Influence of reflecting plane having finite surface density on sound

power level of reference sound sources calibrated in hemi free-field

Keisuke YAMADA1; Hironobu TAKAHASHI1; Ryuzo HORIUCHI1
1
National Metrology Institute of Japan /National Institute of Advanced Industrial Science and Technology, Japan

ABSTRACT
The NMIJ, National Metrology Institute of Japan planned to start calibration service for reference
sound sources (RSSs) by 2015 and we have been developing the RSS calibration system in accordance with
ISO 6926. In our system, hemi-anechoic environment necessary for the calibration is realized by laying
down wooden boards on a wire meshed floor of our anechoic room. In this study, we investigated the
influence of such a reflecting plane having finite surface density on sound power level of the RSS
theoretically and experimentally. We especially examined sound energy transmission through wooden
boards and their vibration caused by the RSS operation. We also experimentally confirmed that our
hemi-anechoic environment satisfies an inverse square law of sound intensity within a tolerance in ISO
3745. Furthermore, sound power level of the RSS determined by our system agreed with that by the SP,
Technical Research Institute of Sweden within a range of SP’s expanded uncertainty. These results show
that our hemi-anechoic environment is suitable to determine sound power level of RSSs in accordance with
ISO 6926.

Keywords: Reference sound source, Sound power level, Free-field over a reflecting plane, hemi-anechoic
room I-INCE Classification of Subjects Numbers: 71.9, 72.4, 73.2

1. INTRODUCTION
Sound power level is used for the evaluation of sound emitted from electrical and mechanical
apparatus. ISO 3740 series prescribe several procedures to determine sound power levels of such
apparatus by using sound pressure and are categorized by the required accuracy [1-4]. Practically, a
reference sound source (RSS) is often used to determine sound power level of the apparatus by
comparison. If sound power level of the RSS is known, that of the apparatus under test can be
precisely determined, with less influence by measurement environment.
However in Japan, we don’t have calibration laboratories which carry out the RSS calibration
service in accordance with ISO 6926 [5]. We have been also requested from RSS users to calibrate
them domestically. Thus, the NMIJ (National Metrology Institute of Japan) determined to develop the
calibration system based on ISO 6926 by ourselves and to start calibration service by 2015. We have
the anechoic room for precise acoustic measurement but it is not convenient for the RSS calibration
because it is not easy to realize spherical measurement surface around the RSS. Thus, hemi-anechoic
environment is selected and realized by laying down wooden boards on a wire meshed floor of the
anechoic room. In this paper, we investigated theoretically and experimentally the influence of a
reflecting plane by wooden boards on sound power level of the RSS because they have finite surface
density. In particular, we examined sound power transmission through wooden boards and their
vibration caused by the RSS operation. Furthermore, we experimentally confirmed that our
hemi-anechoic environment satisfies an inverse square law of sound intensity within a tolerance in
ISO 3745.

1
keisuke.yamada@aist.go.jp

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2. CALIBRATION SYSTEM
2.1 Hemi-anechoic environment

Figure 1 – Calibration system for sound power level of RSS

Figure 1 shows the photo of our calibration environment and apparatus. Hemi-anechoic
environment is realized by laying down wooden boards on a wire meshed floor of the anechoic room.
The dimensions of the anechoic room are 9.5 m in width, 8.0 m in depth and 7.2 m in height,
respectively. The wire meshed floor is fixed 5.6 m below the celling of the room. Cut-off frequency
of sound absorbing wedges is 40 Hz. Wooden boards are 0.92 m by 1.83 m. Their thickness is 24 mm
and surface density is 7.5 kg/m2 . Reflecting plane consists of 16 wooden boards on the wire meshed
floor and another 16 wooden boards stacked on the first layer. Thus, the wooden board floor is 48
mm in thickness and 15.0 kg/m2 in surface density. The wooden board floor is 26.9 m2 in area and
covers 35% of the wire meshed floor.

2.2 Calibration Apparatus

We designed the hemispherical frame for fixing microphones and placed it on the wooden boards.
It is 2.0 m in radius and made by thin steel pipes. Twenty WS2F microphones [6] (type MI-1234,
Onosokki) are fixed to the frame and connected with preamplifiers (type MI-3111, Onosokki). Output
voltages of the microphones are acquired simultaneously by 20 ch FFT analyzer (type DS-2000,
Onosokki). PC controls the FFT analyzer and calculates sound power level, accordingly.

2.3 Calculation of Sound Power Level Radiated from RSS

Sound power level of the RSS, Lw [dB] is calculated as follows:

10 log (1)

where S [m2 ] is the area of the measurement hemisphere, S 0 is 1.0 m2 . C [dB] is correction term to
reference environmental conditions (23 C°, 101.325 kPa). Lpf [dB] is surface sound pressure level. C
and Lpf are calculated as follows:

313.15 296.15
10 log 10 log (2)
101.325 273.15 101.325 273.15

1 .
10 log 10 (3)
20
where B [kPa] is static pressure and t [C°] is room temperature during the calibration. Lpi [dB] is the
time-averaged one-third octave band sound pressure level measured at the ith microphone position.

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3. CHARACTERISTICS OF REFLECTING PLANE MADE BY WOODEN BOARDS

3.1 Influence of Sound Power Transmission through Floor
3.1.1 Theoretical Derivation of Sound Power Transmission
Precisely speaking, the wooden board floor is not acoustically rigid and sound energy radiated
from the RSS will not be perfectly reflected on the floor. Sound energy may be absorbed into the
floor or transmitted through the floor. However, we assumed that sound absorption is negligible
compared with sound transmission by considering the thickness of wooden boards. Thus, we
theoretically evaluated the energy loss by applying a mass law [7]. We also assumed that the RSS is
a point sound source and its acoustic center coincides with geometric center, namely 15 cm above
the bottom of the RSS.
Firstly, we considered simple plane wave. Transmission coefficient τθ of sound power for sound
incident angle θ [rad] is derived as follows:
1
(4)
1 cos
2

where, ω is angular frequency of the sound, ρ [kg/m3 ] is density of air, c [m/s] is sound speed in air
and m [kg/m2 ] is surface density of a reflecting plane.
Then we considered spherical wave based on Eq. (4). Figure 2 shows sound emission from a point
sound source on spherical coordinates (r, θ , ϕ ) and Figure 3 depicts the schematic view of our
calibration system. As shown in Figures 2 and 3, the polar angle θ corresponds to sound incident
angle and changes from 0 to θ max .
Total sound power transmitted through the floor, W t [W] is calculated by integrating the
transmitted sound power at each angle within the range of 0 ≤ θ ≤ θ max and 0 ≤ ϕ ≤ 2π:

sin (5)

where, R [m] is the distance from acoustic center of the sound source to the floor in the θ direction
and w(r) [W/m2 ] is sound intensity in the radial direction on a sphere of radius r.
Thus τcal , the ratio of Wt to total sound power P [W] emitted from the sound source is calculated as
follows:

(6)
sin
.
2

τ cal becomes zero for sufficiently rigid floor.

Finally, we calculate the influence of the sound power transmission on sound power level. The
difference of sound power level ΔLw [dB] between a floor having finite surface density and a rigid
floor is calculated using τcal :
∆ _ _
(7)
10 log 1 .
where, LW_finite and LW rigid [dB] are sound power levels for the floor having finite surface density and
the rigid floor, respectively.

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Figure 2 – Sound emission from point sound source on spherical coordinates (r, θ , ϕ). w(r) is sound
intensity in radial direction.

Figure 3 – Schematic view of sound incident angle θ and θmax

3.1.2 Theoretical Evaluation of Sound Power Transmission

Preceding analysis shows that sound power transmission depends on surface density of the floor.
We simulated two cases and ΔLw is shown in Figure 4: Surface density m is 7.5 kg/m2 and 15.0 kg/m2 ,
corresponding to single-stacked and double-stacked wooden boards, respectively. In both cases, air
density ρ is 1.2 kg/m3 and sound speed c is 340 m/s. As expected, Figure 4 shows that transmitted
sound power depends on the surface density of the floor and increases at lower frequencies. This
result implies that the influence of the surface density on sound power transmission may be predicted
and corrected theoretically for precise calibration, especially at lower frequencies less than 1 kHz.

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Figure 4 – Difference of sound power level between floor having finite surface density and rigid floor
3.1.3 Experimental Evaluation of Sound Power Transmission
Then, sound power transmission was experimentally examined by using the RSS and changing
the thickness of the wooden boards. However, ΔLw cannot be experimentally determined because we
cannot realize sufficiently rigid reflecting plane in our facility. Instead, we determined the difference
of sound power level between 7.5 kg/m2 and 15.0 kg/m2 in the surface density of wooden boards. For
each case, sound power level was measured three times and the average was calculated.
Environmental conditions were 23.3 ± 0.2 C° in temperature and 100.0 ± 0.1 kPa in static pressure
for the former case and 23.2 ± 0.2 C° and 100.9 ± 0.1 kPa for the latter case, respectively. The RSS
is Brüel & Kjær type 4202 and driven by AC 100 V with 50 Hz.
The difference of sound power level ΔLw_density between 7.5 kg/m2 and 15.0 kg/m2 in the surface
density [dB] is defined as follows:
∆ _ _ _ (8)
2
where, Lw_light and Lw_heavy [dB] are sound power levels for the surface density of 7.5 kg/m and 15.0
kg/m2 , respectively.

Figure 5 –Theoretical and experimental difference of sound power level between 7.5 kg/m2 and 15.0 kg/m2
in floor surface density. Error bars represent standard deviations of experimental difference.

Figure 5 shows ΔLw_density and theoretical result is also plotted for reference. Figure 5 shows that
experimental result is in good agreement with theoretical one. The difference between theoretical

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and experimental result is 0.25 dB at 100 Hz. But except for 100 Hz, they agree within 0.1 dB.
Figure 5 implies that sound power transmission through the floor can be theoretically estimated
and corrected. Future study includes the investigation of the difference at 100 Hz.

3.2 Influence of Floor Vibration caused by RSS Operation

Wooden boards are thinner and lighter compared with a concrete floor and may vibrate to some
extent when the RSS is operated. To examine the influence of floor vibration, sound power level of
the RSS was examined by eliminating the vibration. The RSS was physically isolated from the floor
by hanging the RSS from the ceiling of the anechoic room and by using fine steel wires. As a result,
the RSS was positioned 1 cm apart from the floor. For conditions with and without floor vibration,
sound power level was measured five times and the average was calculated. Environmental
conditions during the measurement were 23.3 ± 0.2 C° and 100.8 ± 0.1 kPa.
The difference of sound power levels with and without floor vibration, ΔLw_vibration [dB] is defined
as follows:
∆ _ _ _ (9)
where, Lw_on and Lw_off [dB] are sound power levels with and without floor vibration, respectively.
Figure 6 shows ΔLw_vibration. At some frequencies, differences exceed standard deviations of the
measurement without floor vibration but still less than 0.1 dB. This result implies that the influence
of floor vibration is not significant.

Figure 6 – Difference of sound power levels with and without floor vibration. Error bars represent
experimental standard deviations without floor vibration.

3.3 Verification of Inverse Square Law

An inverse square law was experimentally validated in our hemi-anechoic environment to see if its
acoustic performance meets the qualification requirements of ISO 3745 Annex A.
Measurement frequencies were from 100 Hz to 10 kHz with 1/3 octave sequences. From 100 Hz
to 200 Hz, an omnidirectional loudspeaker (type 4292-L, Brüel & Kjær) was used. Over 250 Hz, a
tweeter (type TW-25B, Mitsubishi Electric Corporation) was used by attaching a board with a φ13
mm hole on its front to realize spherical wave. Sound pressure levels were measured along five
straight paths from the sound source to the room walls. For each path, measurement positions relative
to the sound source ranged from 0.5 m to 2.5 m with 0.1 m interval.
The measured sound pressure levels were compared with theoretical values. Theoretical sound
pressure level Lp [dB] at the distance of r [m] from the sound source is calculated as follows.

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 a 
L p (r ) = 20 log10  , (10)
 r − r0 
where
2
 N  N N N N N
  ri  − N  ri 2  ri  ri qi −  ri2  qi
a=  i =1  i =1
and r0 = − i =1 i =1 i =1 i =1
, (11)
N N N N N N

r q
i =1
i
i =1
i − N  ri qi
i =1
r q
i =1
i
i =1
i − N  ri qi
i =1
where
/
10 (12)
and Lpi [dB] is sound pressure level at the ith measurement position. ri [m] is the distance from the
sound source at the ith measurement position. N is the number of measurement positions along each
microphone path. For the measured sound pressure Lpi at each measurement position, the deviation
ΔLpi from theoretical value is defined as follows.
∆ (13)
For each path and each frequency, the maximum of ΔLpi is determined among all the measurement
positions and shown in Figure 7. For reference, the allowable deviation by ISO 3745 is also plotted.
All the data in Figure 7 are within the allowable deviation. Thus our hemi-anechoic environment
satisfies the requirement of ISO 3745 and thus ISO 6926.

Figure 7 – Maximum deviations of sound pressure level from theoretical values. All the data along five
paths are plotted. Dotted line shows the allowable deviation in ISO 3745.

4. INFORMAL COMPARISON WITH CALIBRATION DATA OF ANOTHER

LABORATORY
To confirm the validation of our calibration system, sound power level of the RSS by our system
was compared with that by another laboratory. The RSS used for the evaluation is Brüel & Kjær type
4204, S/N 2574792. We used the calibration certificate issued by the SP, Technical Research Institute
of Sweden . SP carried out the calibration in hemi-anechoic room and adopted a microphone traverse
method [8]. Correction for air absorption was applied from ISO 9613-1[9]. Sound pressure level was
corrected to the reference environmental conditions.
On the other hand, NMIJ performed the measurement three times and calculated the average. The
environmental conditions were 23.2 ± 0.2 C° and 100.9 ± 0.1 kPa. Sound power level was corrected
to the reference environmental conditions. Standard deviations were from 0.01 dB to 0.04 dB for all
the frequencies. Air absorption correction was also applied.

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The difference of sound power level calibrated by NMIJ and SP, ΔLw_cal [dB] is defined as
follows:
∆ _ _ _ (14)
where, Lw_SP and Lw_NMIJ [dB] are sound power levels calibrated by SP and NMIJ, respectively.
Figure 8 shows ΔLw_cal . The differences are within the expanded uncertainty reported by SP for all
the frequencies. This result means that calibration data by the two labs. are equivalent within the
range of the expanded uncertainty.

Figure 8 – Difference of sound power levels calibrated by NMIJ and SP. Dotted line shows expanded
uncertainty reported by SP.

5. CONCLUSION
This study theoretically and experimentally investigated the influence of using wooden boards as
the reflecting plane on sound power level of the RSS. We concluded that our hemi-anechoic
environment is satisfactory for the RSS calibration in accordance with ISO 6926.
Sound power transmission through the wooden board floor was theoretically estimated and
compared with experimental results. They are in good agreement and it was confirmed that the
influence of sound power transmission on sound power level can be corrected theoretically.
Furthermore, significant influence of floor vibration caused by the RSS operation was not observed.
We also confirmed that our hemi-anechoic environment satisfies the requirement in ISO 3745 by
verifying the inverse square law.
Finally, to confirm the validation of our calibration system, sound power level of the RSS by NMIJ was
compared with that by another laboratory. As a result, it was confirmed that they are equivalent within the
range of the reported expanded uncertainty.

REFERENCES
1. ISO 3745. Determination of sound power levels of noise sources using sound pressure -- Precision
methods for anechoic and hemi-anechoic rooms. 2003.
2. ISO 3741. Determination of sound power levels of noise sources using sound pressure -- Precision
methods for reverberation rooms. 2010.
3. ISO 3744. Determination of sound power levels of noise sources using sound pressure -- Engineering
method in an essentially free field over a reflecting plane. 2010.
4. ISO 3746. Determination of sound power levels of noise sources using sound pressure -- Survey method
using an enveloping measurement surface over a reflecting plane. 2010.
5. ISO 6926. Requirements for the performance and calibration of reference sound sources used for the
determination of sound power levels. 1999.
6. IEC 1094-4. Measurement microphones – Part4: Specifications for working standard microphones.
1995.

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7. Kosten CW. General Review. Acta Acustica united with Acustica. 1954; 4(1):263-270.
8. SP Technical Research Institute of Sweden. Calibration Certificate No. F905894-2. 2009.
9. ISO 9613-1. Attenuation of sound during propagation outdoors -- Part 1: Calculation of the absorption
of sound by the atmosphere. 1993.

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