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第三届“认证杯”数学中国
数学建模国际赛
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我
们的参赛队号为：
1570
我们选择的题目是：
A
参赛队员
(
签名
)
：
队员
2
：李兴
队员
3
：高
安森
参赛队教练员
(
签名
)
：
无
队员
1
：魏祯
Team
# 1570
Page 2 of 17
第三届“认证杯”数学中国
数学建模国际赛
编
号
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用
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参赛队伍的参赛队号：（请各个参赛队提前填写好）：
#1570
竞赛统一编号（由竞赛组委会送至评委团前编号）：
竞赛评阅编号（由竞赛评委团评阅前进行编号）：
Team
# 1570
Page 3 of 17
The most
resounding whistle
Abstract:
In
this
report,
through
the
analysis
of
factors
affecting
the
whistle
sounding loudness, we build gas unitary
flow model and multi structure
model.
In model 1, using the mass conservation equation
and continuity
equation of flow of
energy conservation in, obtained the density,
velocity,
relationship quality force
was established, so that the energy to keep the
optimal
combination
of
maximum;
in
model
2,
through
the
method
of
control variables, to study the impact
of different mouth size on loudness,
simulate and repeated experiments, the
structure and size of the whistle
body
that the strongest sound. Combined with the model
two and model,
we design the loudest
whistle.
Key words:
sounding loudness
gas unitary flow model
energy conservation
the mass
conservation
Team
# 1570
Page 4 of 17
Introduction:
The
whistle ,a device which is through the air quickly
pressed into a
narrow
space
within
the
device
caused
by
the
airflow
disturbance,
sounding
device
to
send
a
strong
sound.
Whistle
in
the
life
and
production have been widely used.
Traffic police using whistles to guide
the vehicle through, soldiers through
the emergency buzzer to achieve the
aim
of
urgent
collection,
sports
events,
refereeing
to
decisions
and
guidance
game
by
whistle,
when
people
are
in
danger,
they
send
out
a
signal of
distress through an intense whistle . So often the
high quality of
whistles
can
play
an
important
role
in
production
and
life.
So
can
we
design a sufficiently
loud whistle is the key to improve the quality of
life
and production efficiency?
Assumptions:
?
The whistle
sound is caused by air turbulence caused by the
vibration,
the airflow of different
intensity will affect the intensity of the sound a
whistle.
?
Humidity and velocity of sound and the
air whistle, the humidity of
the
air
will
cause
varying
degrees
of
impact
on
air
quality,
sound
quality, different
velocity of air will send out different sounds.
?
The sound and
the gas whistle by friction. Will cause friction
whistle
acoustic
energy
body
loss,
would
seriously
weaken
the
intensity
of
sound.
Team
# 1570
Page 5 of 17
?
Flow
fields
disturbance
affected
by
the
whistle
sound,
different
air
will
take
different
routes,
so
that
the
formation
of
the
flow
field
of
different distribution, will cause the
pressure differences occur, which
affects the intensity of the sound.
?
Sound and
whistle on the materials, different materials have
different
timbres,
different
timbres
will
also
affect
the
intensity
of
the
sound
change, so, change
material can also cause the intensity of sound.
?
About
the
reflectivity
of
sound
and
acoustic
whistle
acoustic
reflectivity
assembly, reduces energy loss is reduced in the
process of
communication, which will
increase the intensity of the sound.
?
The structure
and size of sound and the whistle body ,whistle,
whistle
body
concerned,
different
structure,
its
internal
air
flow
will
form
different
can
also
cause
the
occurrence
of
different
strengths,
whistling size will affect the airflow
reversal form, cause significant
influence
on
the
frequency
of
sound
and
vibration,
so
the
structure
and size of the
whistle body Will affect the intensity of the
sound a
whistle.
Problem
analysis:
◆
Problem1
The mechanism of whistle is a complex
process, improve whistle sound
intensity also need some practical
ways. Whistle sound intensity internal
Team
# 1570
Page 6 of 17
and
external
factors.
We
simulate
the
sound
of
a
whistle
relationship
between the factors and the strength
through modeling approach. We will
whistle the air velocity is coupled to
the energy equation and the quality
equation,
caused
by
differences
in
the
energy
flow
rate
established
for
different correlation
equation between the two. Through a comprehensive
analysis of all aspects, and a
discussion of the simulation results of the
model,
and
thus
more
targeted
to
improve
the
strength
of
the
whistle
sound.
◆
problem 2
Through the
whistle sound
intensity
analysis of the
actual situation,
we
found
that
many
factors
will
affect
the
whistle
sound
intensity.
Whistle
sound velocity gas intensity, structure
and whistle of the material, as well
as
the degree of airflow disturbances related to
whistle, but the impact of
the
size
of
the
whistle
sound
intensity
is
more
obvious,
therefore,
our
impact
on
the
sound
of
the
whistle
dimension
of
intensity
were
appropriate model simulation, and made
a further in-depth study. We have
to
study
through
the
use
of
modeling,
and
control
variables
method,
to
explore
the
extent
of
the
impact
on
the
size
of
whistle
whistle
sound
intensity. By controlling the whistle
body make the same amount of gas
entering and sonic vibration image
issued by software simulation whistle.
Variable Declaration:
Team
# 1570
Page 7 of 17
V
Local mean
velocity
?
n
Total friction
caused by viscous and turbulent
q
Heat flux intensity
F
Unit mass force
P
Local pressure
?
Local air density
T
The
local temperature
V
The study on the volume of
fluid within the given time t
S
Surface volume V
v
n
The normal velocity
F
1
The area of the side cross sectional
area of A
F
2
The area of the side cross sectional
area of A
?
Specific internal energy
?
Per unit time
per unit mass release of heat
d
Width
A
Amplitude
Model
establishments:
As everyone knows,
there are a lot of reasons affecting the whistle
sound, sound and gas flow velocity of
the whistle gave a whistle whistle,
structure, materials, elements of sound
reflectivity and the turbulence
degree
have close relationship. The occurrence of
waveform figure
whistle, we can know
the whistle waveform is some continuous sine
Team
# 1570
Page 8 of 17
wave, so how to
increase the wave crests or troughs has become the
key
to increase the whistle sound.
Figure 1: the energy trend
Model
1
Through
the
analysis
,we
know
that
the
air
velocity
will
affect
the
intensity of the sound of the whistle
whistle, through different velocity of
air
would
directly
into
the
whistle
caused
by
different
energy,
different
energy will cause
the intensity of the sound emitted by a marked
change,
so, through the analysis of the
simulation result can formula of different
the
flow
velocity
and
sound
intensity.
Below
is
the
three-
dimensional
simulation
maps
between
acoustic
frequency
and
sound
decibels
by
below, we can analyze the frequency of
sound, the greater the greater the
decibel of sound wave, the frequency of
sound is small and its acoustic
decibels
is
smaller,
therefore,
appropriate
frequency
can
increase
the
frequency
of
sound,
so
as
to
increase
the
loudness
of
sound.
In
flow