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Acoustics - Determination of sound transmission loss in impedance tubes - Transfer matrix method
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GBZ27764-2011: PDF in English GB/Z 27764-2011
GB
GUIDANCE TECHNICAL DOCUMENT FOR
STANDARDIZATION OF THE PEOPLE’S REPUBLIC OF CHINA
ICS 17.140.01
A 59
Acoustics - Determination of sound transmission loss in
impedance tubes - Transfer matrix method
ISSUED ON: DECEMBER 30, 2011
IMPLEMENTED ON: MAY 01, 2012
Issued by: State Administration for Market Regulation;
Standardization Administration of PRC.
Table of Contents
Foreword ... 3
1 Scope ... 4
2 Normative references ... 4
3 Terms and definitions ... 4
4 Principles ... 7
5 Test equipment ... 8
6 Preliminary test ... 15
7 Installation of test pieces ... 16
8 Test steps ... 17
9 Measurement uncertainty ... 21
10 Test report ... 21
Appendix A (Normative) Preliminary test ... 23
Appendix B (Normative) Measurement theory ... 27
Appendix C (Informative) Measurement instructions for flexible sheet materials ... 30
Appendix D (Informative) Sources of error and calculation of measurement uncertainty
... 32
References ... 41
Acoustics - Determination of sound transmission loss in
impedance tubes - Transfer matrix method
1 Scope
This guiding technical document stipulates the measurement of normal incidence sound
insulation (or normal incidence sound transmission loss) of acoustic materials or
acoustic structures, in impedance tubes, by using the transfer matrix method.
This guiding technical document is applicable to the measurement of the normal
incidence sound insulation of locally reactive acoustic materials, such as sponges,
cotton felts, soft thin plates, whose test frequency is in the quality control area (that is,
there is no sound propagation parallel to the material inside the material). It is applicable
to the comparison of sound insulation performance of acoustic materials, in the
development stage. Since the sound transmission loss of a material is closely related to
its physical properties (such as elastic modulus, density, structure factor, etc.), the
measurement methods specified in this guiding technical document can be applied to
relevant basic research and product development.
This guiding technical document is not applicable to the identification test of the sound
insulation performance of the product.
This guiding technical document uses an impedance tube, one or more microphones,
and a digital acquisition & analysis system.
2 Normative references
The following documents are essential to the application of this document. For the dated
documents, only the versions with the dates indicated are applicable to this document;
for the undated documents, only the latest version (including all the amendments) is
applicable to this standard.
GB/T 3947-1996 Acoustical terminology
GB/T 18696.2-2002 Acoustics - Determination of sound absorption coefficient and
impedance in impedance tubes - Part 2: Transfer function method
3 Terms and definitions
The following terms and definitions apply to this document.
3.1
Normal incidence [sound] pressure transmission coefficient
τp
The ratio -- of the sound pressure transmitted through a material or structure TO the
incident sound pressure, when the sound wave is incident on the normal direction.
Note: Rewrite GB/T 3947-1996, Terms and Definitions 12.37.
3.2
Normal incidence [sound] transmission loss
TL
The difference -- between the incident sound power level on one side of the material
and the transmitted sound power level on the other side -- when the sound wave is
incident on the normal direction. The sound transmission loss is equal to the
reciprocal of the square of the sound pressure transmission coefficient, taking the
logarithm to the base 10, in the unit of Bell [B]. However, it is usually measured in
decibels (dB).
Note: Rewrite GB/T 3947-1996, Terms and Definitions 12.26.
3.3
The first reference plane
The cross-section of the impedance tube, which is used to measure the sound
pressure transmission coefficient. If the surface of the test piece is flat, usually take
the front surface of the sample as the first reference plane.
Note: Rewrite GB/T 18696.2-2002, Terms and Definitions 3.3.
3.4
The second reference plane
The cross-section of the impedance tube, which is used to measure the sound
pressure transmission coefficient. If the surface of the test piece is flat and the
thickness of the sample is t, the second reference plane is usually taken at x = t.
Note: Rewrite GB/T 18696.2-2002, Terms and Definitions 3.3.
3.5
Wave number in the air
sequence noise or chirp. Measure the sound pressure, at two positions close to the
sample in the front tube, to obtain the sound pressure transfer function of the two
microphone signals. Similarly, measure the sound pressure, at two positions close to the
sample in the back tube, to obtain the sound pressure transfer function of the two
microphone signals. Calculate the normal incident transmission coefficient of the test
piece (see Appendix B), sound transmission loss, other related acoustic quantities, by
the transfer matrix method.
These quantities are all functions of frequency. Frequency resolution depends on the
sampling frequency and the measurement record length of the digital acquisition and
analysis system. The effective frequency range is related to the lateral dimension or
diameter of the impedance tube, as well as the spacing between the two microphones.
With different sizes or combinations of diameter and spacing, a wide range of
measuring frequencies can be obtained.
Measurements can be made in one of two ways:
a) Four-microphone method (measured by four microphones at a fixed position);
b) Single-microphone method (measured by one microphone at four positions in
sequence).
5 Test equipment
5.1 Structure of impedance tube
The impedance tube is divided into front tube, back tube, test piece holding tube. One
end of the front tube is connected to the sound source, the other end is connected to the
test piece holding tube. One end of the rear tube is connected to the test piece holding
tube, the other end is a closed end with certain sound absorption performance. There
are four microphone mounting holes, two for the front tube and two for the rear tube,
arranged along the tube wall.
The impedance tube shall be straight; its cross-sectional area shall be uniform (the
deviation of diameter or cross-sectional size is within ±0.2%); the wall of the tube shall
be smooth, rigid, dense enough, so that it will not be excited by the acoustic signal.
There is no resonance in the working frequency band of the impedance tube. For round
metal tubes, it is recommended that the wall thickness be taken as about 5% of the tube
diameter. For rectangular tubes, the four corners must have sufficient rigidity, to prevent
deformation of the side plates. It is recommended that the plate thickness be taken as
10% of the cross-sectional size of the impedance tube. The tube wall, which is made of
cement, can be painted with a well-mixed adhesive, to ensure airtightness. The same
measures shall be taken for tube walls, which are made of wood. Cement tube walls
and wooden tube walls shall also be covered with iron or lead, to increase strength and
damping.
if the requirements of formula (4) are met, the distance between the microphones shall
be greater than 5% of the corresponding wavelength of the test low frequency.
Increasing the distance between the microphones can improve the measurement
accuracy.
If it wants to expand the test frequency band, it can use a combination of microphones
with different spacing to achieve it. Note that there needs to be a frequency overlap, at
the connection of each frequency band.
5.3 Impedance tube length
The impedance tube shall be long enough, to generate a plane wave between the sound
source and the test piece.
In addition to plane waves, loudspeakers generally produce non-plane wave modes. For
those non-plane wave modes, which have frequencies below the cutoff frequency, they
will attenuate within a distance of about three tube diameters (for round tubes) or three
times the length of the long side (for rectangular tubes). Therefore, it is recommended
that the distance between the microphone and the sound source shall not be closer than
the above-mentioned distance. In any case, it is better not to be less than one tube
diameter or one long side length.
Test pieces can also cause distortion of the sound field. According to the type of sample,
the recommended minimum distance between the microphone and the sample is:
Flat surface of uniform material: 1/2 of the diameter of the tube or 1/2 of the length of
the long side;
Flat surface of non-uniform structure: 1 times the tube diameter or 1 times the length
of the long side;
Asymmetrical or rough surfaces: 2 times the tube diameter or 2 times the length of the
long side.
5.4 Test piece holding tube
The test piece holding tube can be independent and detachable, OR it can be integrated
with the front tube and the rear tube, OR it can be composed of inner and outer tubes.
5.4.1 Integral test piece holding tube
For the impedance tube made as a whole, it is recommended to make the upper part of
the tube, where the test piece is placed, as a movable cover. The contact surface between
the movable cover and the holding tube shall be carefully ground; it is recommended to
use a sealant (grease) to avoid leaks.
5.4.2 Detachable test piece holding tube
center of the microphone, see A.2.
5.9 Signal processing equipment
The signal processing equipment consists of a signal generator, a power amplifier, and
a four-channel fast Fourier transform (FFT) analyzer. The device measures the sound
pressure at four microphone positions; calculates the Fourier spectrum or transfer
function, at each location. The signal generator shall be capable of generating a source
signal suitable for the analyzer (see 5.11).
Analyzer's dynamic range shall be greater than 65 dB. The estimation error of the
transfer function, due to the nonlinearity, resolution, instability, temperature sensitivity
of the signal processing equipment, shall be less than 0.2 dB.
When the single-microphone method is used, the analyzer shall be able to calculate the
transfer function Hij, from the generator signal and two successively measured
microphone signals.
5.10 Loudspeakers
The diaphragm loudspeaker (or the high-frequency pressure-cavity type loudspeaker
with the horn as the transmission unit of the impedance tube) shall be placed, at the end
of the front tube, as opposite to the test piece holding tube. The loudspeaker's diaphragm
shall cover at least 2/3 of the cross-section of the impedance tube. The loudspeaker can
be coaxial with the impedance tube, or inclined, or connected to the impedance tube
through an elbow.
The loudspeaker shall be enclosed in a sound-insulating box, to avoid lateral air
transmission to the microphone. Elastic vibration isolation pads are used, between the
impedance tube and the speaker frame and speaker box (preferably between the
impedance tube and the microphone), to avoid exciting the solid sound of the
impedance tube.
5.11 Signal generator
The signal generator shall be able to generate a balanced signal, which has flat spectral
density, in the test frequency range. It generates according to test requirements: one or
more of random noise, pseudo-random noise, periodic pseudo-random noise, linear FM
signal.
In the case of the single-microphone method, deterministic signals are recommended;
periodic pseudorandom sequences are well suited for this method. The first step in the
processing is to perform m-sequence correlation calculations, followed by fast Hartman
(Hadamard) transformations to generate impulse responses. The frequency response is
then obtained, from the Fourier transform of the impulse response.
For the calibration of impedance tubes (see Appendix A), the generation and display of
discrete frequency signals is necessary. The accuracy of frequency signal generation
and display shall be better than ±2%.
5.12 Loudspeaker ends
Resonance of the air column in the impedance tube will always occur. An effective
sound-absorbing material, which has a length of 100 mm to 200 mm, shall be laid near
the loudspeaker in the impedance tube, to suppress these resonances. It is recommended
to use a low-density porous sound-absorbing material.
5.13 Thermometers and barometers
The temperature in the impedance tube shall be measured and kept stable during the
measurement process. The front tube and the rear tube shall be consistent; the allowable
fluctuation shall not be greater than ±1 K.
The accuracy of the temperature sensor shall be better than ±0.5 K.
Atmospheric pressure shall also be measured; the allowable fluctuation is not more than
±0.5 kPa.
6 Preliminary test
Assemble the test equipment as shown in Figure 4. It shall be calibrated by a series of
tests, before formal use. Calibration helps eliminate sources of error or meet minimum
requirements. Calibration can be divided into two categories: calibration before and
after each test; regular calibration, all in accordance with Appendix A. No matter what
kind of calibration is carried out, the loudspeaker shall work at least 10 min before the
measurement, to stabilize the working state.
If the surface of the sample is uneven or irregular, the microphone position shall be
selected far enough, so that the measured transfer function is in the plane acoustic wave
region.
If the test structure is uneven, at least two samples, which have the same installation
conditions, shall be used for repeated tests.
If there is a regular transverse structure on the test item (such as perforated panels and
resonators, etc.), then the sample shall be cut along the line of symmetry of the structure.
If the size of the composite structural unit of the test object is not equal to the cross-
section of the impedance tube, the samples cut from different positions of several
structures shall be measured separately. For materials inhomogeneous in transverse
directions (such as mineral wool products), it is also necessary to perform repeated
measurements on several samples, which are cut from different parts of the test object.
8 Test steps
8.1 Determination of datum plane
After the sample is installed according to the requirements in Chapter 7, the first step
in the measurement of its acoustic characteristics is to identify the first and second
datum planes (x = 0, x = t). Typically, the reference plane is the surface of the test piece.
However, if the surface of the sample is uneven OR has an uneven transverse structure,
then the reference plane shall be located, at a certain distance in front of the surface of
the test piece. The distance -- from the datum to the nearest microphone -- shall comply
with the recommendations in 5.3. The position of the reference plane, as relative to the
microphones 1 and 4 (see Figure 1), shall be specified; the accuracy shall be better than
±0.5 mm.
8.2 Determination of sound velocity and wavelength
Before starting the measurement, first measure the sound velocity in the tube. Then
calculate the wavelength corresponding to the measurement frequency.
Knowing the air temperature in the tube, the sound velocity (unit: m/s) can be estimated
according to formula (5):
Where:
T - Air temperature, in Kelvin (K).
The wavelength λ0 is obtained by formula (6):
8.3 Selection of signal amplitude
When measuring at the selected position of the microphone, the signal amplitude of all
measurement frequencies shall be at least 10 dB higher than the background noise.
Due to the existence of the anechoic end at the sample position, the frequency response
of the loudspeaker shall be best equalized, so that the sound pressure response, which
is measured at this position, is flat. During the test, any component 60 dB lower than
the maximum frequency response shall be filtered out; however, due to the presence of
samples, the equalization of the frequency response shall also be carried out.
8.4 Selection of mean
The random error caused by noise can be effectively suppressed by averaging the signal
spectrum, which is measured at the position of the microphone. The required mean is
related to the test material and the required accuracy of the transfer function estimate
(see Appendix D.3).
8.5 Correction of microphone mismatch
Using the four-microphone method, a correction factor shall be determined in advance,
to correct the measured transfer function for channel-to-channel mismatch. Each
channel consists of a microphone, preamplifier, analyzer.
In the case of the single-microphone method, since only one microphone is used, there
is no need to correct for microphone mismatch, in the estimation of the transfer function.
Calibration is performed with an empty tube (i.e., no test piece installed); the calibration
is valid for all subsequent measurements, since the state of the microphone remains
unchanged after calibration. When doing calibration measurements, the mounting holes
of the microphones, that are not used temporarily, shall be properly sealed, such as
plugging the dumb head of the microphone, OR leaving the unused microphones in
their original positions.
The microphone is installed according to the layout method I (see Figure 5 for the
standard method); the measured transfer function is stored. Exchange the two
microphones A and B, as shown in Figure 6.
When exchanging microphones, it shall be ensured that the position of microphone A
in arrangement II is exactly the position of microphone B in arrangement I, and vice
versa. Do not connect the microphone to the preamplifier or signal analyzer, when
exchanging.
Appendix A
(Normative)
Preliminary test
A.1 Before and after the test
A.1.1 Calibration of microphone sensitivity
Before and after each test, the sensitivity of the microphone shall be calibrated, with a
stable sound source, within the operating frequency range; the sound level accuracy of
the sound source shall be better than ±0.3 dB. If the microphone is known to have a
linear frequency response over the operating frequency range, then a single-frequency
sound source, such as a pistonphone, is considered sufficient.
A.1.2 Temperature measurement
Before and after each test, the air temperature shall be measured, using a temperature
measuring device, which has a measurement accuracy better than ±0.5 K, meanwhile
written into the test report.
A.1.3 Signal-to-noise ratio
Before each test, the sound pressure spectrum, when the noise source is switched on
and off, shall be determined at each microphone position. The sound pressure spectrum
of the noise source shall be at least 10 dB higher than the background noise, at all test
frequencies. The frequency, with which test results do not comply with this requirement,
shall be recorded in the test report.
A.2 Periodic calibration
A.2.1 Impedance tube attenuation
A.2.1.1 Correction of impedance tube attenuation
Due to viscous loss and heat conduction loss, the incident sound wave pI (x) and the
reflected sound wave pR (x) are generally attenuated, during the propagation process.
The main effect of attenuation is that, the amplitude of the sound pressure minima
increases monotonically with increasing distance from the reflecting surface. Under
normal circumstances, this will not affect the results measured using the method of this
technical guidance document. However, when the distance -- from the surface of the
sample to the nearest microphone -- is greater than three times the diameter of the
impedance tube (round tube) or the length of the long side (rectangular tube), then it is
necessary to make corrections, when evaluating the acoustic characteristics measured
S12 - The cross-spectrum of the signal of microphone 1 and the signal of microphone
2;
S11 - The auto-spectrum of the signal of microphone 1;
S22 - The auto-spectrum of the signal of microphone 2.
Note: There are deviations, which are caused by the signal record length (or frequency
resolution) and the reverberation effect in the tube in the determination of the coherence
function. In the case of a highly reflective tip, the coherence will be less than 0.5, at the
frequency corresponding to the sound pressure node, where either microphone is positioned. In
addition, it can be expected that the coherence between the microphone signals will be greater
than 0.9.
D.4 Calculation of sound transmission loss uncertainty
The measurement uncertainties of sound transmission loss are derived from
measurements of transfer function, spacing, temperature. The measurement uncertainty
of temperature has little effect on the uncertainty of sound transmission loss, so it can
be ignored; only the influence of the uncertainty, which is introduced by transfer
function measurement and spacing measurement on the uncertainty of sound
transmission loss, is calculated.
D.4.1 Spacing measurement uncertainty
The uncertainty of spacing measurement mainly depends on the uncertainty u1 of the
measurement dispersion and the uncertainty u2 of the scale error of the scale used. The
uncertainty caused by other temperature effects and elastic effects can be omitted.
The uncertainty of measurement dispersion is obtained by statistical methods, which
belongs to category A assessment, using the Bessel method; the scale uncertainty is
obtained from the accuracy of the measuring scale used, which belongs to category B
assessment.
D.4.1.1 Spacing measurement dispersion
Assuming that the spacing is measured n times, x1, x2, ..., xn are obtained.
Its average value is the best value:
Where:
xi - The value of the i-th measurement.
Its standard deviation is its standard uncertainty u1:
......
Source: Above contents are excerpted from the PDF -- translated/reviewed by: www.chinesestandard.net / Wayne Zheng et al.
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