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Acoustic center determination on anechoic half-space
Applied Acoustics, Vol. 48, No. 4, pp. 357-361, 1996 Copyright 0 1996 Ekevier Science Ltd Printed in Great Britain. All rights reserved 0003-682X/96/$15.00 + 0.00
PII:SOOO3-682X(96)00011-4
ELSEVIER
Technical Note
Acoustic Center Determination on Anechoic Half-Space Francisco Parentes de Rezende CorrEa Rua Paulo Alves, 110/401-Bl. E, 24.210440 Niterbi, Rio de Janeiro, Brazil (Received 26 March 1995; revised version received 26 January 1996) ABSTRACT The acoustic center height of a B&K 4204 reference sound source is determined using the model proposed by H. Larsen [Bruel & Kjaer Technical Review (1973)]. The results predicted by the model are compared with the experimental results, and the acoustic center height is calculated for several microphone positions of the array proposed by Finke / (Internoise (1993)]. The Larsen theory is also applied to the sound power measurements made with the IS0 3745 standard array, and some of its limitations are shown. Copyright 0 1996 Elsevier Science Ltd Keywords: Acoustic
center,
fixed microphone
array.
INTRODUCTION The acoustic center of a sound source is the place from which the sound waves are emitted. If a sound source that is symmetrical relative to its vertical axis is used, the acoustic center can be located by the determination of its height, using the formula proposed by Larsen.’ A series of measurements using a calibrated B&K 4204 sound source was made, using two different microphone arrays and four different radii for the measurement hemisphere (1 .O, 1S, 2.0 and 2.5 m).2 The acoustic center height is calculated for several microphone positions, and the limitations of Larsen’s model are discussed. 357
358
F. P. de Rezende C’orr~a
direct wave
reflected wave Fig. I. Measurement
set-up.
THEORY On a semi-anechoic half-space, the sound pressure level of a source is the sum of two waves: the direct wave and the reflected wave (see Fig. 1). According to Larsen,’ when the difference between the reflected and direct ways is an odd integer, destructive interference will occur. The relationship between microphone height (h), acoustic center height (b), wavelength (X) and hemisphere radius (R) is then given by: 11= n 2
6
[h/R]’ - [nh/4R12
(1)
where n = 1, 3, 5 ,....
DATA
ANALYSIS
Figure 2 shows the third-octave spectra taken at two microphone positions where destructive interference occurs at 630 Hz, at 1.0 and 2.0 m from the source, and the microphone at a height of 0.55 and 1.10 m, respectively. They are compared with the average sound pressure level of 10 microphone positions on a hemispherical measuring surface with R = 2.0 m (SPL/AVRG). The pressure decrease caused by interference can be clearly seen at 630 Hz. Both microphone heights correspond to position 2 of the array proposed by Finke.” Positon 2 on the Finke array3 corresponds to z/R= 0.55.If R = 1.0 m, h = z = 0.55 and X = 0.55 (C = 343.8 m s-~’ andf= 630 Hz); the acoustic center height can be calculated by eqn (1). The interference frequencies on the other positions of the array, and the corresponding acoustic center heights can be found in a similar way. It can be seen in Fig. 2 that the interference frequency is the same for each microphone position.
Acoustic center determination on anechoic half-space
359
TABLE 1
Acoustic center heights-Finke Position
array microphone positions
1
2
3
4
5
6
7
8
9
1600 0.21 0.25
630 0.25 0.55
400 0.24 0.85
2500 0.24 0.15
800 0.24 0.45
500 0.22 0.75
8000 0.20 0.05
1250 0.20 0.35
500 0.26 0.65
b (m): acoustic center height. f (Hz): frequency microphone vertical ordinate on the array.
of destructive
interference.
h/R=z/R:
Supposing that the acoustic center height is a funcion of frequency, it could be possible to predict the microphone heights where there will be destructive interference for the other measurement surfaces tested (Table 1). Table 2 shows that the calculated heights have practically the same value of the Finke array heights where destructive interference occurs. Finke and Bethke3 showed that their array does not have the systematic errors of IS0 3745 because it uses a different height for each microphone. In Fig. 3, the calibration chart of the sound source used, taken at the PTB (Germany) on 1993, using the spiral method of IS0 69264, is compared with the results of sound power measurements using the Finke and IS0 37455 arrays at R = 2.0 m. It can be seen that the Finke array measurement has quite good agreement with the calibration chart, and the interference effects of the IS0 3745 array are clearly shown. The IS0 3745 array does not fit with the others on frequencies of 2500 and 3 150 Hz. The interference at 2500 Hz, according to the Larsen formula, should occur at h/R = 0.15, that is to say, positons 2, 3 and 4 of the IS0 array. A similar effect would be expected at 800 Hz (h/R=0.45-positions
F. P. de Rezende Corrka
360
TABLE 2 heights using Larsen’s theory and the Finke array
Calculated Radius imi
1.5 2.0
Position I
Position 2
Larsen
Finke
Larsen
Finke
0.41 0.54
0.48 0.50
0.80 I .07
0.83 1.10
Position 8 ~Larsen Finke 0.56 0.75
0.53 0.70
cnJ.lmwm cnwr
4, 5 and 6) and 500 Hz (h/R=0.75-positions 7, 8 and 9) according to the theory proposed by Larsen. However, there are no visible interference effects at 800 and 500 Hz on the measurements using the IS0 array. There is a difference between the reflected wave path and the direct wave path (see Fig. l), and that difference, when R = 2 m, is 0.07 m for h/R = 0.15; 0.22 m for h/R=0.45; 0.33 m for h/R=0.75. On a free field, a longer path means a smaller sound pressure level, and the interference between the reflected and direct waves should be attenuated. Free-field theory says that the sound pressure level difference between two points on a free field at distances yI and r2 from the source is given by A = 20 log?
(2) r2
Applying that formula to the IS0 array positions, the sound pressure level differences given in Table 3 are found. The sound pressure level difference between the direct and reflected waves is approximately 1 dB when h/R is 0.45 and 0.75, and it is almost zero at h/R = 0.15. That should explain, at least partially, the IS0 3745 array effects.
Acoustic center determination on anechoic half-space
361
TABLE 3
Sound pressure level differences
0.15 0.45 0.75
2.07 2.15 2.33
2.0 2.0 2.0
-0.3 -0.6 -1.3
CONCLUSIONS
(1) The Larsen formula predictions agree with the experimental results. Despite of its limitations, it can be used to calculate the acoustic center height for some sound sources if the interference frequencies are known. (2) Fixed microphone arrays should not have more than one microphone at a given height, to minimize the interference effects. The Finke array, with the microphones at different heights, does not show the deviations observed with the traditional set-up of IS0 3745.
REFERENCES 1. Larsen, H., An easy and accurate method of sound power measurement. In: Bruel & Kjaer Technical Review. Bruel & Kjaer, 1973. 2. Correa, F. P. R. & Araujo, M. A. N., Interference effects on sound power measurement. In: Znternoise ‘9.5,Yokohama, Japan. 3. Finke, H.-O. & Bethke, C., Different results of sound power measurements as a consequence of standardization? In: Znternoise ‘93, Louvain, Belgium. of Sound Power Levels of Noise Sources4. IS0 6926, Acoustics. Determination Requirements
for the Performance
and Calibration
of Reference
Sound Source.
International Standards Organization, Geneva, 1990. of the Sound Power Level of Noise Sources5. IS0 3745, Acoustics. Determination Precision Methods for Anechoic and Semi-Anechoic Rooms. International Standards Organization, Geneva, 1977.
PII:SOOO3-682X(96)00011-4
ELSEVIER
Technical Note
Acoustic Center Determination on Anechoic Half-Space Francisco Parentes de Rezende CorrEa Rua Paulo Alves, 110/401-Bl. E, 24.210440 Niterbi, Rio de Janeiro, Brazil (Received 26 March 1995; revised version received 26 January 1996) ABSTRACT The acoustic center height of a B&K 4204 reference sound source is determined using the model proposed by H. Larsen [Bruel & Kjaer Technical Review (1973)]. The results predicted by the model are compared with the experimental results, and the acoustic center height is calculated for several microphone positions of the array proposed by Finke / (Internoise (1993)]. The Larsen theory is also applied to the sound power measurements made with the IS0 3745 standard array, and some of its limitations are shown. Copyright 0 1996 Elsevier Science Ltd Keywords: Acoustic
center,
fixed microphone
array.
INTRODUCTION The acoustic center of a sound source is the place from which the sound waves are emitted. If a sound source that is symmetrical relative to its vertical axis is used, the acoustic center can be located by the determination of its height, using the formula proposed by Larsen.’ A series of measurements using a calibrated B&K 4204 sound source was made, using two different microphone arrays and four different radii for the measurement hemisphere (1 .O, 1S, 2.0 and 2.5 m).2 The acoustic center height is calculated for several microphone positions, and the limitations of Larsen’s model are discussed. 357
358
F. P. de Rezende C’orr~a
direct wave
reflected wave Fig. I. Measurement
set-up.
THEORY On a semi-anechoic half-space, the sound pressure level of a source is the sum of two waves: the direct wave and the reflected wave (see Fig. 1). According to Larsen,’ when the difference between the reflected and direct ways is an odd integer, destructive interference will occur. The relationship between microphone height (h), acoustic center height (b), wavelength (X) and hemisphere radius (R) is then given by: 11= n 2
6
[h/R]’ - [nh/4R12
(1)
where n = 1, 3, 5 ,....
DATA
ANALYSIS
Figure 2 shows the third-octave spectra taken at two microphone positions where destructive interference occurs at 630 Hz, at 1.0 and 2.0 m from the source, and the microphone at a height of 0.55 and 1.10 m, respectively. They are compared with the average sound pressure level of 10 microphone positions on a hemispherical measuring surface with R = 2.0 m (SPL/AVRG). The pressure decrease caused by interference can be clearly seen at 630 Hz. Both microphone heights correspond to position 2 of the array proposed by Finke.” Positon 2 on the Finke array3 corresponds to z/R= 0.55.If R = 1.0 m, h = z = 0.55 and X = 0.55 (C = 343.8 m s-~’ andf= 630 Hz); the acoustic center height can be calculated by eqn (1). The interference frequencies on the other positions of the array, and the corresponding acoustic center heights can be found in a similar way. It can be seen in Fig. 2 that the interference frequency is the same for each microphone position.
Acoustic center determination on anechoic half-space
359
TABLE 1
Acoustic center heights-Finke Position
array microphone positions
1
2
3
4
5
6
7
8
9
1600 0.21 0.25
630 0.25 0.55
400 0.24 0.85
2500 0.24 0.15
800 0.24 0.45
500 0.22 0.75
8000 0.20 0.05
1250 0.20 0.35
500 0.26 0.65
b (m): acoustic center height. f (Hz): frequency microphone vertical ordinate on the array.
of destructive
interference.
h/R=z/R:
Supposing that the acoustic center height is a funcion of frequency, it could be possible to predict the microphone heights where there will be destructive interference for the other measurement surfaces tested (Table 1). Table 2 shows that the calculated heights have practically the same value of the Finke array heights where destructive interference occurs. Finke and Bethke3 showed that their array does not have the systematic errors of IS0 3745 because it uses a different height for each microphone. In Fig. 3, the calibration chart of the sound source used, taken at the PTB (Germany) on 1993, using the spiral method of IS0 69264, is compared with the results of sound power measurements using the Finke and IS0 37455 arrays at R = 2.0 m. It can be seen that the Finke array measurement has quite good agreement with the calibration chart, and the interference effects of the IS0 3745 array are clearly shown. The IS0 3745 array does not fit with the others on frequencies of 2500 and 3 150 Hz. The interference at 2500 Hz, according to the Larsen formula, should occur at h/R = 0.15, that is to say, positons 2, 3 and 4 of the IS0 array. A similar effect would be expected at 800 Hz (h/R=0.45-positions
F. P. de Rezende Corrka
360
TABLE 2 heights using Larsen’s theory and the Finke array
Calculated Radius imi
1.5 2.0
Position I
Position 2
Larsen
Finke
Larsen
Finke
0.41 0.54
0.48 0.50
0.80 I .07
0.83 1.10
Position 8 ~Larsen Finke 0.56 0.75
0.53 0.70
cnJ.lmwm cnwr
4, 5 and 6) and 500 Hz (h/R=0.75-positions 7, 8 and 9) according to the theory proposed by Larsen. However, there are no visible interference effects at 800 and 500 Hz on the measurements using the IS0 array. There is a difference between the reflected wave path and the direct wave path (see Fig. l), and that difference, when R = 2 m, is 0.07 m for h/R = 0.15; 0.22 m for h/R=0.45; 0.33 m for h/R=0.75. On a free field, a longer path means a smaller sound pressure level, and the interference between the reflected and direct waves should be attenuated. Free-field theory says that the sound pressure level difference between two points on a free field at distances yI and r2 from the source is given by A = 20 log?
(2) r2
Applying that formula to the IS0 array positions, the sound pressure level differences given in Table 3 are found. The sound pressure level difference between the direct and reflected waves is approximately 1 dB when h/R is 0.45 and 0.75, and it is almost zero at h/R = 0.15. That should explain, at least partially, the IS0 3745 array effects.
Acoustic center determination on anechoic half-space
361
TABLE 3
Sound pressure level differences
0.15 0.45 0.75
2.07 2.15 2.33
2.0 2.0 2.0
-0.3 -0.6 -1.3
CONCLUSIONS
(1) The Larsen formula predictions agree with the experimental results. Despite of its limitations, it can be used to calculate the acoustic center height for some sound sources if the interference frequencies are known. (2) Fixed microphone arrays should not have more than one microphone at a given height, to minimize the interference effects. The Finke array, with the microphones at different heights, does not show the deviations observed with the traditional set-up of IS0 3745.
REFERENCES 1. Larsen, H., An easy and accurate method of sound power measurement. In: Bruel & Kjaer Technical Review. Bruel & Kjaer, 1973. 2. Correa, F. P. R. & Araujo, M. A. N., Interference effects on sound power measurement. In: Znternoise ‘9.5,Yokohama, Japan. 3. Finke, H.-O. & Bethke, C., Different results of sound power measurements as a consequence of standardization? In: Znternoise ‘93, Louvain, Belgium. of Sound Power Levels of Noise Sources4. IS0 6926, Acoustics. Determination Requirements
for the Performance
and Calibration
of Reference
Sound Source.
International Standards Organization, Geneva, 1990. of the Sound Power Level of Noise Sources5. IS0 3745, Acoustics. Determination Precision Methods for Anechoic and Semi-Anechoic Rooms. International Standards Organization, Geneva, 1977.