Sound absorption coefficient of membrane backed with air cavity

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Accepted Answer

VBBV
VBBV on 17 Jan 2023
Edited: VBBV on 17 Jan 2023
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 Comments
RAJA KUMAR
RAJA KUMAR on 18 Jan 2023
First of all sir, I thank you for your valuable comment. I had not used the second equation as it had said that the both the equations are same. I will work on your suggestions and update you.
The paper had said that both equations give the same result but now it can be clearly seen that the both the equations are not even approximately same right ?
VBBV
VBBV on 18 Jan 2023
Edited: VBBV on 18 Jan 2023
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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