// calculates transformation matrix for a single cone of an instrument's profile
func stageMatrix2(radiusIn, radiusOut, radiusCenter, length, radianFrequency float64) [4]complex128 {
xi := complex(radiusIn, 0) // m
xi1 := complex(radiusOut, 0) // m
l := complex(length, 0) // m
w := radianFrequency // rad / s
centerPlaneArea := pi * radiusCenter * radiusCenter // m2
sm := centerPlaneArea
sphericalAreaIn := 4 * pi * radiusIn * radiusIn // m2
si := sphericalAreaIn
rv := math.Sqrt(p * w * sm / (n * pi)) // rad^1/2
r0 := p * c / si // kg/(m4*s) or Pa*s, units of impedance
k := w / c // wavenumber, rad / m
zc := complex(r0, 0) * complex(1+0.369/rv, -0.369/rv) // Pa*s/sqrt(rad)
g := complex(k, 0) * complex(1.045/rv, 1+1.045/rv) // sqrt(rad)/m
gl := g * l // sqrt(rad)
cosh_gl := cmplx.Cosh(gl) // mangled sqrt(rad)
sinh_gl := cmplx.Sinh(gl) // mangled sqrt(rad)
a11 := xi1 / xi * (cosh_gl - sinh_gl/(g*xi1)) // unitless (more mangled sqrt(rad))
a12 := xi / xi1 * zc * sinh_gl // Pa*s + mangle
a21 := 1 / zc * ((xi1/xi-1/(g*g*xi*xi))*sinh_gl + (gl*cosh_gl)/(g*g*xi*xi)) // 1/(Pa*s) + mangle
a22 := xi / xi1 * (cosh_gl + sinh_gl/(g*xi)) // unitless + mangle
return [4]complex128{a11, a12, a21, a22}
}
func test0(val, val0 complex128) complex128 {
return val * cmplx.Sqrt(cmplx.Cosh(val*val*val)) * val0
}