Propagation of sound in a square duct with inlet and outlet located on results in a reduced exit area. As a result, the ventilation function is reduced. To improve this problem, in this work a square characterized by an inlet and an outlet located on the crossed right-angle face is proposed. First, the output sound pressure at the input uniform velocity is obtained based on the wave equation and boundary conditions. Subsequently, we demonstrate that the experimental results are in reasonable agreement with our theoretical predictions. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay Along with remarkable economic development, environmental problems, including road noise, have worsened in developing countries in recent years in countries belonging to tropical regions. Yano et al [1] measured road traffic noise on the main road in Vietnam for 24 hours and reported that a noise level above 75 dB occurred almost all day on the road with the highest noise level. On the other hand, ventilation holes are widely used in tropical region countries, which are installed in the center of the window and roof. However, street noise passes through the ventilation hole and travels into the living space. As a result, there is practically no difference in the noise level between the room and the outside, and people living in the room feel more and more uncomfortable with the noise that increases from year to year, even if they have a remarkable familiarity and patience. In newer homes, a glass pane is provided outside the door ventilation hole to ensure sound insulation. With these measures indoors, attenuation levels of just 10 dB - 15 dB can only be achieved, but the noise discomfort for people is significantly reduced. However, most residential houses in Southeast Asia do not have air conditioning equipment, so by closing the glass pane during the day, it is not possible to ventilate the room inside. A previous study [2] discussed a rectangular soundproof ventilation unit with an inlet and outlet located on the opposite face resulting in a small outlet area. As a result, the ventilation function is reduced. To improve this problem, in this work a square is proposed characterized by an entrance and an exit that are located on the front at a crossed right angle. Inside the chamber there are two types of waves, namely the standing wave which propagates in the axial direction and the transverse wave which propagates in the radial direction. The transverse wave occurs in the high frequency range. As for the circular cylindrical chamber, the noise will have a tendency to increase in this frequency range, far from decreasing depending on the resonance of the higher modes. In this paper, we first obtain the output sound pressure at the given uniform input velocity based on the wave equation and boundary conditions. Subsequently, we demonstrate that the experimental results are in reasonable agreement with our theoretical predictions. Analysis method Insertion loss IL insertion loss defined by [3]IL=10log W_r/W_0 =20log|U_1/U_2 | (1)Here, W_r and W_0 are the power radiated to a point in space with or without the acoustic element inserted between that point and the source. The ratio between U_1/U_2 isequal to the D parameter of the quadripolar parameters, as regards the constant speed source. When three acoustic elements are connected in series, since the cross-sectional area of elements 1 and 3 is small enough to be compared with those of element 2 the D parameter of the entire system can be described by the following approximate equation(*** (A&B@C&D))=(***(A_1&B_1@C_1&D_1 ))(***(A_w&B_w@C_w&D_w ))(***(A_3&B_3 @C_3&D_3))D=(coskl_1)(C_w)(jZ_3 sinkl_3) ( 2)where C_w indicates the C parameter of element 2. To obtain a reliable IL effect, the D parameter must be sufficiently high. In other words, the design of element 2 is required to have a sufficiently high C_w parameter. Cw of square SVU Model of the rectangular soundproof ventilation unit that has a dimension of a×a×dis shown in Figure 1. Size of an input and outputs are(a_i2-a_i1)×(b_i2-b_i1) and(a_02- a_01)×(d_02-d_01) positioned on the face that has a sectional area of S_ab=a×a and S_ad=a×d, respectively.Figure 1. Square soundproofing fan unitThe wave equation in terms of velocity potential is given by(∂^2/(∂x^2 )+∂^2/(∂x^2 )+∂^2/(∂x^2 ))Φ=1/c ^2 ∂^2/(∂t ^2 ) Φ (3)where c is the speed of sound. Let Φ=√2∅exp⁡(jωt)(j^2=-1,ω=kc,k: wave number ) then the general solution of Eq.(3) can be given as ∅=(Aexp( μZ)+ Bexp(-μZ))× ( Csenαx+Dcosαx)× (Esin√(s^2-α^2 ) y+Fcos√(s^2-α^2 ) y )(4)where μ^2 =s^ 2-k^2, A, B, C, D, E and F are arbitrary constants determinable from the boundary conditions, other symbols are constants. Let-∂∅/∂x,-∂∅/∂y and -∂∅/ ∂zare the velocity component in the x, y and z directions respectively. Assuming that the cavity walls are perfectly rigid and that the wall loss can be neglected, the boundary conditions are:[1] ax=0 -(∂∅)/∂x=0 (5)[2] ax= a -(∂∅)/∂x =0 (6)[3] at 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 speed at the entrance, F_i (x,z)is defined as(11)Let ∅=∅_a+∅_bthen -∂∅/∂x=-∂∅_a/ ∂x+-∂∅_b/∂x, so we have the following boundary conditions[1a] at x=0 -(∂∅)/∂x =0 (12)[2a] at x=a -(∂∅)/ ∂x =0 (13)[3a] in y=0 -(∂∅)/∂y =0 (14)[4a] in y=a -(∂∅)/∂y=V_0 F_0 (x,z) (15)[5a] at 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 on the above boundary conditions ∅_abecome〖 ∅〗_a=4V_i/S_ab ∑_ (m= 0)^∞▒∑_(n=0)^∞▒(coshμ_(m,n) (zd))/(μ_(m,n) sinhμ_(m,n) d)I_(m,n ) cos( mπx/a)cos(nπy/a) (22)where〖 I〗_(m,n)=∫_(a_i1)^(a_i2)▒cos(mπx/a)dx× ∫_(a_i1) ^(a_i2 )▒cos(mπy/a)dy (23)Similarly, 〖 ∅〗_b becomes〖 ∅〗_b=4V_0/S_ad ∑_(m=0)^∞▒∑_(n=0)^∞▒ 〖cosh nπ /d(zd)〗〖× O〗_(m,n) cos(mπx/a)cos(nπy/a) (24)where〖 O〗_(m,n)=∫_(a_i1) ^(a_i2 )▒cos(mπx/a)dx× ∫_(a_i1)^(a_i2)▒〖cos nπ/d (zd)dy〗 (25)The average sound pressure at the outlet is found as(P_0 ) ̅ =1/ S_0 ∫_(a_02)^(a_02)▒∫_(d_01)^(d_02)▒〖P(x,b,z)dxdz〗=jk ρc/S_0 ∑_(m=0)^∞▒ ∑_( n=0)^∞▒[4 V_i/S_ab (I_(m,n) cos(nπ))/(μ_(m,n) sinhμ_(m,n) d)┤×∫_(a_02) ^(a_02 )▒∫_(d_01)^(d_02)▒〖cosμ_(m,n) (zd) 〗 cos(mπx/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 nπ/d (zd) 〗 ├ cos(mπx/a)dxdz](26 )whereU_i= V_i S_i is the velocity of the volume supplied by the input.〖 Z〗_0=ρc/S_(0 )is the characteristic impedance of the output.ExpandingEq.(26) with m=0 and n=0 the equation previous becomes (P_0 ) ̅=j4Z_0 [1/sinkd (〖-O〗_0,0 U_i+(S_0/S_ad coskd) U_0 ) ┤+1/k ∑_*^∞▒∑_*^∞▒((I_( m,n) O_ (m,n) cos(nπ))/(S_ad S_0 μ_(m,n) sinhμ_(m,n) d)┤ U_i├ +├ U_0/(S_ad S_0 ) O_(m,n) /(β_(m ,n) tanβ_(m,n) d)) ](27)The Cw of SVU can be found from Eq. (27) as(28)Results and discussionThe average output sound pressure is derived from Eq. (27) where the first term in parentheses represents the plane wave and the second represents the higher-order modal wave. First of all,.

Topic > Propagation of sound in a square duct with inlet and outlet located on results in a reduced exit area. As a result, the ventilation function is reduced. To improve this problem, in this work a square characterized by an inlet and an outlet located on the crossed right-angle face is proposed. First, the output sound pressure at the input uniform velocity is obtained based on the wave equation and boundary conditions. Subsequently, we demonstrate that the experimental results are in reasonable agreement with our theoretical predictions. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay Along with remarkable economic development, environmental problems, including road noise, have worsened in developing countries in recent years in countries belonging to tropical regions. Yano et al [1] measured road traffic noise on the main road in Vietnam for 24 hours and reported that a noise level above 75 dB occurred almost all day on the road with the highest noise level. On the other hand, ventilation holes are widely used in tropical region countries, which are installed in the center of the window and roof. However, street noise passes through the ventilation hole and travels into the living space. As a result, there is practically no difference in the noise level between the room and the outside, and people living in the room feel more and more uncomfortable with the noise that increases from year to year, even if they have a remarkable familiarity and patience. In newer homes, a glass pane is provided outside the door ventilation hole to ensure sound insulation. With these measures indoors, attenuation levels of just 10 dB - 15 dB can only be achieved, but the noise discomfort for people is significantly reduced. However, most residential houses in Southeast Asia do not have air conditioning equipment, so by closing the glass pane during the day, it is not possible to ventilate the room inside. A previous study [2] discussed a rectangular soundproof ventilation unit with an inlet and outlet located on the opposite face resulting in a small outlet area. As a result, the ventilation function is reduced. To improve this problem, in this work a square is proposed characterized by an entrance and an exit that are located on the front at a crossed right angle. Inside the chamber there are two types of waves, namely the standing wave which propagates in the axial direction and the transverse wave which propagates in the radial direction. The transverse wave occurs in the high frequency range. As for the circular cylindrical chamber, the noise will have a tendency to increase in this frequency range, far from decreasing depending on the resonance of the higher modes. In this paper, we first obtain the output sound pressure at the given uniform input velocity based on the wave equation and boundary conditions. Subsequently, we demonstrate that the experimental results are in reasonable agreement with our theoretical predictions. Analysis method Insertion loss IL insertion loss defined by [3]IL=10log W_r/W_0 =20log|U_1/U_2 | (1)Here, W_r and W_0 are the power radiated to a point in space with or without the acoustic element inserted between that point and the source. The ratio between U_1/U_2 isequal to the D parameter of the quadripolar parameters, as regards the constant speed source. When three acoustic elements are connected in series, since the cross-sectional area of elements 1 and 3 is small enough to be compared with those of element 2 the D parameter of the entire system can be described by the following approximate equation(*** (A&B@C&D))=(***(A_1&B_1@C_1&D_1 ))(***(A_w&B_w@C_w&D_w ))(***(A_3&B_3 @C_3&D_3))D=(coskl_1)(C_w)(jZ_3 sinkl_3) ( 2)where C_w indicates the C parameter of element 2. To obtain a reliable IL effect, the D parameter must be sufficiently high. In other words, the design of element 2 is required to have a sufficiently high C_w parameter. Cw of square SVU Model of the rectangular soundproof ventilation unit that has a dimension of a×a×dis shown in Figure 1. Size of an input and outputs are(a_i2-a_i1)×(b_i2-b_i1) and(a_02- a_01)×(d_02-d_01) positioned on the face that has a sectional area of S_ab=a×a and S_ad=a×d, respectively.Figure 1. Square soundproofing fan unitThe wave equation in terms of velocity potential is given by(∂^2/(∂x^2 )+∂^2/(∂x^2 )+∂^2/(∂x^2 ))Φ=1/c ^2 ∂^2/(∂t ^2 ) Φ (3)where c is the speed of sound. Let Φ=√2∅exp⁡(jωt)(j^2=-1,ω=kc,k: wave number ) then the general solution of Eq.(3) can be given as ∅=(Aexp( μZ)+ Bexp(-μZ))× ( Csenαx+Dcosαx)× (Esin√(s^2-α^2 ) y+Fcos√(s^2-α^2 ) y )(4)where μ^2 =s^ 2-k^2, A, B, C, D, E and F are arbitrary constants determinable from the boundary conditions, other symbols are constants. Let-∂∅/∂x,-∂∅/∂y and -∂∅/ ∂zare the velocity component in the x, y and z directions respectively. Assuming that the cavity walls are perfectly rigid and that the wall loss can be neglected, the boundary conditions are:[1] ax=0 -(∂∅)/∂x=0 (5)[2] ax= a -(∂∅)/∂x =0 (6)[3] at 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 speed at the entrance, F_i (x,z)is defined as(11)Let ∅=∅_a+∅_bthen -∂∅/∂x=-∂∅_a/ ∂x+-∂∅_b/∂x, so we have the following boundary conditions[1a] at x=0 -(∂∅)/∂x =0 (12)[2a] at x=a -(∂∅)/ ∂x =0 (13)[3a] in y=0 -(∂∅)/∂y =0 (14)[4a] in y=a -(∂∅)/∂y=V_0 F_0 (x,z) (15)[5a] at 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 on the above boundary conditions ∅_abecome〖 ∅〗_a=4V_i/S_ab ∑_ (m= 0)^∞▒∑_(n=0)^∞▒(coshμ_(m,n) (zd))/(μ_(m,n) sinhμ_(m,n) d)I_(m,n ) cos( mπx/a)cos(nπy/a) (22)where〖 I〗_(m,n)=∫_(a_i1)^(a_i2)▒cos(mπx/a)dx× ∫_(a_i1) ^(a_i2 )▒cos(mπy/a)dy (23)Similarly, 〖 ∅〗_b becomes〖 ∅〗_b=4V_0/S_ad ∑_(m=0)^∞▒∑_(n=0)^∞▒ 〖cosh nπ /d(zd)〗〖× O〗_(m,n) cos(mπx/a)cos(nπy/a) (24)where〖 O〗_(m,n)=∫_(a_i1) ^(a_i2 )▒cos(mπx/a)dx× ∫_(a_i1)^(a_i2)▒〖cos nπ/d (zd)dy〗 (25)The average sound pressure at the outlet is found as(P_0 ) ̅ =1/ S_0 ∫_(a_02)^(a_02)▒∫_(d_01)^(d_02)▒〖P(x,b,z)dxdz〗=jk ρc/S_0 ∑_(m=0)^∞▒ ∑_( n=0)^∞▒[4 V_i/S_ab (I_(m,n) cos(nπ))/(μ_(m,n) sinhμ_(m,n) d)┤×∫_(a_02) ^(a_02 )▒∫_(d_01)^(d_02)▒〖cosμ_(m,n) (zd) 〗 cos(mπx/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 nπ/d (zd) 〗 ├ cos(mπx/a)dxdz](26 )whereU_i= V_i S_i is the velocity of the volume supplied by the input.〖 Z〗_0=ρc/S_(0 )is the characteristic impedance of the output.ExpandingEq.(26) with m=0 and n=0 the equation previous becomes (P_0 ) ̅=j4Z_0 [1/sinkd (〖-O〗_0,0 U_i+(S_0/S_ad coskd) U_0 ) ┤+1/k ∑_*^∞▒∑_*^∞▒((I_( m,n) O_ (m,n) cos(nπ))/(S_ad S_0 μ_(m,n) sinhμ_(m,n) d)┤ U_i├ +├ U_0/(S_ad S_0 ) O_(m,n) /(β_(m ,n) tanβ_(m,n) d)) ](27)The Cw of SVU can be found from Eq. (27) as(28)Results and discussionThe average output sound pressure is derived from Eq. (27) where the first term in parentheses represents the plane wave and the second represents the higher-order modal wave. First of all,.