ASSESING
THE
EFFECTS
OF
TEMPERATURE
ON
UNDERWATER
ACOUSTIC
WAVE
ATTENUATION
Group
6:
Elizabeth
Subjeck,
Steven
Gillmer*,
Andrew
Scala
4/28/2010
Abstract
We
have
developed
a
method
to
measure
the
effects
of
temperature
variation
on
underwater
acoustic
wave
attenuation
at
shallow
depths
over
short
distances.
We
determined
that
the
optimal
spacing
of
the
transducers
in
a
wider
tank
was
11
cm
compared
to
the
5
cm
spacing
used
in
a
narrower
tank.
These
results
indicate
that
the
resonant
frequency
of
the
walls
of
the
tank
have
a
negative
impact
on
the
quality
of
sound
propagation
through
the
water.
Likewise,
we
determined
that
increasing
the
angle
of
the
transducers
with
respect
to
one
another
also
greatly
deteriorated
the
quality
of
results.
After
carrying
out
our
experiment
at
various
temperatures,
we
found
that
our
voltage
received
by
the
transducer
decreased
with
increasing
temperature.
We
determined
a
relationship
between
Attenuation
and
voltage
and
proved
that
sound
attenuation
increases
with
increasing
temperature.
Introduction
The
ability
of
sound
to
move
through
a
medium
is
essential
for
communication.
While
the
medium
humans
normally
encounter
is
the
air
around
us,
water
is
also
a
very
common
medium,
as
can
be
seen
by
the
importance
of
the
sonar
systems
used
for
both
military
and
civilian
oceanic
operations.
The
use
of
devices
such
as
underwater
speakers
and
sound
systems
is
also
affected
by
the
way
sound
moves
in
this
medium.
The
aforementioned
propagation
of
sound
waves
underwater
depends
mainly
on
three
factors:
salinity,
pressure,
and
temperature.
We
are
investigating
the
effects
of
temperature
on
the
attenuation
of
acoustic
waves
through
water.
Attenuation
is
formally
defined
as
“a
weakening
in
force
or
intensity,”
[1].
Therefore,
a
lower
attenuation
would
refer
to
a
stronger
signal,
as
less
of
it
is
weakened,
while
a
higher
attenuation
refers
to
a
dimmer
signal.
Studying
the
effects
of
temperature
on
acoustic
propagation
will
facilitate
a
better
understanding
of
how
these
variations
affect
communication
for
both
manned
underwater
craft,
like
submarines,
as
well
as
in
smaller
scale
applications
such
as
underwater
speakers
in
a
swimming
pool.
We
propose
to
generate
acoustic
waves
in
a
relatively
shallow
water
tank
under
varying
temperature
conditions.
We
will
determine
how
the
attenuation
changes
as
a
result
of
water
temperature
variation.
A
great
deal
is
already
known
about
underwater
sound
propagation
under
varying
temperatures
over
large
distances
and
at
great
depths
[2].
However,
little
research
has
been
done
to
investigate
the
variation
of
acoustic
waves
at
shallow
depths
and
over
short
distances
(which
could
be
very
applicable
to
swimming
pool
speakers).
Therefore,
we
hope
to
shed
some
light
on
the
matter
by
conducting
our
experiment
in
such
an
environment.
We
hypothesize
that
the
sound
wave
will
have
a
lower
attenuation
at
higher
temperatures
based
on
our
knowledge
of
the
fact
that
the
velocity
of
sound
increases
as
temperature
increases
[2].
2
The
kinetic
energy
equation
of
moving
fluids
creates
a
directly
proportional
relationship
between
fluid
velocity
and
kinetic
energy:
KE=1/2MV2
(1)
Where
M
is
defined
as
a
mass
flow
rate
of
the
fluid
in
equation
1.
Even
if
the
equation
comparing
acoustic
wave
energy
and
wave
velocity
is
slightly
different
than
this
kinetic
energy
equation,
intuitively
we
feel
that
no
matter
the
substance
being
measured,
energy
and
velocity
should
be
directly
proportional.
Therefore,
we
believe
that
there
should
be
less
attenuation
where
there
is
a
greater
energy
(at
higher
temperatures
with
higher
velocities).
In
addition
to
testing
acoustic
attenuation
with
temperature,
we
also
wanted
to
investigate
the
effects
of
transducer
alignment
and
the
effects
of
the
resonant
frequencies
from
the
tank
walls
on
the
quality
of
the
sound
signal.
We
hypothesize
that
even
slight
misalignment
of
transducers
will
reduce
the
quality
of
our
results,
and
likewise,
the
resonant
frequencies
from
the
walls
of
the
tank
will
interfere
with
our
acoustic
signal
and
diminish
our
readings.
Both
of
these
studies
will
serve
as
preliminary
investigations
to
improve
the
quality
of
our
results
when
testing
with
varying
temperatures.
Formulation/
Procedure
In
2009,
Jenson
and
Anderson
(referred
to
as
“JA”
below)
[3]
performed
a
similar
experiment
in
which
they
tested
the
dependence
of
underwater
acoustic
velocity
on
varying
salinity
levels.
Our
project
will
follow
a
similar
procedure,
but
we
will
change
temperature
instead
of
salinity.
JA
used
a
long,
narrow
tank
for
their
testing
(Dimensions
in
Appendix
A,
Table
1),
and
they
hypothesized
that
a
larger
tank
would
have
increased
the
quality
of
results
by
reducing
the
interference
of
the
resonant
frequencies
from
the
tank
wall.
Unfortunately,
time
ran
short
and
they
were
never
able
to
test
their
theory.
Therefore,
we
chose
a
deeper
and
wider
tank
than
JA,
hoping
this
would
cause
less
interference
in
the
waves,
giving
us
better
results.
The
dimensions
of
our
new
tank
can
be
seen
in
Table
1
below.
We
3
calculated
the
resonant
frequencies
from
the
walls
of
our
tank,
in
a
similar
manner
to
JA.
Since
the
first
resonant
frequency
would
occur
at
½
the
length
of
the
tank,
we
used
equation
2,
where
T
is
the
period,
L
is
the
tank
length
and
c
is
the
speed
of
sound
in
water
at
room
temperature
(approximately
1490
m/s
at
23oC).
We
then
calculated
the
frequency
with
equation
3
and
the
wavelength
with
equation
4.
These
results
apply
to
the
first
harmonic
resonant
wave
impulse
and
can
be
seen
in
table
1,
with
each
of
the
tank
dimensions.
T=L/c
(2)
f = 1/T
(3)
λ = c /f
(4)
Tank
Dimensions
Resonant
Frequencies
From
Each
Surface
Width=28.8
cm
2586.8
Hz
Length=59
cm
1262.7
Hz
Height=30
cm
4966.7
Hz
Table
1.
Resonant
Frequencies
of
the
Tank
We
used
two
200
kHz
piezoelectric
transducers;
one
generated
a
sound
wave
and
the
other
acted
as
a
hydrophone
to
acquire
the
signal.
We
chose
200kHz
because
this
frequency
was
greater
than
all
the
resonance
frequencies
from
the
tank.
Using
a
signal
generator
that
we
attached
to
the
first
transducer,
we
produced
the
200kHz
sound
wave,
all
the
while
monitoring
the
visual
representation
of
our
generated
wave
with
an
oscilloscope.
To
take
temperature
readings,
we
also
used
three
Type
E
Thermocouples,
two
on
opposite
sides
of
the
tank
and
the
third
as
a
control
in
ice.
To
complete
our
preliminary
experiment
on
resonant
interference,
we
repeated
the
transducer
separation
procedure
in
our
large
tank
that
was
originally
performed
by
JA
in
their
smaller
tank.
In
this
4
experiment,
we
increased
the
spacing
between
the
transducers
in
1
cm
increments
and
observed
the
decrease
in
output
voltage
readings.
By
comparing
our
results
to
that
of
JA,
we
can
determine
how
much
(if
any)
of
an
impact
the
resonance
frequency
interference
has
on
our
output
voltage
readings.
In
the
process,
we
were
also
able
to
determine
the
optimal
spacing
of
our
transducers
to
carry
out
our
main
temperature
experiment.
This
distance
must
be
large
enough
that
there
is
enough
water
between
the
transducers
that
the
changing
temperature
will
have
a
noticeable
effect
on
the
sound
wave,
but
also
not
too
big
so
that
we
would
still
get
good
amplitude
readings
from
the
hydrophone
transducer.
Next
we
had
to
complete
our
preliminary
experiment
on
transducer
alignment.
The
Prowave
literature
for
our
piezoelectric
200kHz
transducers
stated
that
our
transducers
emitted
waves
at
a
20
degree
beam
angle.
The
degree
angle
on
our
plot
is
measured
from
the
centerline
between
the
two
transducers.
Therefore,
according
to
the
Prowave
literature,
the
signal
strength
should
die
off
heavily
at
around
10
degrees.
Beginning
with
the
transducers
head
on
with
one
another
(0o
angle),
kept
at
a
constant
spacing
of
11
cm,
we
proceeded
to
rotate
the
first
transducer
at
approximately
5o
increments
away
from
the
second
hydrophone
transducer.
A
schematic
of
this
experiment
can
be
seen
in
figure
1.
We
used
a
protractor
to
measure
each
angle
as
accurately
as
possible.
If
results
show
a
major
decrease
in
voltage
output
with
increasing
angle,
this
would
stress
the
importance
of
ensuring
the
transducers
were
accurately
aligned
before
proceeding
with
any
more
experimentation.
Figure
1.
Schematic
of
Experimental
Design
to
test
importance
of
transducer
alignment
5
Finally,
to
perform
our
main
experiment
regarding
temperature
change,
we
needed
efficient
ways
to
cool
and
heat
the
water.
To
cool
our
water,
we
filled
two
medium
sized
garbage
cans
with
water
and
put
them
in
a
large
freezer
for
several
hours.
As
the
temperature
of
the
freezer
was
unknown,
we
were
unsure
how
long
we
would
need
to
cool
the
water
to
our
desired
temperature
of
1
to
2
degrees
Celsius.
Using
a
trial‐and‐error
approach,
we
determined
that
the
water
would
cool
to
approximately
6
degrees
in
about
5
hours.
Our
next
step
was
to
determine
how
to
increase
the
temperature
of
our
water
efficiently.
We
determined
the
easiest
method
to
do
this
was
to
simply
remove
4
cups
of
the
cold
water
and
add
4
cups
of
warm
water
(about
35
degrees
Celsius).
We
stirred
the
water
thoroughly
to
ensure
a
uniform
temperature
distribution
throughout
the
tank.
We
also
had
to
develop
a
LabView
VI
that
could
take
voltage
readings
from
both
our
Hydrophone
Transducer
(which
performed
best
with
a
sampling
size
of
131,072
at
a
rate
of
400,000)
and
our
Type
E
Thermocouples
(which
performed
best
with
a
sampling
size
of
1,024
at
a
rate
of
4,000).
A
schematic
of
the
Front
Diagram
of
our
VI
during
one
of
our
experiments
can
be
seen
in
figure
2.
The
temperature
data
(in
voltages)
can
be
seen
on
the
left,
while
the
frequency
(200
kHz)
and
amplitude
data
can
be
seen
on
the
top
right
and
bottom
right,
respectively.
6
Figure
2.
Screen
Display
of
our
LabView
VI,
mid‐experiment
Results
Once
our
new
tank
was
set
up
and
the
VI
was
running
correctly,
we
were
able
to
successfully
take
voltage
measurements
concurrently
with
temperature
measurements.
First,
we
needed
to
test
the
effect
of
distance
on
the
ratio
of
input
to
output
voltage,
and
thus
determine
the
effect
of
resonant
frequency
on
the
quality
of
results.
In
the
process,
we
also
determined
our
optimum
transducer
spacing.
In
the
experiment,
our
input
voltage
remained
at
a
steady
2.2
V.
Figure
3
shows
the
reduction
in
output
voltage
as
we
separated
the
transducers
across
the
entire
length
of
the
tank.
The
highest
voltage
readings
were
achieved
in
approximately
the
first
13
cm
of
separation,
followed
by
a
sharp
decline
in
the
readings.
Therefore,
we
repeated
this
experiment
over
only
the
first
13
cm
(figure
4).
Figure
3.
Voltage
as
a
Function
of
Transducer
Separation
7
Figure
4.
Voltage
as
a
Function
of
Transducer
Separation
up
to
13
cm
Based
on
the
data,
we
chose
an
optimal
transducer
separation
of
11
cm,
predicting
this
distance
would
give
us
the
greatest
voltage
outputs,
with
a
reasonable
amount
of
space
for
temperature
effects
from
the
water.
To
determine
the
effect
of
resonance
on
the
output
voltage,
we
compared
our
output
voltage
values
to
those
obtained
by
JA
(Figure
5).
Figure
5.
Transducer
Separation
vs.
Distance,
Jenson
and
Anderson,
2009
8
As
can
be
observed,
our
values
are
much
higher,
even
at
a
much
greater
separation.
This
evidence
supports
JA’s
original
hypothesis
and
we
were
able
to
conclude
that
there
was
resonant
frequency
interference
caused
by
the
walls
of
the
tank
and
the
surface
of
the
water,
and
a
larger
test
space
would
achieve
greater
results.
Continuing
with
our
experimentation,
we
had
to
determine
the
importance
of
transducer
alignment
on
voltage
output.
After
aligning
our
transducers
head‐on
(0o)
with
one
another,
we
took
voltage
readings
at
approximately
5o
increments.
The
results
can
be
seen
in
Figure
6.
Figure
6.
Voltage
Diminishing
as
the
Transducer
Angle
Increases
The
data
in
figure
6
tells
us
that
lining
up
our
transducers
evenly
was
extremely
important.
We
took
the
proper
precautions
to
line
up
our
transducers
by
attaching
both
to
the
same
straight
metal
bar
which
stretched
the
length
of
the
tank.
Finally,
we
had
to
determine
the
attenuation
of
the
sound
wave
at
different
water
temperatures.
As
we
increased
the
temperature,
our
VI
showed
that
the
voltage
picked
up
by
the
hydrophone
steadily
decreased
(Figure
7).
9
Figure
7.
Decreasing
Voltage
Received
with
Increasing
Temperature
As
can
be
easily
seen,
there
is
a
negative
relationship
between
the
output
voltage
of
the
hydrophone
and
the
temperature
of
the
water.
Our
next
step
was
to
determine
how
this
voltage
was
related
to
attenuation
of
the
acoustic
wave.
We
used
equation
5
to
calculate
the
attenuation
coefficient
in
units
of
(dB/cm*MHz)
[4].
Next,
we
used
equation
6
to
convert
this
attenuation
coefficient
into
attenuation
(dB).
(
5)
(
6)
In
equation
5,
the
Iin
and
Iout
values
correspond
to
the
“intensity
in”
and
the
“intensity
out.”
We
assumed
that
these
values
related
to
our
initial
voltage
input
(2.2
V)
and
our
final
voltage
output
(expressed
in
figure
7).
Where
η
represents
the
dynamic
viscosity
of
the
water
which
varied
with
temperature,
ω
is
the
frequency
of
the
wave
(200
kHz
in
our
case)
and
ρ
is
the
density
of
the
water
at
varying
temperatures.
We
were
then
able
to
determine
a
relationship
between
voltage
and
attenuation,
10
calculating
voltages
at
certain
temperatures
using
the
trend
line
calculated
in
figure
7.
These
results
are
shown
in
figure
8.
Figure
8
displays
our
relationship
of
Attenuation
vs.
Velocity,
calculated
using
equations
5
and
6.
Figure
8.
Relation
of
Output
Voltage
to
Attenuation
Combining
our
data
from
figures
7
and
8,
we
were
able
to
determine
a
relationship
between
attenuation
and
temperature,
shown
in
figure
9.
Figure
9.
Increasing
Attenuation
With
Increasing
Temperature
11
Figure
9
shows
that
attenuation
and
temperature
have
a
direct
relationship,
the
opposite
of
what
we
initially
hypothesized.
Conclusions
In
our
first
preliminary
experiment,
we
were
able
to
conclude
that
interference
from
the
resonant
frequencies
of
the
sides
of
the
tank
had
a
major
impact
on
the
output
voltage
readings.
We
also
found
that
the
optimal
transducer
spacing
in
our
tank
was
11
cm.
In
our
second
experiment,
we
determined
that
the
alignment
of
the
transducers
also
had
a
major
impact
on
the
quality
of
output
voltage
readings.
Using
the
results
from
both
of
these
experiments,
we
were
able
to
determine
the
optimal
conditions
at
which
to
take
measurements
for
our
temperature
experiment:
With
the
transducers
perfectly
aligned,
spaced
11
cm
apart.
These
results
also
both
supported
our
initial
hypotheses.
The
results
for
our
overall
temperature
experiment,
however,
do
not
support
our
hypothesis.
The
temperature
of
the
water
increased
as
the
attenuation
of
the
sound
wave
increased.
Evidently,
our
initial
assumption
that
the
kinetic
energy
of
the
sound
wave
is
directly
proportional
to
the
velocity
of
the
wave
is
incorrect.
Rather,
there
must
be
some
other
aspect
of
sound
wave
traveling
through
water
that
causes
it
to
attenuate
greater
at
higher
temperatures
than
at
lower
temperatures.
To
make
assumptions
regarding
the
potential
causes
of
this
attenuation,
we
investigated
the
variation
of
different
water
properties
with
temperatures.
These
values
can
be
seen
in
Appendix
B,
Table
1.
As
shown,
the
density
and
the
dynamic
viscosity
of
water
both
decrease
with
increasing
temperature.
We
can
assume
that
the
decrease
in
one
or
both
of
these
properties
causes
the
water
to
attenuate
at
a
higher
degree.
Perhaps
since
the
water
is
able
to
travel
more
easily
through
water
of
lower
densities
and
viscosities
(hence
the
increasing
velocities
at
higher
temperatures),
the
sound
wave
may
more
easily
dissipate
as
it
travels
through
the
medium.
This
would
cause
a
greater
attenuation
at
higher
temperatures,
as
less
of
the
original
wave
would
make
it
to
the
second
transducer.
12
Future
work
could
be
to
test
the
effects
of
density
and
dynamic
viscosity,
both
separately
and
concurrently,
on
the
attenuation
of
an
acoustic
wave.
In
these
experiments
all
other
factors
(i.e.
temperature)
would
need
to
be
kept
constant.
These
experiments
would
help
to
determine
what
properties
of
water
actually
cause
sound
waves
to
attenuate
more
at
higher
temperatures
than
at
lower
temperatures.
13
References
1. Wordnet
Search‐3.0
http://wordnetweb.princeton.edu/perl/webwn?s=attenuation
2. Lurton,
Xavier.
An
Introduction
to
Underwater
Acoustics:
Principles
and
Applications
Springer‐Praxis:
Chichester,
UK
(2002)
3. Jenson,
Christopher,
and
Tim
Anderson.
“Sound
Attenuation
In
Water.”
(2009):
n.
pag.
Web.
01
Feb
2010.
<http://www.me.rochester.edu/courses/ME241/SoundAttenuation(10).pdf>.
4. Dukhin,
Andrei,
and
Goetz,
Philip.
“Bulk
Viscosity
and
Compressibility
Measurement
Using
Acoustic
Spectroscopy.”
Journal
of
Chemical
Physics
130.12
(2009):
n.
pag.
Web.
18
Apr
2010.
<http://jcp.aip.org/jcpsa6/v130/i12/p124519_s1?view=fulltext>.
14
Appendix
A
Tank
1
Dimensions
Length
3.045
m
Width
0.15
m
Depth
0.145m
Table
1.
Dimensions
from
Original
tank
(Jenson
and
Anderson,
2009)
15
Appendix
B
FRESH
WATER
Temperature
(oC)
0
5
10
15
20
25
30
Dynamic
Viscosity
(kg/m*s)
Speed
of
Sound
(m/s)
density
(kg/m3)
1.79E‐03
1403
999.9
1.53E‐03
1427
1000
1.31E‐03
1447
999.7
1.14E‐03
1.00E‐03
1481
998.2
8.91E‐04
7.98E‐04
1507
995.7
Data
recorded
from
Young,
Munson,
Okiishi
and
Huebsch,
A
Brief
Introduction
to
Fluid
Mechanics,
4th
Edition.
John
Wiley
&
Sons,
Inc.
2007;
Table
B.2,
p.
472
16