradually increases. When N=5, a series of changes occurs in the
sound transmission loss values. After the first peak of 3677.9Hz occurs, the
values gradually change to the second peak of 3938.3Hz, resulting in a
widening of the resonance peak. When N=5, the number of annular cavities
increases compared to N=1,2,3,4. Therefore, the interaction between the
particle vibration in the sound propagation direction in the circular duct and
the particle vibration perpendicular to the sound propagation direction in the
annular cavity becomes strong. In this case, not only the effect of eddy, but
also the intrinsic interaction of acoustic metamaterial has a considerable
influence on the sound propagation. Of course, the fact that the largest peak
frequency in the figure has been lowered to 3677.9Hz shows that the eddy
effect still plays a large role at this time. However, the newly revealed
widening properties in the figure reflect that the intrinsic interaction of
acoustic metamaterials has a significant effect on sound propagation. In the
case of Fig. 6(b), as Ma increases, the effect of convection becomes larger
than that in the case of Ma=0.02. This can be known well by seeing that the
peak frequency shifted to 3824.7Hz when Ma=0.05 and N=5. However, in this
case, the widening property is not significantly different from the case of
Ma=0.02. In the case of Fig. 6(c), the effect of convection becomes stronger,
and the widening property appears from N=4. In the case of Ma = 0.15 and Ma =
0.17, the intrinsic interaction effect due to the geometry of the acoustic
metamaterial, the effect of convection, and the effect of eddy become similar.
As a result, in Fig. 6(d) and Fig 7(a), widening property appears from N=1.
However, in the case of Ma = 0.17, the effect of convection was greater than
in the case of Ma = 0.15, and the peak frequencies were shifted to a larger
frequency. When Ma is continuously increased and Ma = 0.20, 0.22 is reached,
the effect of convection becomes much larger than the effect of eddy and the
geometrical interaction effect of acoustic metamaterial, so the widening
property does not appear and the peak frequency moves to a larger frequency
(Figure 7(b),(c)). Fig. 7(d) is a graph that investigates the sound
transmission loss while increasing the number of annular cavities in the
velocity range of Ma = 0.15 where the three interactions are similar. Fig.
7(d) shows that in the case of Ma = 0.15, the geometric interaction effect of
acoustic metamaterial begins to play a leading role only when N is 7 or more.

Figure 8:  Sound pressure level results for the radii of annular cavity in
case Ma = 0.15.

Fig. 8 shows the sound pressure level results for the radii of the annular
cavity when Ma = 0.15. In the case of Ma=0.15, it is affected by convection
and eddy, but as in the case of Ma=0, as the radius increases, the resonance
frequency for the sound pressure level decreases. This fact shows that the
particle vibration in the annular cavity analyzed when Ma = 0 is a mechanism
that cannot be ignored even in the acoustic propagation analysis with
turbulent flow.

##  4 Conclusion

In this study, we discussed the influence of the geometric structure,
convection, and eddy on sound propagation in acoustic metamaterial with
turbulent flow. First, in order to evaluate the influence of the geometric
structure, the acoustic pressure of the acoustic metamaterial was investigated
in the case of no flow. Looking at the sound pressure levels corresponding to
the frequencies of the sound wave, it has resonance properties, and as the
number of annular cavities increases, the resonance strength becomes stronger.
Also, as the radius of the annular cavity increases, the resonant frequency
decreases. This shows that the sound propagation properties of acoustic
metamaterial are closely related to the geometry.

To discuss the problem of sound propagation when turbulent flows into the
acoustic metamaterial, not only the effect of convection and eddy, but also
the effect of the intrinsic interactions reflecting the geometric structure of
the acoustic metamaterial must be considered. Here, the intrinsic interaction
refers to the interaction between the particle vibration in the sound
propagation direction in the circular duct and the particle vibration
perpendicular to the sound propagation direction in the annular cavity. It is
not an easy matter to interpret this because all three effects contribute
sound transmission. Of course, both convective and eddy effects reduce the
intrinsic interaction of acoustic metamaterial in the circular duct, thus
reducing the resonant peak intensity for sound transmission. However,
considering that the direction of convection is the same as the direction of
sound propagation and the direction of eddy is opposite to the direction of
sound propagation, the effect of convective flow is opposite to that of eddy.
In other words, the convection effect moves the resonance peak in the
direction where the frequency is large, and the eddy effect moves the
resonance peak in the direction where the frequency is low. However, when
these are combined with the unique interaction properties of the acoustic
metamaterial, the widening property of the resonance peak appears. In short,
when all three effects cannot be ignored, competition phenomena appear with
each other, and as a result, the resonance peak widens and the intensity
decreases. In conclusion, the effects of convection, eddy, and intrinsic
interactions arising from the unique geometry of acoustic metamaterial appear
as the shift of the resonant frequency and the widening properties of the
resonant peak.

By using the shift of the resonant frequency and the widening property of the
resonant peak studied here, even when turbulence flows, it is possible to
block noise by properly controlling the geometric size and shape of the
acoustic metamaterial. In particular, this can be used to block noise in
transport systems such as train, car, and ship.

## Acknowledgments

It is a pleasure to thank Un Chol Ri, Yong Kwang Jong and Chol Su Ri for
useful discussions. This work was supported by the National Program on Key
Science Research of Democratic People’s Republic of Korea (Grant No. 20-15-5).

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#  ALTo: Ad Hoc High-Accuracy Touch Interaction Using Acoustic Localization

Arvind Seshan  Fox ChapelPA

###### Abstract.

Millions of people around the world face motor impairments due to Parkinson’s,
cerebral palsy, muscular dystrophy and other physical disabilities. The goal
of this project is to increase the usable surface-area of devices for users
with these disabilities by creating a simple, inexpensive, and portable way to
enable high accuracy touch interaction with large surfaces such as a table or
even a wall.

This project uses a novel approach that analyzes the acoustic signals at four
piezoelectric microphones placed on the interactive surface to identify sounds
related to the same event (e.g. a finger tap) at each of the microphones. ALTo
(Acoustic Localized Touch) uses the results of this signal processing to
compute the time difference of arrival (TDOA) across the microphones. The
collected TDOA data is used to compute an approximate location of a sound
source (e.g., a finger tap) using a collection of hyperbolic equations.

An experimental evaluation of a system prototype was used to identify a number
of software and signal processing optimizations needed to significantly
improve accuracy and create a usable system. The results of the research
indicate that it is possible to detect the location of a touch with high
accuracy. The ALTo prototype achieves an accuracy of 1.45cm in the x-direction
and 2.72cm the y-direction which is within the range for the target usage (ie.
those with motor impairments).

time difference of arrival, TDOA, HCI, touch interaction, acoustic
localization, piezoelectic discs, pseudo range multilateration, accessibility,
motor impairment

##  1\. Introduction

Mobile devices are becoming more and more important to daily life. Recent
studies estimate that almost 80 percent of all Americans (including children)
own a smartphone (sma, 2020b). These devices are also becoming more diverse;
most recently smart watches have become increasingly popular (1 in 6 adults in
the US own a smart watch) (Whitwam, 2019). The design of these devices face
two requirements that prove challenging to meet simultaneously. First, they
must be small enough to be unobtrusive – e.g., fit in a pocket or on a wrist.
Second, touch remains the predominant user interface and these devices must be
easy to interact with accurately. The result of these conflicting
requirements, is that devices are often as small as possible while providing a
usable touch surface.

While the end result has been numerous popular and useful devices, the
disappointing consequence of this design tradeoff is that they have become
inaccessible for those with motor impairments due to illness or age. These
users find it challenging to interact with such small surfaces (Naftali and
Findlater, 2014) (Findlater and Moffatt, 2017). Given the importance of these
devices to professional (e.g. email), social (e.g. Facebook), and emergency
(e.g. AMBER Alerts) communication, it is vital that these devices provide
better accessibility to all users.

Many mobile devices do provide a range of accessibility features, including
screen magnification support, larger text/UI element sizing, and UI elements
that are easier for users with motor impairment to use. However, none of these
address the fundamental issue that existing device screens are too small for
motor-impaired users to interact with. An alternative is to move to non-touch
interfaces such as voice. While voice interaction has improved dramatically
since the introduction of tools such as Apple Siri in 2011 (sir, 2020), voice
controls are not appropriate for many tasks where touch dominates and voice
controls cannot be used in many settings (e.g. in a classroom).

Figure 1. High-Level Vision for ALTo

The goal of this work is to address the fundamental issue of interactive
surface size by making it possible to use any nearby surface (e.g., a desk, a
wall or a chalkboard) for interaction. See Figure 1. This project introduces
an acoustic approach to solving the problem. It applies acoustic time
difference of arrival in a novel way to approximate the location of a user’s
tap on a large surface. This method allows for an inexpensive and portable
solution to achieve high-accuracy touch localization on any surface.

The study focuses on tapping because tapping is by far the most common
touchscreen interactive technique (Findlater and Moffatt, 2017). When a user
taps on a surface, microphones pick up the sound. The time it takes for the
sound to reach each microphone is directly related to the distance away from
the sound source. This principal is essential to finding the location of the
tap. The project analyses the difference in time between microphones to
approximate the location of a tap by computing a collection of hyperbolic
equations and solving for the intersection.

An experimental evaluation of the ALTo (Acoustic Localized Touch) system was
used to identify a number of software and signal processing optimizations
needed to significantly improve accuracy and create a usable system. The
results of the research indicate that it is possible to detect the location of
a touch with high accuracy.

The rest of this paper is organized as follows. Section 2 describes the design
for the ALTo system, including the system requirements and the methods used.
Section 3 focuses on the software design for both the data collection and
analysis portions of the project. Section 4 provides a detailed description of
the results and an analysis of the data from this study.

##  2\. System Overview

In this section, I describe the design of ALTo. I first describe the key
requirements that any system designed to provide ad hoc touch interaction for
mobile devices must address. Second, I discuss some of the underlying
techniques that ALTo relies on. Finally, I describe the details of the ALTo
design and implementation.

###  2.1. System Requirements

The goal of this system is to enable applications to use arbitrary surfaces as
an input source much like a touch screen or mouse. This would allow for a wide
range of application designs with larger interaction elements needed by motor-
impaired users. For example, the application or device could project an image
onto a surface for interaction (Figure 2). To enable such applications,
whenever the user taps a surface, the ALTo system must be able to determine
the (x,y) coordinates of taps and pass this information on to the application.

Figure 2. Interactive Surface Sample. Image Source: (Harrison, 2020)

In addition to meeting this high-level goal, the design of the ALTo system
needs to meet the following important requirements:

  * •

Instrumentation. There should be no prior instrumentation of the surface
required. Many existing approaches to enabling this type of interaction, such
as Smart Rooms (sma, 2020a) and gesture recognition systems (Nelson-Miller,
2020), require significant specialized infrastructure to be added to the room.
This may include cameras, active sensors, or beacons.

  * •

Portable. Any sensors or components needed by the system must be either
integrated into the mobile device or be similar in size/portability as the
mobile device. Given the battery life constraints of mobile devices, the
solution should use little if any power.

  * •

Surface Support. The user should be able to use a wide range of accessible
surfaces, which may be made of a variety of materials.

  * •

Accurate. The system must have high accuracy. User taps on a surface should be
localized with an error less than 2cm in any direction. This accuracy is based
on the target use by motor impaired individuals. Previous studies indicate
that those with motor impairments can have up to an 18mm error when using a
touch screen (Findlater and Moffatt, 2017).

  * •

Inexpensive. The system components must not add too much expense to the
device.

###  2.2. Approach: Multilateration

Based on these requirements, the project applies an approach known as
multilateration. This technique has been used since World War II in navigation
systems, but has been recently been replaced by the Global Positioning System
(GPS). Multilateration is also used in air traffic management and surveillance
systems (mul, 2020). Muiltilateration uses the Time Difference of Arrival
(TDOA), i.e. the different arrival times of a common source signal at each of
three or more receivers, to locate the position of a signal source.

Figure 3 illustrates the basic idea behind multilateration. If the user
creates a signal at the point indicated by the finger, the signal will
propagate outward from that point in all directions at a constant speed. In my
system, the user creates the signal by tapping a surface and the signal itself
is the acoustic wave that moves outward from this tap location through the
material of the surface. The movement of the signal is represented by the
concentric circles centered at the signal source. Each circle represents the
locus of points at which the signal is located after a particular delay after
the signal was generated. The delay is indicated as $t_{1},t_{2},t_{3}$ and
$t_{4}$. On the part (a) of the figure, the labels show the absolute time
after the tap was generated (i.e. time of the tap is 0 seconds). The green
points represent locations where the signal is observed by some type of
receiver, such as a sensor. If the absolute delay for the arrival of the
signal at each sensor and the speed of propagation of the signals is known, it
is easy to compute the distance from each sensor to the origin of signal. This
implies that the origin must be located on the circles drawn around each
sensor shown in part (c) of the figure. Finding the intersection of these
circles identifies the precise location of the signal origin. This approach is
known as true range multilateration. This approach requires knowing the
precise distance from each of the sensor to the signal origin, which was
determined based on the absolute time after the signal was generated. However,
in practice, the system will not know when the user signal (in this system,
when the user taps a surface) was generated.

In ALTo, the first observation of a signal is not when the tap is generated
but when the signal reaches the closest sensor. In Figure 3(b), the rightmost
sensor receives the signal at some time $t_{i}$. The signal still propagates
as it did in Figure 3(a), reaching each of the sensors at the appropriate
times. However, in this case each sensor simply observes when it receives the
signal relative to the time that the rightmost sensor received the signal. The
difference in time between any two sensors receiving the signal is equal to
the difference in distance to the signal source divided by the speed of the
signal. From this observation, any pair of sensors can determine that the
signal origin must be located along the locus of points on the surface that
have the computed distance difference between the sensors. The locus of points
with a constant distance difference from to points in space is known as a
hyperbola. Part (d) of the figure shows the hyperbolas that would be computed
indicating possible locations relative to the top-bottom sensor pair and
right-left sensor pair. Note only one half of a traditional mathematical
hyperbola is shown since the system knows that the signal source is closer to
one of the sensors in a pair due to the difference in delay that is measured.
In addition, the figure has only two hyperbolas drawn; however, the hyperbolas
between any sensor pair can be drawn based on the measurements shown in part
(a) of the figure. There are, in fact, six hyperbolas that can be drawn using
the 4 sets of sensors. In general, $n$ sensors would give information to
generate $n(n-1)/2$ total hyperbolic equations to use. As with true range
multilateration, the location of the signal source can be computed by
determining the intersection of the possible locations (i.e. the intersection
of the hyperbolas in this case). Note that while the drawings in Figure 3 show
the tap location within the set of sensors, the approach can localize taps
outside the set of sensors as well. This approach to localization is known as
pseudo range multilateration (aka TDOA multilateration or hyperbolic
navigation). ALTo uses pseudo range multilateration.

|
---|---
(a) | (b)
|
(c) | (d)
True Range | Pseudo Range
Multilateration | Multilateration
Figure 3. Illustration of multilateration techniques.

###  2.3. ALTo Hardware Design

The ALTo hardware design must address a few key issues. The first of which is
how to collect the sensor observations needed for pseudo range multilateration
while addressing the requirements described in Section 2.1.

The key components of the system are just the four piezoelectric disks to
detect sound propagation through a hard surface. Piezoelectric disks are
particularly good hardware for this project because they are inexpensive and
compact. In addition, they are relatively easy to attach to any surface with
some light adhesive and collecting observations from these sensors incurs
little additional energy cost to the mobile device.

Figure 4. ALTo hardware used in the prototype

The piezoelectric disks are connected to the microphone input of a computing
device. Four disks require the use of two stereo inputs. While most mobile
devices do not provide 2 sets of stereo inputs, the cost of such inputs is
relatively small. In my experimental testbed, I use a standard desktop
computer which has both a stereo microphone and line-in input for its standard
motherboard audio interface. To connect the piezoelectric two wire output to
the standard 3.5mm audio plug available on most computing devices, I
cannibalized a pair of earphones and soldered their ear-plug connecting wires
to the piezoelectric outputs. In later prototypes, I replaced the earphones
with a 3 screw terminal to 3.5mm headphone jack converter to provide a more
secure connection. (See Figure 4)

The above hardware design addresses several of the system requirements of
being portable, inexpensive and easy to implement. However, the key
requirement that is not clearly addressed is accuracy, especially across a
wide range of surfaces. I address this concern through the project. The main
challenge in addressing accuracy is that the time difference of arrival
measurements made by the sensors must be precise. The speed of sound in air
(at temperature 32C) is approximately 1260 km/h or 350 m/s. However, the speed
of sound in materials such as wood is much faster, 3500 m/s, with some
variation depending on the type of wood. This means that the sound signal can
travel 1cm in a surface in as little as 1/350000 s or 3$\mu$s. The
measurements from the system need to be accurate within this time range to
provide the level of accuracy desired. This requires careful software design
which I describe in Section 3.

Figure 5. Flowchart representing the high level software structure for data
collection with a single sensor. Figure 6. Flowchart representing the high
level software structure for the two dimensional location estimate.

##  3\. ALTo Software Design

There are two major parts of the ALTo software – data collection and analysis.

###  3.1. Data Collection

The Flowchart in Figure 5 provides a high-level view of the code used to
collect the needed sensor readings from a pair of piezoelectric microphones.
The code (listed in Appendix A) to implement this data collection is written
in Python3 and uses the pyaudio library to collect and process audio data.
Using pyaudio, the audio interface is configured with a sample rate and a
buffer size. A read from the audio device completes when the buffer is full at
which point the system returns a chunk of audio sample data for the left and
right audio channels (i.e. the two piezoelectric microphones). This is where
the flowchart begins with the step ”Read next chunk”. The audio samples in the
chunk are encoded as 16-bit values representing the amplitude of the audio
signal at that time in the recording. A value above 1000 for the sample
amplitude indicates a loud noise such as a tap on the surface. The code in the
function hit_test() iterates over the samples of a chunk looking for value
above 1000. This is done for both the data from the left and right audio
channels. If a loud noise was found in both audio channels, the sample number
of the start of the loud sound is recorded for each channel and compared.
Depending on which channel detected the tap noise earlier, the difference in
sample number is computed (as either left_sample_number - right_sample_number
or right_sample_number - left_sample_number). This difference in sample number
is converted to a time difference by dividing by the configured sampling rate
of the audio device.

Extending this data collection to use four sensors adds some additional
complexities. As shown in Figure 6, I begin by replicating the data collection
workflow from the left and right sensor to the top and bottom sensor. Each
pair of sensors is on a different audio device. As a result, the reading and
processing of chunks is done independently. For example, the left and right
sensors read of audio data always completes at the same time and their chunks
are processed together. Similarly, the top and bottom sensor reads also
complete simultaneously and are processed together. However, there is no
relationship between the timing of left/right to top/bottom data read
completion times. The implication of this is that the time difference
computation between the matching pair of sensors (e.g. left and right) based
on a natural common synchronized timing – the sample number from the
associated audio interface. However, to compare the time difference from a
signal between a non-matching pair (e.g. right and up sensors) requires that
the system compensates for the timing offset of their different audio device
reads. I found that the accuracy requirements of the system made this
impractical. As mentioned in Section 2.3, ALTo requires accuracy on the order
of $\mu$s. Introducing cross-device synchronization introduces too much error
to meet this accuracy goal. As a result, I chose to rely solely on the time
differences computed by paired sensors as part of tap localization.

Another challenge associated with the four sensor configuration was supporting
concurrent processing of the independent sensor feeds. There were four
different designs tested for this purpose:

  * •

Sequential. I began by using sequential reads of the audio device, relying on
the buffering associated with the pyaudio interface to accommodate sequential
processing of the data feeds. Unfortunately, this proved too slow and audio
samples were dropped by the system, resulting in a non-working system.

  * •

Python Threads. The data collection system was tested using a single python
thread for each audio device. This would allow the devices to collect and
process data concurrently and still share data in a light-weight fashion.
Unfortunately, Python’s Global Interpreter Lock (GIL) (GIL, 2020) prevents
Python threads from making use of multiple CPU cores. As a result, the delays
between getting a particular thread scheduled for execution were significant.
This also resulted in a non-working system design. It may have been possible
to use more recent Python extensions for multiprocessing support; however, I
choose to consider other options.

  * •

Asynchronous Callbacks. The pyaudio system supports asynchronous callbacks to
perform processing when audio data was ready. This allows light-weight
multiplexing of audio processing. However, while this performed better than
the sequential implementation, it also suffered from performance problems that
made it non-working.

  * •

Multiple Processes. The fourth approach was to use multiple independent Python
processes – one per audio device used. Since these are independent processes
they can run on concurrently on independent CPU cores - eliminating any issues
with scheduling or resource contention. The key challenge was sharing the
output from the two devices to compute an output coordinate. This could be
done using a variety of inter-process communication methods, including
sockets, shared memory, pipes or files. The goal of the current prototype is
to show the feasibility of the approach, and, as a result, I choose to record
the data and use an offline process to compute the tap coordinates.

Figure 7. Sensor pair data analysis. Image Source: (Learning, 2020)

###  3.2. Data Analysis

Once a time difference between a pair of sensors is computed, ALTo converts
this to an distance estimate, $\Delta$, based on measurements of the speed of
sound in the surface being used (Section 4.3). Note that knowing the speed of
sound is not necessary if applications do not need coordinate values in terms
of normal units. For example, computations and calibrations can be made in
terms of the size of a used region rather than absolute measurements. Here, I
keep the discussion in terms of real units to simplify any descriptions.

The distance $\Delta$ that is computed above is the difference in distance of
the tap location relative to the two sensors. Figure 7 helps illustrate this
visually. The coordinate $(-c,0)$ and $(c,0)$ represent the coordinates of the
two sensors. If the user tapped at location $(x,y)$, the distance to the two
sensors would be $d_{1}$ and $d_{2}$. The distance $\Delta$ represents the
value of $(d_{2}-d_{1})$. Note that there are many locations in the two-
dimensional surface that would have this same difference in distance. The
collection of such points describes the hyperbola shown in the Figure. For
this particular hyperbola, $a=\Delta/2$ since the intercept with the x-axis is
at $(a,0)$.

In my prototype of ALTo (described in Section 4.3, the left and right sensors
are located 26cm away from the origin. Given a measurement $\Delta$ and its
corresponding x-axis intercept $a$, the equation describing the relevant
hyperbola would be:

(1) $\frac{y^{2}}{(26-a)^{2}}-\frac{x^{2}}{(26^{2}-(26-a)^{2})}=1$

This simplifies to:

(2) $\frac{y^{2}}{(26-a)^{2}}-\frac{x^{2}}{(52a-a^{2})}=1$

The prototype also has top and bottom sensor located vertically 26cm away from
the origin. Given a measurement $\Delta$ for the signal arrival between these
sensors, ALTo computes a corresponding y-axis intercept $b=\Delta/2$. This
hyperbola is described by the equation:

(3) $\frac{x^{2}}{(26-b)^{2}}-\frac{y^{2}}{(26^{2}-(26-b)^{2})}=1$

This simplifies to:

(4) $\frac{x^{2}}{(26-b)^{2}}-\frac{y^{2}}{(52b-b^{2})}=1$

Solving these equations simultaneously, results in:

(5)
$x=\pm\frac{(a-26)\sqrt{b}\sqrt{-(-a^{2}b+52a^{2}+52ab-2704a+b^{3}-104b^{2}+3380b-35152)}}{\sqrt{-(676a^{2}-35152a+676b^{2}-35152b+456976)}}$

(6)
$y=\pm\sqrt{\frac{(-a^{4}+a^{2}x^{2}+104a^{3}-52ax^{2}-3380a^{2}+35152a)}{(-a^{2}+52a-676)}}$

Note that using the two hyperbola equations produces four intersections. To
determine which intersection is the correct one, I looked at which sensors
detected the tap first. The tap must be closer to the ones that detected the
tap first. (e.g. if the top sensor and right sensor detected the tap before
the bottom sensor and left sensor respectively, the tap must be in the
intersection that is in Quadrant I). This produces a single $(x,y)$ that ALTo
can provide to programs to use.

##  4\. Experimental Results

The goal of this experimental evaluation is to show that ALTo can provide
accurate $(x,y)$ coordinate information for applications to use. This done
through a sequence of experiments that:

  * •

Show that a ALTo can accurately measure the change in signal delays as a
user’s taps move from one sensor to another (Section 4.1)

  * •

Show that adjustments to the sampling rate can improve accuracy (Section 4.2)

  * •

Compute the speed of sound in using a prototype (Section 4.3)

  * •

Measure the $(x,y)$ accuracy of ALTo (Section 4.4)

---
(a) Logical diagram of 1D prototype
(b) Image of physical 1D prototype
Figure 8. Prototype to evaluate accuracy of ALTo with a single sensor pair.

###  4.1. Baseline Test for Linearity

To evaluate the feasibility of ALTo, I began with a simple experiment to
measure one dimensional accuracy, only using two piezoelectric disks. The
configuration of this prototype used for this experiment is shown in Figure 8.
I tapped every 2.5 centimeters only along a line between the two microphones.
This simplified the analysis of the data since the measured time difference
would simply be proportional to the progress along the line. At each location,
I tapped ten times to determine how consistently the program readings were for
specific locations.

Figure 9 (a) shows that the time difference of arrival (TDOA) follows linear
relationship to the difference in distance between two microphones. This is
expected because the speed of sound should be a constant through this
material. The correlation coefficient, or $R^{2}$ value, was high, showing
that the data has a very strong linear correlation. Figure 9 (b) shows the
standard deviation at each location of data collection. While the standard
deviation may seem small, in relation to the expected time difference, it was
very high. The variability of the readings was relatively high compared to the
magnitude of the readings. This produces inaccurate distance estimates.

(a) Plot of the time difference between the two piezo disks as the tap
location changes  (b) Standard deviation at each tap location

Figure 9. Test of one dimensional accuracy at 44100Hz

###  4.2. Impact of sampling frequency on accuracy

The source of the inaccuracy in the above experiements is the fact the speed
travels very quickly and the resulting TDOA is very small. For example, the
default configuration of the audio device is to sample at 44100 Hz. Even
traveling through air, sound travels approximately 0.78cm in 1/44100 seconds.
In a hard surface like a wooden board, it travels even more quickly.

To address this issue, I explored the use of higher sampling frequencies. I
altered the sampling rate from 44100 Hz to 192000 Hz. This significantly
reduced the variability of the readings. This can be seen by the much lower
standard deviation values in Figure 10 (b). The readings were more accurate
and provided a better $R^{2}$ value as well, as shown in Figure 10 (a).

---
(a) Plot of the time difference between the two
piezo disks as the tap location changes
(b) Standard deviation at each tap location
Figure 10. Test of one dimensional accuracy at 192000 Hz.
---
(a) Logical diagram of 2D prototype
(b) Image of physical 2D prototype
Figure 11. Prototype to evaluation accuracy of ALTo with a two sensor pairs
for $(x,y)$ tap localization.

###  4.3. Surface Calibration

In order to make the algorithm function on multiple surfaces with varying
acoustic properties, I needed to create a system for calibrating to a surface.
This experiment was executed on a 2D prototype depicted in Figure 11. This
prototype has 2 pairs of piezoelectric sensors to enable full 2D localization
of taps. The goal was to have ALTo produce $(x,y)$ coordinate pairs on this
board that represented absolute measurements using centimeters. To achieve
this goal, I needed to measure the speed of sound in the board’s material.

For the calibration, I recorded 10 taps at each centimeter along the x and y
axis of my board and recorded the difference in time to the sensor pair along
that axis. Figure 12 shows a plot of the difference in distance on the y-axis
and the difference in time on the x-axis. I performed a linear fit to the data
on this graph. Note that the slope of the linear trendline is the speed of the
sound through the material in centimeters per second. Surprisingly, the speed
of sound was different in the x and y direction - 45014cm/s in the x direction
and 37259cm/s in the y direction. I conjecture that this is due to the
inconsistencies in the material. For example, it is known that the grain of
wood can impact the propagation of sound (Montes, 2005).

---
(a) Data for the x direction
(b) Data for the y direction
Figure 12. Plot of the time difference between the two piezo disks as the tap
location changes. Error bars on the graph represent standard deviation.

###  4.4. Overall accuracy in two dimensions

The final test to analyze the accuracy of ALTo was to do a test along a two
dimensions coordinate plane. This allowed me to analyze the accuracy and
precision of the data when the x-coordinate and y-coordinate system is
combined. I tapped 10 times every 10cm along the coordinate plane to test the
accuracy and precision after combining x and y data. Accuracy is the deviation
of the data from the colored square in Figure 13. Precision is represented by
the error bars that indicate standard deviation. The data shows that tap
detection was highly accurate and precise because of closeness of the data to
the expected position and the small error bars. Overall, the average of the
absolute value of the error is 1.45cm in the x direction and 2.72cm in the y
direction. In Figure 13, it is noticeable that the lower half of the board has
y-coordinate estimates that are biased lower than the actual tap location. I
conjecture that this is a result of non-uniform sound propagation in the
underlying material. This could be caused by factors such non-uniform density
of the material, or defects such as cracks or knots in wood (Montes, 2005).

As mentioned in Section 2.1, my goal was to get accuracy in the range of that
needed by motor impaired users - i.e. around 2cm. The system prototype is
close to achieving this target and there are promising ways to improve
accuracy further as discussed in Section 5.

Figure 13. Two dimensional coordinate plane with tap locations every 10 cm.
Error bars represent standard deviation. The squares represent the true
location of the taps. Data points are colored to match their corresponding
square’s color.

##  5\. Discussion

The results shared in the previous section indicate that acoustic
multilateration is a viable method for touch localization. Furthermore, the
project proves that a portable, accurate, and inexpensive solution can be
created to address the issue of small touch interactive surface area. No prior
instrumentation is necessary, allowing for an easy to implement solution. The
issue of varying surfaces is addressed though a calibration system that
calculates the speed of the acoustic impulse through the material. Although
the project met the main constrains defined at the beginning of the paper,
there are some limitations. These limitations include the following.

  * •

Surface Material. The reliability of the data varies slightly by surface based
on its acoustic properties. While the calibration does help, there is still
lower accuracy. This may be because the sound does not travel in a perfectly
linear fashion in some materials. The issue may be caused by factors such as
metal supports under a table or warps in wood. This could be fixed by
computing a non-linear model of the sound wave through the surfaces or by
using machine learning techniques to identify a piece-wise linear fit for
sound propagation speeds across the material surface.

  * •

Detecting the start of the acoustic impulse. Currently, the software uses an
amplitude over a certain value to detect a tap. However, based on the loudness
of the tap, this can vary. This causes error because when one microphone is
further away from another, the sound is less loud to that microphone (lower
amplitude values). One way to fix this is to match up the shape of the
amplitude to find the actual start. Using this approach, ALTo may also be able
to support interactions beyond just taps. For example, ALTo may be able to
track drawing operations by continuously matching the sounds shapes heard
across different microphones.

  * •

Streamlining software. Currently, the software is split into two separate
python programs with most of the analysis done later. In the future, the
software could be created into one single program that does all of the
computation at once.

##  6\. Related Work

As mentioned earlier, multilateration is not a new concept. It has been used
in air traffic control systems and pre-GPS systems for localization.

The Toffee system from CMU (Xiao et al., 2014) uses similar acoustic TDOA
methods to estimate the angle of a tap relative to the device to create
virtual buttons on large surfaces. ALTo differs from this project as it aims
to accurately identify the exact location of a tap anywhere along a coordinate
plane with high accuracy, allowing for a much more natural mapping of existing
application designs to arbitrary surfaces.

Accurate acoustic-based localization has been used in a variety of other
systems. For example, many smart whiteboard systems (e.g., (Arch, 2019))
localize pens using an ultrasonic transmitters located in the pen along with
microphones embedded in the whiteboard. Similarly, past research (e.g.,
Cricket from MIT (Priyantha et al., 2000)) has explored the use of ultrasonic
transmitters embedded in the environment to help mobile devices localize
themselves. These systems differ from ALTo in that they all use active
transmitters to help in localization. As a result, they either require power
or infrastructure deployed in advance. In addition, using natural sounds such
as taps prove more difficult to localize accurately.

##  7\. Conclusion

The results of the study prove that acoustic localization can be used to
detect touch interaction on large surfaces with high accuracy. This is a
promising first step towards creating a simple way to make any surface touch-
interactive.

The system created in this project fulfills the requirements.

  * •

It is able to transform any surface into a touch interactive surface. No prior
installation of materials or change to the room is required.

  * •

It is small and easy to implement as it only requires inexpensive
piezoelectric disks

  * •

It is able to accurately identify the origination of a tap.

Some of the next steps are to test on even larger surfaces and create specific
zones where a user can tap and see how small the zones can be and still
maintain accuracy.

## References

  * (1)
  * mul (2020) 2020\.  http://www.multilateration.com/index-2.html
  * GIL (2020) 2020\.  Global Interpreter Lock.  https://wiki.python.org/moin/GlobalInterpreterLock
  * sir (2020) 2020\.  Siri.  https://www.apple.com/siri/
  * sma (2020a) 2020a.  Smart Room.  https://vismod.media.mit.edu/vismod/demos/smartroom/
  * sma (2020b) 2020b.  Top Countries by Smartphone Users.  https://newzoo.com/insights/rankings/top-countries-by-smartphone-penetration-and-users
  * Arch (2019) Arch. 2019.  Interactive Board Ultrasonic Open Source.  https://www.techjunkie.com/interactive-board-ultrasonic-open-source/
  * Findlater and Moffatt (2017) L Findlater and et. al Moffatt, K. 2017.  Comparing Touchscreen and Mouse Input Performance by People With and Without Upper Body Motor Impairments. In _Proceedings of the 2016 CHI Conference on Human Factors in Computing Systems_. 1934–1946.  http://dx.doi.org/10.1145/3025453.3025603
  * Harrison (2020) Chris Harrison. 2020\.  Desk Topography.  https://www.chrisharrison.net/index.php/Research/Desktopography
  * Learning (2020) Lumen Learning. 2020\.  Equations of Hyperbolas.  https://courses.lumenlearning.com/waymakercollegealgebra/chapter/equations-of-hyperbolas/
  * Montes (2005) ETSI Montes. 2005\.  Acoustics of Wood.  http://www.multilateration.com/index-2.html
  * Naftali and Findlater (2014) M. Naftali and L. Findlater. 2014.  Accessibility in Context: Understanding the Truly Mobile Experience of Smartphone Users with Motor Impairments. In _Proceedings of ASSETS_. 209–216.  https://faculty.washington.edu/leahkf/pubs/ASSETS2014-naftali.pdf
  * Nelson-Miller (2020) Nelson-Miller. 2020\.  What is Gesture Recognition Technology and How Does It Work?  http://www.nelson-miller.com/gesture-recognition-technology-work/
  * Priyantha et al. (2000) Nissanka B. Priyantha, Anit Chakraborty, and Hari Balakrishnan. 2000.  The Cricket Location-Support System. In _Proceedings of the 6th Annual International Conference on Mobile Computing and Networking_ _(MobiCom ’00)_. Association for Computing Machinery, New York, NY, USA, 32–43.  https://doi.org/10.1145/345910.345917
  * Whitwam (2019) Ryan Whitwam. 2019\.  1 in 6 US Adults Now Own a Smartwatch.  https://www.extremetech.com/mobile/285724-1-in-6-us-adults-now-own-a-smartwatch
  * Xiao et al. (2014) Robert Xiao, Greg Lew, James Marsanico, Divya Hariharan, Scott Hudson, and Chris Harrison. 2014\.  Toffee: Enabling Ad Hoc, around-Device Interaction with Acoustic Time-of-Arrival Correlation. In _Proceedings of the 16th International Conference on Human-Computer Interaction with Mobile Devices and Services_ _(MobileHCI ’14)_. Association for Computing Machinery, New York, NY, USA, 67–76.  https://doi.org/10.1145/2628363.2628383

##  Appendix A Code

###  A.1. Horizontal Left-Right Sensors

Below is the code for collecting data from the left and right sensors. Note
that the data collection process for the other two sensors is similar and
omitted for space.

⬇

1try:

2 import os

3 import pyaudio

4 import numpy as np

5 import pylab

6 from pylab import *

7 import matplotlib

8 import matplotlib.pyplot as plt

9 from scipy.io import wavfile

10 import time

11 import sys

12 import seaborn as sns

13 import threading

14 import logging

15 import math

16except:

17 print ("Something didn’t import")

18## open(’leftsamples.txt’, ’w’).close()

19## open(’rightsamples.txt’, ’w’).close()

20

21hit = False

22hit1 = False

23hit2 = False

24hit3 = False

25done = False

26counter=0

27i=0

28FORMAT = pyaudio.paInt16 # We use 16bit format per sample

29CHANNELS = 2

30RATE = 192000 #192000

31CHUNK = 8192 # (8192) 1024bytes of data read from a buffer

32RECORD_SECONDS = 0.1

33WAVE_OUTPUT_FILENAME = "file.wav"

34left_channel = 0

35right_channel = 1

36

37audio = pyaudio.PyAudio()

38

39# start Recording

40stream = audio.open(format=FORMAT,

41 channels=CHANNELS,

42 rate=RATE,

43 input_device_index = 1,

44 input=True)

45

46global keep_going

47keep_going = True

48

49def hit_test (piezo, amplitude):

50 for x in range(len(piezo)):

51 if abs(piezo[x]) >= amplitude:

52 return x

53 return False

54

55def detect_tap_lr() :

56 global hit

57 global hit1

58 global ltime

59 global rtime

60 global ltime2

61 global rtime2

62 global location

63 global counter

64 global done

65

66 if done==False:

67 if hit_test(left_samples, 1000) != False :

68 ltime = ((hit_test(left_samples, 500))/RATE)

69 hit = True

70 if hit_test(right_samples, 1000) != False :

71 rtime = ((hit_test(right_samples, 500))/RATE)

72 hit1 = True

73 if hit==True and hit1==True:

74 list = [ltime, rtime]

75 if list.index(min(list)) == 0 :

76 ltime2=0

77 rtime2=rtime-ltime

78 location=-22248.5249228*rtime2+26.4164968363

79 if list.index(min(list)) == 1 :

80 ltime2=ltime-rtime

81 rtime2=0

82 location=22557.1202678*ltime2+26.6288158189

83 hit = False

84 hit1 = False

85 done=True

86 counter=0

87 print(ltime2, rtime2, location)

88 print(hit_test(left_samples, 500), hit_test(right_samples, 500))

89 print("good")

90

91## with open(’leftsamples.txt’,’ab’) as f:

92## np.savetxt(f, left_samples, fmt=’%5d’, delimiter=’,’)

93## with open(’rightsamples.txt’,’ab’) as f:

94## np.savetxt(f, right_samples, fmt=’%5d’, delimiter=’,’)

95

96 else:

97 if counter>4:

98 done=False

99 counter = counter+1

100

101# Open the connection and start streaming the data

102stream.start_stream()

103print ("\n+---------------------------------+")

104print ("| Press Ctrl+C to Break Recording |")

105print ("+---------------------------------+\n")

106

107# Loop so program doesn’t end while the stream callback’s

108# itself for new data

109while keep_going:

110 try:

111 # When reading from our 16-bit stereo stream, we receive 4 characters
(0-255) per

112 # sample. To get them in a more convenient form, numpy provides

113 # fromstring() which will for each 16 bits convert it into a nicer form
and

114 # turn the string into an array.

115 raw_data = stream.read(CHUNK) # always read a whole buffer.

116

117 samples = np.fromstring(raw_data, dtype=np.int16)

118 # Normalize by int16 max (32767) for convenience, also converts everything
to floats

119 # normed_samples = samples / float(np.iinfo(np.int16).max)

120 # split out the left and right channels to return separately.

121 # audio data is stored [left-val1, right-val1, left-val2, right-val2, ...]

122 # so just need to partition it out.

123 left_samples = samples[left_channel::2]

124 right_samples = samples[right_channel::2]

125

126 detect_tap_lr()

127

128 except KeyboardInterrupt:

129 keep_going=False

130

131# Close up shop (currently not used because KeyboardInterrupt

132# is the only way to close)

133stream.stop_stream()

134stream.close()

135

136audio.terminate()