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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.