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Proceedings of 20th International Congress on Acoustics, ICA 2010

23-27 August 2010, Sydney, Australia

ICA 2010 1

Acoustical effects of columns, beams and furniture on sound fields in small enclosures

Kazushi Eda (1), Yosuke Yasuda (2) and Tetsuya Sakuma (1) (1) Department of Socio-Cultural Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5

Kashiwanoha, Kashiwa, Chiba, 277-8563 Japan (2) Department of Architecture, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama,

Kanagawa, 221-8686 Japan [email protected] / [email protected] / [email protected]

PACS: 43.55.FW, 43.55.KA, 43.55.MC

ABSTRACT

In acoustic design of small enclosures, it is a considerably important matter to control eigenmodes at low frequencies, so that many researches have been done on the effect of overall shapes of rooms on the eigenmodes, such as optimi-zation of room dimensions ratio. However, overall room shapes are usually restricted to rectangular forms due to easy construction, therefore it is desirable to improve sound fields only by changing partial elements in rectangular rooms. In the present paper, the effects of additional elements, such as columns, beams and furniture, on the sound field in a small rectangular room are investigated through wave-based numerical analysis. Supposing a room for listening use with a loudspeaker, the effects are evaluated regarding the flatness of frequency response and the uniformity of spa-tial distribution in a listening area. The results show that: the effect of columns is small but more than beams; that of closed-type shelves is relatively large but not so much as open-type shelves; the size and the arrangement of every element have unnegligible effects. It is also seen that the additional elements generally lead to positive effects in flat-ness of frequency response and special uniformity even at low frequencies, although in a specific case.

1. INTRODUCTION

In acoustic design of small enclosures, such as for audio lis-tening, music practice and so on, it is a considerably im-portant matter to control eigenmodes at low frequencies. The main factors affecting eigenmodes and distribution of eigen-frequencies are overall shapes of rooms, arrangement of ab-sorbers (absorbing properties) and wall surface shapes (re-flection properties). The effect of overall room shapes is most fundamental, so that many researches have been done on the effect on eigenmodes, such as optimization of room dimen-sions ratio [1-3]. However, overall room shapes are usually restricted to rectangular forms due to easy construction, therefore it is desirable to improve sound fields only by changing partial elements in rectangular rooms.

Regarding the unevenness of wall surfaces in small enclo-sures, it has been reported that small unevenness against wavelength has relatively large effect at lower frequencies [4,5]. In addition, it has been reported that a slight shape change of a mixing console affects acoustic properties in a studio [6,7]. Furthermore, Malsuki [8] has reported that furni-ture contributes to the control of peak and dip at low frequen-cies by arranging its pieces at the corners of a small room. The above reports generally suggest that there is a possibility to improve sound fields with partial elements even in small rooms. In the present paper, the effects of additional elements, such as columns, beams and furniture, on the sound field in a small rectangular room are investigated through wave-based numerical analysis.

2. NUMERICAL SET-UP

Supposing a small rectangular room for listening use, a nor-mal analysis model of 2.7×3.6×2.4 m3 with one loud-speaker (left channel) is given as shown in Figure 1. In a listening area, 25 receiving points are fixed at intervals of 20 cm, and the center point R is considered as the representative point. This listening area generally follows the optimum rela-tive dimentions of a listening room proposed by Olson [9]. Based on the normal case, a variation of 29 models is given by adding pillars, beams and furniture in some positions as shown in Figure 2.

Regarding the boundary conditions, a real part of normal impedance corresponding to the normal incidence absorption coefficient α = 0.15 is given to all wall surfaces; α = 0.01 is given to the surfaces of the speaker, and a vibration speed (piston vibration) is given to the vibrating plane. The theo-retical reverberation time (Eyring) of the normal model is 0.47s; its Schroeder frequency is 282 Hz. In the following examination, frequency responses from 56 Hz to 280 Hz are calculated at intervals of 2 Hz using the fast multipole BEM. The obtained results are evaluated regarding the flatness of frequency response (SDf, Eq. 1) and the uniformity of spatial distribution in the listening area (SDs, Eq. 2). Moreover, the mean values of each receiving point for SDf, and in each frequency band for SDs are calculated to evaluate the sound fields in two dimensions. These values are denoted by

and , respectively. Additionally, a combined value to-

23-27 August 2010, Sydney, Australia Proceedings of 20th International Congress on Acoustics, ICA 2010

2 ICA 2010

evaluate the flatness characteristics in the domains of fre-quency and space (SDf,s, Eq. 3) are calculated.

, (1)

, (2)

, (3)

where is the j-th octave band level at the i-th receiving point, is the number of octave bands, is the number of receiving points. The above evaluation is based on 1/12 octave band levels.

x

y

z

3.61.35

2.4

receiving point Rlistening area

1.2

O

0.980.81

2.650.54

-1.35

0.945

0.5

0.10.1

0.35

0.1

0.3vib.plane

speaker unit: m

Figure 1‐A rectangular room with a source.

v20_w v40_w

v20_bs v40_bs

0.6 0.61.5

2.7

1.2

1.2 v20_bc v20_rcv20_lc

v20_bl v20_br v20_rb

s20_bc s20_rcs20_lc

s20_bl s20_br s20_rb

1.2

1.2

t = 0.025

v40_bccent

erar

rang

emen

t

20 cm depth20 cm depth 40 cm depthclosed open

corn

erse

para

tew

ide

Furniture

Columns

v40_bl v40_br

0.20.2

c_blc_brc_bc_f c_flc_fr b_f b_b0.2 0.4

0.2

0.2

b_ch b_cv

unit: m

Beams

Explanatory notes: c: column, b: beam, v: volume, w: wide volume, s: shelf, f: front, b: back, r: right, l: left, 20: 20 cm thick, 40: 40 cm thick

Figure 2‐The analysis cases.


ICA 2010 3

3. RESULTS AND DISCUSSION

3.1. FREQUENCY RESPONSES AND SDS

Figure 3 illustrates frequency responses at the center receiving point R, and SDs of the listening area. As for the supplementation, to de-cide the evaluation area of SDs, SDs of the listening area have been compared with that of the space where the listening area was expand-ed in the cross-sectional direction by ±0.1 m. Though the graphs are omitted, the result shows that the tendency of both values have been almost resembled, so that we show SDs calculated by one section.

-35-30-25-20-15-10

-505

1015

0

3

6

9

Normalc_f c_b

Normalb_f b_bb_ch b_cv

SPL

[dB]

SDs [

dB]

80 100 125 160 200 25063 80 100 125 160 200 25063

Columns Beams

eigenfrequency

1/3 oct. band center frequency [Hz]

Columns

Columns effect on the sound fields at high frequencies by arranging them near the sound source (c_f). The average value of difference in SDs from the normal model is ‐1.30 dB. This means that columns contribute to improve uniformity of spatial distribution, but not so much as when the columns are arranged far from the sound source (c_b). It can be understand the results that elements effect largely when they are arranged near sound sources.

Beams

Even when beams are arranged where, they effect on the positions of peaks and dips of frequency responses, but the effects are small. The effects on SDs are at the same level as columns, but it cannot be concluded that the ele-ments improve the sound field.

Furniture

As for the closed-type shelves, it doesn’t depend on the arrangement position, the effects are relatively large at wide range of frequency responses. Although the effects of thick furniture are large, the tendencies don’t depend on their thickness. The effects of the defferences in the arrangement of the furniture indicate the similar tendency in the case arranged in corner position (bs) and the case arranged in back wall widely (w), but the in case of ar-ranged in the center of walls (bc) is different. Moreover, a similar behaviour is admitted in Figure 4 that shows sound pressure distributions including the listening area. About the average values of the difference in SDs from the normal model, it is 0.44 dB in v20_bc, it is 0.27 dB in v20_bs, and it is ‐0.60 dB. As mentioned above, the uniformity of spatial distribution is improved greatly when the furniture is arranged in corner of the room than center of walls.

-35-30-25-20-15-10

-505

1015

0

3

6

9

SPL

[dB]

SDs [

dB]

Normalv20_bc v20_bsv20_w

Normalv40_bc v40_bsv40_w

1/3 oct. band center frequency [Hz]80 100 125 160 200 25063 80 100 125 160 200 25063 80 100 125 160 200 25063 80 100 125 160 200 25063

Furniture (closed, 20 cm) Furniture (closed, 40cm) Furniture (open, center) Furniture (open, corner)

Normals20_bc s20_lcs20_rc

Normals20_bl s20_brs20_rb

Figure 3‐Frequency responses at R, and SDs in the listening area. Eigenfrequencies are calculated from room size ratio of the nor-mal model.


4 ICA 2010

3.2. SDF

To evaluate the flatness of frequency responses, SDf at the re-ceiving points contained in listening area were calculated. Fig-ure 5 shows that differences in SDf from the normal model classified by 1 dB. The result shows the tendency that is almost similar to past examination. However, there are cases which the standard deviations are increased remarkably at a lot of receiv-

ing points around the representative receiving point R though the value at R is greatly decreased shown in the previous result like v40_w. Therefore, it can be concluded that the examination including not only a representative receiving point but also around the point for frequency responses is necessary even if the room has limited listening position.

Normal

125

Hz

v40_bc v40_bs v40_w

y [m

]

0

0

1

2

3

250

Hz

y [m

]

0

1

2

3

x [m]-1 1 0

x [m]-1 1 0

x [m]-1 1 0

x [m]-1 1

sp

3 dB

Figure 4‐Relative SPL distributions on a plane (z = 1.2).

v20_bc

c_b c_br c_bl b_bb_fc_f b_chc_flc_fr b_cv

v40_bc s20_bc

s20_bl

xy

s20_lc

s20_br

s20_rc

s20_rbv40_bl v40_brv20_bl v20_br

v20_bs v40_bs

v20_w v40_w

v20_rc

v20_rb

v20_lc

Max: 2.38 dB (v40_w), Min: -3.43 dB (v20_rb)

more than 1 dB decrease+1 dBmore than 1 dB increase

0.6 0.61.5

2.7

1.2

1.2

1.2

1.2

t = 0.025

cent

er

closed open

corn

erse

para

tew

ide

Furniture

Columns0.2

0.2

0.2 0.4

0.2

0.2

Beams

arra

ngem

ent

20 cm depth20 cm depth 40 cm depth

Figure 5‐Differences from the normal model in SDf at 25 receiving points in the listening area.


ICA 2010 5

3.3. AND

In the above examination, SDf were calculated for every re-ceiving point and SDs were calculated for every frequency band. In the following, to evaluate the sound fields more easily, it concerning the mean value of SDf and that of SDs. Figure 6 shows the results arranged two dimensions. In addi-tion, both axes are normalized by the values of the normal model.

Columns

Although the effect of columns is small, in the cases which they were arranged near the sound source, both axes are in the tendency for the values to decrease. This means that both the uniformity of spatial distribution and flatness of fre-quency responses are improved.

Beams

The effects of beams are small, but show a tendency to change for the worse about uniformity of sound fields. Espe-cially, when installing beams in the distance from the sound source, the tendency appeared strongly.

Furniture

The effects of closed-type shelves are larger than that of col-umns and beams, and improvement tendency is shown by all the cases. Although the effects of thick furniture are large, the tendencies don’t depend on the thickness. On the other hand, the effects of open-type shelves are small and these are com-parable as columns or beams. However, only when the open-type shelves are in the position where sound incident into the side of them directly, they effect on the sound fields com-parable as closed-type shelves. Additionally, the correlation coefficient of SDf and SDs is 0.61 in this examination.

3.4. SDF,S

Next, to evaluate the sound fields by the frequency domain and the spatial domain simultaneously, SDf,s were calculated. The results normalized by the value of the normal model are shown in Figure 7. It is shown that these results are similar to the aforementioned results in general; The effects of columns and beams are small; Although the effects of open-type shelves is small, an improvement tendency is indicated rela-tively large only s20_lc. The improvement effects of closed-type shelves are large, especially thicker one. However, the tendency to the effects is different in any case depending on their arrangement position.

H

H

H

H

H

H

fl

ch cvfr

f

b fb

blbr

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Diff

eren

ce in

SD

s [dB

]

Difference in SDf [dB] Difference in SDf [dB]

HE

columnbeam

E EE

E(4.75)

-1 -0.8 -0.6 -0.4 -0.2 0(6.46)

0.2 0.4

B

B

B

B

B

B

B

B

G GG

G

G

I II

I

I

I

bc

lcrc

bc

bl

brrb

bc

lc

rcbl

brrb

bl

br

bs

bs ww

-1 -0.8 -0.6 -0.4 -0.2 0(6.46)

0.2 0.4

BG

close 20 cmclose 40 cm

I open 20 cm

Figure 6‐Differences in and from the normal model.


6 ICA 2010

c_f

c_b

c_bl

c_br

c_fl

c_fr

b_f

b_b

b_ch

b_cv

v20_

bcv2

0_bs

v20_

wv2

0_bl

v20_

brv2

0_lc

v20_

rbv2

0_rc

v40_

bcv4

0_bs

v40_

wv4

0_bl

v40_

brs2

0_bc

s20_

bls2

0_br

s20_

lcs2

0_rb

s20_

rc

-1

-0.8

-0.6

-0.4

-0.2

0(6.86)

0.2

0.4D

iffer

ence

in S

Df,s

[dB

]

column beam closed 20 cm 40 cm open

Figure 7‐Differences in SDf,s from the normal model.

4. CONCLUSIONS

In the present paper, the effects of additional elements, such as columns, beams and furniture, on the sound fields in a small rectangular room are investigated through wave-based numerical analysis. The results show that: the effect of col-umns is small but more than beams; that of closed-type shelves is relatively large but not so much with open-type shelves; The size and the arrangement of every element have unnegligible effects. It is also seen that the additional ele-ments generally lead to positive effects in flatness of fre-quency response and spatial uniformity even at low frequen-cies, although in specific case. Especially, when the elements are large or arranged near a sound source, the effects come to be large. Therefore, from these results, it is desirable to examine in detail the effects of arrangement of partial room elements in acoustic design of small enclosures.

ACKNOWLEDGMENTS

This project was supported by the Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (No. 19206062, 21360275).

REFERENCES

1 M. Louden, “Demension ratios of rectangular rooms with good distribution of engenton,” Acustica, 24, pp. 101–104 (1971).

2 J. Milner, “An investigation of the modal characteristics of non-rectangular reverberation rooms,” Journal of The Acoustical Society of America, 84, pp. 772–779 (1989).

3 T. Samejima, K. Hirate and M. Yasuoka, “Optimum de-sign of room shape and arrangement of absorptive patches by evaluating the distribution of poles of a trans-fer function in an acoustic system,” Journal of Architec-ture, Planning and Environmental Engineering (transac-tions of AIJ), 511, pp. 9-14 (1998).

4 Y. Yasuda, K. Eda and T. Sakuma, “Effect of acoustic diffusers on the sound field in a small room: steady-state analysis of sound fields in rooms with unevenly-distributed acoustic absorbers,” Summaries of Technical Papers of Annual Meeting Architectural Institute of Ja-pan, D-2, pp. 315-316 (2009).

5 K. Eda, Y. Yasuda and T. Sakuma, “Effect of acoustic diffusers on the sound field in a small room: transient analysis of sound fields in rooms with unevenly-distributed acoustic absorbers,” Summaries of Technical Papers of Annual Meeting Architectural Institute of Ja-pan, D-2, pp. 317-318 (2009).

6 M. Nakahara, A. Omoto and Kyoji Fujiwara, “The effect of a mixing console on the monitoring response in a mix-ing room,” Acoustical Science and Technology, 26, pp. 90–101 (2005).

7 A. Ikeda, M. Nakahara, C. Kai and A. Omoto, “The acoustical effect of audio equipment and furniture in a mixing room,” Journal of Acoustical Society of Japan (E), 26, pp. 233-236 (2005).

8 S. Maluski and B. Gibbs, “The effect of construction material, contents and room geometry on the sound field in dwellings at low frequencies,” Applied Acoustics, 65, pp. 31–44 (2004).

9 H. Olson, “Music, Physics and Engineering,” Dover Pub-lications, New York (1967).

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