7.4.6.c) clear all close all clc %% Part A figure % Plot Colors C = ['k','r','g','b']; % Characteristic Impedance (assume water) pc = 1.54e6; % velocity amplitude U = 1; % r/a x1 = 0:.01:10; % pressure values p1(4,1001) = 0; hold on for ka = 3:3:12 p1(ka/3,:) = 2*pc*U*abs(sin(.5*ka*x1.*(sqrt(1+(1./x1).^2)-1))); plot(x1,p1(ka/3,:),C(ka/3)) end % format plot title('On-Axis Pressure Amplitude vs. r/a') xlabel('r/a') ylabel('Pressure') legend('ka = 3','ka = 6','ka = 9','ka = 12') %% Part B figure % pressure values hold on p2(4,1001) = 0; for ka = 3:3:12 x2 = x1(x1 > ka/2); % only r/a greater than ka/2 par1 = .5*pc*U*(1./x2)*ka; p2(ka/3,:) = [nan(1,1001-length(x2)),par1]; plot(x2,p1(ka/3,1002-length(x2):end)./p2(ka/3,1002-length(x2):end),C(ka/3)) end % format plot axis([0,10,.9,1]) title(‘Pressure Ratio vs. r/a') xlabel('r/a') ylabel('Pressure Ratio') legend('ka = 3','ka = 6','ka = 9','ka = 12') %% Part C figure % pressure values p3(1,1001) = 0; % ka f = 4000; w = 2*pi*f; c = 1500; k = w/c;

a = .2; ka = k*a; % pressure values (eqn 1) p31 = 2*pc*U*abs(sin(.5*ka*x1.*(sqrt(1+(1./x1).^2)-1))); % pressure values (eqn 2) x2 = x1(x1 > ka/2); % only r/a greater than ka/2 par1 = .5*pc*U*(1./x2)*ka; p32 = [nan(1,1001-length(x2)),par1]; % pressure ratio pr = p31(1,1002-length(x2):end)./p32(1,1002-length(x2):end); % plot plot(x2,pr) axis([0,10,.9,1]) title(‘Pressure Ratio vs. r/a') xlabel('r/a') ylabel('Pressure Ratio') % find r/a = .9 i = 1; while pr(i) < .9 i = i+1; end % r x2(i-1)*a

a)

b)

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5x 10

6 On-Axis Pressure Amplitude vs. r/a

r/a

Pre

ssur

e

ka = 3ka = 6ka = 9ka = 12

0 1 2 3 4 5 6 7 8 9 100.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1Pressure Ratio vs. r/a

r/a

Pre

ssur

e R

atio

ka = 3ka = 6ka = 9ka = 12

c)

r = 0.3500 m

0 1 2 3 4 5 6 7 8 9 100.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1Pressure Ratio vs. r/a

r/a

Pre

ssur

e R

atio