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Measurement of the sound-absorption coefficient on egg cartons using the tone burst method

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A low-cost solution for noise level reduction in an enclosed space, such as a room, is the installation of egg carton materials or fruits box materials (for example apple, pear or peach tree). The Tone Burst method may be used to measure the sound absorption coefficient of a material at any desired angle of incidence. The goal for this paper is to demonstrate that egg cartons are a myth when they are used to reduce sound level in an enclosed space.
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Measurement of the sound-absorption coefficient in situ in
eggs cartons using the Tone Burst Method
QUINTERO RINCON ANTONIO
Departamento de Ingeniería Electrónica
Instituto Tecnológico de Buenos Aires
Av. Eduardo Madero 399
ARGENTINA
aquinter@itba.edu.ar
Abstract: A typical solution in an enclosed space, such as a room, is that the reduction in sound
level is the results from the installation of eggs cartons materials or fruits cartons materials (for
example apple, pear or peach tree). The Tone Burst method is used to measure the sound
absorption coefficient of a material at any desired angle of incidence. The goal for this paper is
demonstrate that these cartons are a myth when they are used like reducer of the sound level in
an enclosed space.
Key-words: Tone Burst – Absorption Materials – Reflection Factor - Eggs Cartons – NRC -
Sound Power Level.
1. Introduction
The basic parameters of acoustic materials
are the impedance and the surface shape.
Other information such as angle-dependent
impedance, porosity, tortuosity, etc., is
required. These material data include all
necessary information required for
calculation of the reflected and the
transmitted field. In many cases of sound
prediction, however, the absorbed or
transmitted energy is a sufficient quantity
[1].
The law of the conservation of energy states
that energy can neither be created nor
destroyed, but it can be changed from one
form to another. Absorption converts sound
energy into heat energy. It is useful for
reducing sound levels within rooms but not
between rooms. Each material with which a
sound wave interacts absorbs some sound.
The most common measurement of that is
the absorption coefficient, typically denoted
by the Greek letter α. The absorption
coefficient is a ratio of absorbed (Ea) to
incident sound energy (Ei). The reflect
coefficient is a ratio of reflect (Er) to
incident sound energy (Ei) A material with
an absorption coefficient is 0 reflects all
sound incident upon it. If a material absorbs
all sound incident upon it, its absorption
coefficient is 1 and if a material reflects all
sound incident upon it, its reflect coefficient
is 0, the reflect coefficient is typically
denoted by the Greek letter τ, if the reflect
coefficient is near to zero, then the
transmitted energy is minor. Therefore,
absorption coefficients range between 0 and
1. See figure 1.
Fig. 1. Sound Absorption and Sound
Reflection
E
r
Ei
E
t
Ea
Ea
Er: Reflected Energy
Ei: Incident Energy
Et: Transmitted Energy
Ea: Absorbed Energy
Absorption coefficients range 0 α 1 Æ α = Ea / Ei
Reflect coefficients range 0 τ 1 Æ τ = Et / Ei
In practice, all materials absorb some
sound, so this is a theoretical limit [2].
Sound absorptive materials are widely used
for the control of noise in a variety of
different situations. Sound-absorptive
materials exist in many different forms:
Glass-fiber materials, open-cell acoustical
foams, fiber board, hanging baffles, felt
materials, curtains and drapes, thin porous
sheets, head liners, carpets and hollow
concrete blocks with a small opening to the
outside – to create a Helmholtz resonator.
One characteristic common to nearly all
sound-absorptive materials is that they are
porous. That is, there is air flow through the
material as a result of a pressure difference
between the two sides of the material.
Porous materials are frequently fragile, and,
as a result, it is necessary to protect the
exposed surface of the material. Porous
materials are frequently fragile, and, as a
result, it is necessary to protect the exposed
surface of the material. Typical protective
surfaces include: thin impervious
membranes of plastic or other material;
perforated facings of metal, plastic or other
material; fine wire-mesh screens; spayed-on
materials such as neoprene, and thin porous
surfaces [3]. An egg carton is a carton
designed for carrying and transporting
whole eggs, no for acoustic. These cartons
have a dimpled form in which each dimple
accommodates an individual egg and
isolates that egg from eggs in adjacent
dimples. This structure helps protect eggs
against stresses exerted during
transportation and storage by absorbing a
lot of shock and limiting the incidents of
fracture to the fragile egg shells. An egg
carton can be made of various materials,
including Styrofoam, clear plastic or may
be manufactured from recycled paper and
molded pulp by means of a mechanized
Papier-mâché process. An “egg crate
mattress”, while following a similar form,
is not used for egg transport. It is a light
weight camping mattress which makes use
of the dimpled structure to distribute and
cushion human weight. This foam structure
is also occasionally used in packaging to
dampen impact of sensitive material during
travel.
Fig 2. Egg Carton
Similarly, acoustic foam tiles which help in
sound proofing and the limitation of
acoustic resonance have a similar form to
egg crates. Egg crate mattresses are
occasionally used as an inexpensive
substitute [4].
Sound absorption coefficients are
frequently measured in octave bands, and
the noise reduction coefficient (NRC) is the
average absorption in the 250, 500, 1000
and 2000 Hz. This average is expressed to
the nearest multiple of 0.05.
Reflection can occur when a wave impinges
on a boundary between two media with
different wave propagation speeds. Some of
the incident energy (Ei) of the wave is
reflected back into the original the original
medium, and some of the energy is
transmitted (Et) and refracted (Er) into the
second medium. See Fig. 1. This means that
the wave incident on a boundary can
generate two waves: a reflected wave and a
transmitted wave whose direction of
propagation is determined by Snell’s law.
2. The Method
At a given frequency, the absorption
coefficient of any material varies with the
angle of incidence of the sound waves. In a
room, sound waves strikes materials at
many different angles. For this reason,
published coefficient of commercial
materials are generally measured in a
laboratory reverberation room in which
Ld
tdLct
c
≅<
22
222
2
2
ld h d d
t
cc
hct
d
ct
−+
≤=
=
222
2
3
3595
hct
ct
ct
hh
t
c
=
==
min
595
f
h
=
3
0.577
3
h
dctc h
c
⎛⎞
== =
⎜⎟
⎜⎟
⎝⎠
L= 2ct
sound waves are nearly diffuse, so that they
strike the test sample from many directions.
The Tone Burst is a short signal used in
acoustical measurements to make possible
differentiating desired signals from
spurious reflections, The American Society
for Testing and Materials (ASTM) have
investigation with this method; in acoustic
the technique is applicable to many areas
such as measurement of distortion, early
reflections, absorption, and phase response
[5]. In this experiment the tone burst was
generated with the Spectral Lab software
and the loudspeaker is a E-MU's PM5
Precision Monitor.
One of the basic problems in room acoustic
measurements has always been to
determine the direction of a certain
reflection, and more important, its
frequency content. For example, ¿what is
the acoustic influence of an eggs carton in
an enclosed space?
The simple implementation of the Tone
Burst measurement is as described in [5],
the measurement procedure is:
1. Place the loudspeaker and measuring
microphone (B&K Type 2250) along the
longest axis of the room. Center the
microphone/loudspeaker combination with
respect to all three axes of the room.
Assume a room (see Fig. 3.) with the
transducers equally spaced between floor
and ceiling (h, the height of the room is
assumed the smallest of the room's
dimensions). First, we will only consider
reflections from side walls, ceiling and
floor. The pulse length (t) must then be
shorter than the difference between the time
it takes to travel the reflected (2l/c) and the
direct path (d/c). Hence
(1)
(2)
The criterion that the microphone should be
at least one wavelength from the
loudspeaker gives
d ct (3)
where t is the period at the lowest
frequency which also corresponds to the
pulse length which contains one period at
the lowest frequency. Setting Equations (2)
and (3) equal we obtain the optimum pulse
length and corresponding transducer
spacing:
(4)
The reciprocal of which gives the lower
frequency limit f
min
(5)
At the distance between transducers of
(6)
Which is the optimum spacing between
transducers for a given minimum room
dimension h.
For reflections from the end walls of the
room along its longest dimension (L), the
length of the pulse must be shorter than the
difference between the time it takes for the
first reflection to return to the microphone
(L/c) and the time it takes for the direct
sound to reach the microphone (d/c).
Hence (7)
Now reflections from the far wall only
become a limitation when the minimum
distance of Equation (7) is equal to, or less
than that of Equation (3). Setting the two
equal
(8)
2
L= 3h=1.15h
3
2688
LL
t
c
==
2
L
d
and substituting t from Equation (4) we get
(9)
Hence the length of the room must be at
least 15% longer than the smallest
dimension in order for Equations 4-6 to be
valid.
However, with reflections from the end
walls setting the limits, the pulse length
must be (from Equation 8.)
(10)
with an optimum distance between
transducers of (combining Equations 3. and
8.)
(11)
Fig. 3. The geometry environment
2. Begin with a relatively short tone burst
about 3 ms at about in the wished frequency
and observe the received waveform on the
B&K Type 2250. See Fig. 4.
Figure 4. Emitted Tone Burst and
Received Signal
The size of the loudspeaker must also be
considered in determining the far field. The
microphone should be placed at a distance
at least equal to the largest dimension of the
loudspeaker. Unfortunately, due to practical
restrictions on room size, these criteria are
often ignored, thus leading to non
reproducible measurements. Certain
standards, of course, also call for fixed
distances.
3. At a given angle between the
loudspeaker and the barrier and a distance
de d/2 between the loudspeaker and the
B&K type 2250, note that the total distance
is d, see fig. 6. The short tone burst is
emitted again and the B&K type 2250
receives the direct and reflected signals, see
fig 5. Note the point of the first reflections
and increase the duration of the tone burst.
If the tone burst is too long, the received
signal will have overlap.
Fig. 5. The Direct and Reflect Sound
4. With the direct and reflected signals, the
Sound Power Level (L
w
) are calculated and
compared for a same way: incident angle
and frequency in octave bands. Sound
intensity may be used for measuring sound
absorption in situ.
d/2
B&K
Type
2250
Loudspeake
r
Tone
Burst
h/2
h/2
(L-d)/2
(L-d)/2
d/2
L
h
Direct
Reflection
Direct
Reflection
10
0
10log ( )
w
W
L
dB
W
=
0
0
cos
cos
r
i
Z
Z
P
R
P
ZZ
ϑ
ϑ
==
+
22
2
2
1
ir
i
R
ρρ
α
ρ
==
11
cos 1
R
R
ξ
ϑ
+
=
1
()
FjwT
x
K
Kx T e T
=
Fig. 6. The geometry environment
with angles
A tone burst contains not only the
frequency of the sine wave contained in the
burst but also a band of frequencies
centered around the sine wave frequency.
These frequencies arise due to the square
wave by which the sine signal is gated.
Advantages: It is not necessary to have a
reverberation chamber to the
accomplishment of the test; samples of
different material can be measurement in
situ with different angles.
Disadvantage: The tone Burst Method is
effective beginning in 1000 Hz,
consequently it is limited in low
frequencies; it is necessary excellent
measurements instruments.
3. Experiment and Results
The sound power level of a source in
decibels, is given by
(12)
Where W is the power of the source in watts
and W
0
is the reference power in watts.
The reflection Factor R is related to the wall
impedance Z by:
(13)
Z
o
=ρ
o
c is the characteristic impedance of
air. The wall impedance Z is defined as the
ratio of sound pressure to the normal
component of particle velocity, both
determined at the wall [1].
The Absorption coefficient, is given by
(14)
And the specific impedance
(15)
For example for a frequency of 2 KHz with
an angle of 45°, the power W measurement
in the B&K type 2250 was 3.16 watts, can
be corroborated with the Power Spectral
Density of the signal
(16)
With the information: The reflection Factor
R=0.31 (Equations 12. and 13.), the
specific impedance ζ=2.68 (Equation 15.),
the absorption coefficient is α=1-0.31=0.69
(Equation 14) and the NRC= 0.4725.
The Absorption coefficients measured in
octave bands are:
Hz α
θ
125 0.04
250 0.30
500 0.42
1000 0.48
2000 0.69
4000 0.69
Table 1. Absorption Coefficients in
octave bands.
Fig. 7. Absorption Coefficients in
octave bands
φ°
Barrier
d/2
B&K
Type
2250
Loudspeaker
Tone
Burst
d/2
Sample
This method was corroborate with the Bell
Acoustic Panel y the result was similar to
the technical specifications of the material
α= 0.75 for the data show in the example.
4. Conclusions
The egg carton has a good absorption
coefficient begin in 2 KHz. For frequencies
smaller to 2 KHz it does not serve at all.
The egg carton does not have reflected
properties, so it can not use for acoustic
solution.
5. References
[1] Michael Vorländer, Auralization,
RWTH First Edition (Springer 2008).
[2] Cyril M. Harris, Handbook of
Acoustical Measurements and Noise
Control, 3 Edt. (Acoustical Society of
America 1998)
[3] Thomas D. Rossing Edition, Springer
handbook Acoustic, (Springer 2007).
[4]
http://en.wikipedia.org/wiki/Egg_carton
.
[5] MФller Henning and Thomsen Carsten,
Electro Acoustic free field measurements in
ordinary rooms using gating techniques,
Brüel & Kjaer, (Applications notes 1975)
In memory to engineering Fernando von
Reichenbach.
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... According to [4], for the device in Figure 2, the pulse length t must then be shorter than the difference between the time it takes to travel the reflected (2x/c) and the direct path (x/c). ...
... According to [4], the distance between the loudspeaker and the microphone should satisfy ...
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Electro Acoustic free field measurements in ordinary rooms using gating techniques, Brüel & Kjaer, (Applications notes 1975) In memory to engineering Fernando von Reichenbach
  • Mфller Henning
  • Thomsen Carsten
MФller Henning and Thomsen Carsten, Electro Acoustic free field measurements in ordinary rooms using gating techniques, Brüel & Kjaer, (Applications notes 1975) In memory to engineering Fernando von Reichenbach.