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Sound distribution in a squareducthaving an intake



A previous analyze discussed a rectangular soundproofing ventilation unit having an outlet and an electrical outlet located on the reverse face resulting in a reduced wall plug area. Therefore, the ventilation function is decreased. To boost this problem, rectangular one showcasing an outlet and an electrical outlet which are located on the crossed proper angle confront is recommended in this operate. First, store sound pressure to the presented inlet homogeneous velocity is usually obtained depending on the say equation plus the boundary circumstances. Next, the experimental answers are shown to be in reasonable contract with our assumptive predictions.

Along with the remarkable economic development, in recent years in developing countries environmental challenges including road noise have been getting more serious in countries belonging to exotic regions. Yano and others [1] measured car related noise on the main highway of Vietnam for 24 hours and reported that a noise level greater than 75 deutsche bahn occurred almost all day on the road with the maximum noise level. On the other hand, ventilation holes are trusted in countries in tropical regions, that are installed in the middle of the windowpane and the roof top.

Nevertheless , the noise of the highway passes throughout the ventilation gap and advances to the living area. As a result, there exists virtually no big difference in the sound level between the space and the outside, and people moving into an environment will be increasingly uncomfortable with noise increasing year by season even though you will find considerable understanding and patience. In recent houses, a glass plate is definitely indicated in

the outside of the doorway ventilation opening to provide soundproofing measures. With this actions indoors simply attenuation numbers of only twelve dB 15 dB can be acquired, but folks are considerably decreased discomfort to noise. Nevertheless , most household houses in Southeast Asia do not have air-conditioning equipment, consequently by final the cup plate throughout the day, the air out the room indoors cannot be performed. A previous study [2] talked about a rectangular soundproofing ventilation device having a great inlet and an outlet situated on the opposite confront which results in a lower outlet location. As a result, the ventilation function is lowered. To improve this problem, square a single featuring an inlet and an outlet which are located on the entered right angle confront is definitely proposed with this work. You will discover for two kinds of waves inside chamber, namely the position wave that propagates in the axial way and the traverse wave that propagates inside the radial direction. The navigate wave happens in the high frequency range. About the circular cylindrical chamber, the noise may have a tendency to improve in this consistency range, far from decreasing depending on resonance of the higher ways.

From this paper, in the beginning the outletsound pressure to the given inlet uniform speed is acquired based on the wave equation and the boundary conditions. Up coming, the experimental results are shown to be in reasonable agreement with our theoretical estimations.


Insertion Loss

Insertion loss ELLE defined by [3]

IL=10log W_r/W_0 =20log|U_1/U_2 | (1)

Here, W_r and W_0 are the radiated power for one reason for space with or with no acoustic component inserted among that point as well as the source. Precisely U_1/U_2 can be equal to the D parameter of the four-pole parameters, so far as constant speed source concern yourself.

Once three traditional acoustic elements connected in series, as the sectional part of element 1 and a few are completely small to match up against those of element 2 of the D unbekannte of the complete system can be described by following estimated equation

( (A[emailprotected]D))=( (A_1[emailprotected]_1D_1 ))( (A_w[emailprotected]_wD_w ))( (A_3[emailprotected]_3D_3 ))

D=(coskl_1)(C_w)(jZ_3 sinkl_3) (2)

where C_w denoted the C parameter of element 2 . To be able to obtain a reliable IL impact, D unbekannte must be high enough. In other words, the design of element-2 to get a high enough parameter C_w can be demanded.

Cw of square SVU

Model of the rectangular soundproofing ventilation device which has a aspect of a×a×dis shown in Figure 1 . Dimension of an input and output are(a_i2-a_i1)×(b_i2-b_i1) and(a_02-a_01)×(d_02-d_01) they located on the confront which has a section area of S_ab=a×aand S_ad=a×d, correspondingly.

Figure1. Squaresoundproofing air flow unit

Waveequation in terms ofvelocity potential has by

(‚^2/(‚x^2 )+‚^2/(‚x^2 )+‚^2/(‚x^2 ))Φ=1/c^2 ‚^2/(‚t^2 ) Φ (3)

where c is a sound speed. Let Φ=š2…exp¡(jωt)(j^2=-1, ω=kc, e: wave number ) then this general solution of Frequency. (3) may be given because


× ( Csinαx+Dcosαx)

× (Esinš(s^2-α^2 ) y+Fcosš(s^2-α^2 ) sumado a )


where μ^2=s^2-k^2, A, M, C, G, E and F will be arbitrary constants determinable from your boundary conditions, other emblems are constants.

Let-‚…/‚x, -‚…/‚y and -‚…/‚zare the speed component in the x, con and unces directions, correspondingly. Assuming the walls of the cavity to be properly rigid plus the loss in the wall may be neglected in that case boundary conditions are:

[1] at x=0 -(‚…)/‚x=0 (5)

[2] at x=a -(‚…)/‚x =0 (6)

[3] in y=0 -(‚…)/‚y =0 (7)

[4] at y=a -(‚…)/‚y=V_0 F_0 (x, z)(8)

[5] at z=0-(‚…)/‚z=V_i F_i (x, z)(9)

[6] at z=d-(‚…)/‚z=0(10)

where V_(i )is the driving velocity at the suggestions, F_i (x, z)is defined as


Permit …=…_a+…_bthen -‚…/‚x=-‚…_a/‚x+-‚…_b/‚x, therefore we now have the following boundary conditions

[1a] at x=0 -(‚…)/‚x =0 (12)

[2a] at x=a -(‚…)/‚x =0 (13)

[3a] at y=0 -(‚…)/‚y =0 (14)

[4a] at y=a -(‚…)/‚y=V_0 F_0 (x, z)(15)

[5a] in z=0-(‚…)/‚z=0(16)

[1b] at x=0 -(‚…)/‚x =0 (17)

[2b] at x=a -(‚…)/‚x =0 (18)

[3b] at y=0 -(‚…)/‚y =0 (19)

[4b] at y=a -(‚…)/‚y=0(20)

[5b] at z=0-(‚…)/‚z=V_i F_i (x, z)(21)

Based upon the above boundary conditions …_abecomes

〖 …〗_a=4V_i/S_ab ‘_(m=0)^ž’‘_(n=0)^ž'(coshμ_(m, n) (z-d))/(μ_(m, n) sinhμ_(m, n) d)

I_(m, n) cos(mπx/a)cos(nπy/a) (22)


〖 I〗_(m, n)=«_(a_i1)^(a_i2)’cos(mÏ€x/a)dx

× «_(a_i1)^(a_i2)’cos(mÏ€y/a)dy (23)

Similarly, 〖 …〗_b turns into

〖 …〗_b=4V_0/S_ad ‘_(m=0)^ž’‘_(n=0)^ž’〖cosh nÏ€/d(z-d)〗

〖× O〗_(m, n) cos(mπx/a)cos(nπy/a) (24)

exactly where

〖 O〗_(m, n)=«_(a_i1)^(a_i2)’cos(mÏ€x/a)dx

× «_(a_i1)^(a_i2)’〖cos nÏ€/d (z-d)dy〗 (25)

The average sound pressure for the output is found as

(P_0 ) Ì…=1/S_0 «_(a_02)^(a_02)’«_(d_01)^(d_02)’〖P(x, w, z)dxdz〗

=jk ρc/S_0 ‘_(m=0)^ž’‘_(n=0)^ž'[4 V_i/S_ab (I_(m, n) cos(nÏ€))/(μ_(m, n) sinhμ_(m, n) d)¤

׫_(a_02)^(a_02)’«_(d_01)^(d_02)’〖cosμ_(m, n) (z-d) 〗 cos(mÏ€x/a)dxdz

+4V_0/S_ad O_(m, n)/(β_(m, n) tanβ_(m, n) d)

׫_(a_02)^(a_02)’«_(d_01)^(d_02)’〖cos nÏ€/d (z-d) 〗 œ cos(mÏ€x/a)dxdz]


whereU_i=V_i S_i is the quantity velocity delivered from the type. 〖 Z〗_0=ρc/S_(0 )is the characteristic impedance of the outcome.

ExpandingEq. (26) with m=0 and n=0 the above mentioned equation becomes

(P_0 ) Ì…=j4Z_0 [1/sinkd (〖-O〗_0, 0 U_i+(S_0/S_ad coskd) U_0 ) ¤

+1/k ‘_*^ž’‘_*^ž'((I_(m, n) O_(m, n) cos(nÏ€))/(S_ad S_0 μ_(m, n) sinhμ_(m, n) d)¤ U_i

œ +œ U_0/(S_ad S_0 ) O_(m, n)/(β_(m, n) tanβ_(m, n) d)) ]


The Cw of SVU could be found from Eq. (27) as



The average of wall socket sound pressure is derived from Eq. (27) in which the first term in the group represents issues the plane wave as well as the second signifies the higher buy mode say. First, with respect to the plane wave, the 1st term of Eq. (27), the sound pressure level is fantastic at the frequencies where the denominator sin¡(kd) turn into zero.


kd=ηπ´f=η c/2d (η=1, 2, ¦) (29)

Similarly, with respect to higher order mode surf, the second term of Eq. (27), the sound pressure level becomes great at the eq given the following:

sinhμ_(m, n) d=0

´f_(m, n)=c/2Ï€ š((mÏ€/a)^2+(nÏ€/a)^2+(ηπ/d)^2 )

=c/2a š(m^2+n^2+(ηa/d)^2 )

(η=0, 1, 2, ¦) (30)

The spectrum of any plane influx and higher order mode are showed in Figure installment payments on your

Remember that, in the case of square SVU, the resonance frequencies are

f_(m, n)=c/2Ï€ š((mÏ€/a)^2+(nÏ€/b)^2+(ηπ/d)^2 )

(η=0, 1, 2, ¦) (31)

By Eq. (30) and Eq. (31), it is clear that the number of resonance frequencies produced inside the sq . SVU is less than those of rectangular SVU.

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Published: 03.24.20

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