Extrema of the Jinc function

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Extrema of the Jinc function
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sinc(kL/2sinq) vs. jinc (kd/2sinq)
circle
d2a
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theta -pi/2.01pi/2

• polar(theta, abs(2 besselj(1, ka sin(theta))
  ./ (ka sin(theta))))

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Circular piston, rigid baffle, ka1
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Circular piston, rigid baffle, ka3
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Circular piston, rigid baffle, ka6
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Circular piston,rigid baffle,ka12
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near field (blue) vs. far field (red)
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Matlab commands

• r 0.0164
• plot(r, abs(sin(pi (sqrt(r.2 a2) - r))))
• hold on
• r1 16.0164
• plot(r1, a2 pi ./ r1 / 2, 'r')
• xlabel('normalized axial distance (r / \lambda)')
• ylabel('normalized pressure P / (2 \rho_0 c
  U_0)')
• title('a / \lambda 4')
• legend('a2 \pi / (2 r \lambda)', 'sin ((r2
  a2)1/2 - r) \pi / \lambda')
• grid
• fix_axis