# Sound absorption coefficient of membrane backed with air cavity

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RAJA KUMAR 2023 年 1 月 17 日

I am trying to learn the membrane backed by air cavity in the following paper, figure 2. My code result does not match the paper result. can somebody point out the error?
I Have used equation no 3, 4, 5, and 9 to obtain figure 2 (a)
clc
clear all;
f= (100:2:1600);
omega= 2*pi*f;
rho_s=0.265; T=76.53*(1+1j*0.005); D=0.1; a=0.05; % Fig 2 a
c=343; rho_0=1.213; Z_0 = rho_0*c;
k0=omega/c;
km=omega.*sqrt(rho_s/T);
%% Impedance of membrane with air cavity only
Z_m = (1j*omega*rho_s)./(1-((2./km*a).*(besselj(1, km*a)./besselj(0,km*a))));
Z_w = -1j*Z_0*cot(k0*D);
Z_s = Z_m + Z_w;
Z_s =Z_s/Z_0;
R = (Z_s - 1)./(Z_s + 1);
alpha_1 = 1 - ((abs(R)).^2);
figure(1)
set(gca,'FontSize',16)
plot(f,alpha_1);
xlabel('Frequency (Hz)')
ylabel('Sound absorption coefficient')
grid on
grid minor
ylim([0 1])
set(gca, 'XScale', 'log')
set(gca, 'YScale', 'log')

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### 採用された回答

VBBV 2023 年 1 月 17 日

clc
clear all;
f= (100:2:1600);
omega= 2*pi*f;
rho_s=0.265;
T=76.53*(1+1j*0.005);
D=0.1;
a=0.05; % Fig 2 a
c=343;
rho_0=1.213;
Z_0 = rho_0*c;
k0=omega/c;
km=omega.*sqrt(rho_s/T);
%% Impedance of membrane with air cavity only
% Z_m = (1j*omega*rho_s)./(1-((2./km*a).*(besselj(1, km*a)./besselj(0,km*a))));
Z_m = (1j*omega*rho_s)./(((besselj(0, km*a)./besselj(2,km*a))));
Z_w = -1j*Z_0*cot(k0*D);
Z_s = Z_m + Z_w;
Z_s = Z_s/Z_0;
R = (Z_s - 1)./(Z_s + 1);
alpha_1 = 1 - ((abs(R)).^2);
figure(1)
set(gca,'FontSize',16)
plot(f,alpha_1); % check using semilogx
%xticklabels(xL)
xlabel('Frequency (Hz)')
ylabel('Sound absorption coefficient')
grid on
grid minor
ylim([0 1])
set(gca, 'XScale', 'log')
The plot was drawn using the below equation
Z_m = (1j*omega*rho_s)./(((besselj(0, km*a)./besselj(2,km*a)))); % Eq (3) where he writes as it
% can also be written as,
and not with equation you used. Convert the log representation of xlabels using xticklabels
##### 3 件のコメント表示非表示 2 件の古いコメント
VBBV 2023 年 1 月 18 日

Apparently, the results show that they are different equations, applied for a specific context in their study. if it solved your problem pls accept the answer,

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