Flute acoustics: measurement, modelling and design - School of ...

APPENDIX B. PROGRAM LISTINGS 199
double ka = k*a;
complex d;
double modR;
complex Z0 = charZ(c, rho, a), Z;
/* define the end correction for the low frequency limit */
d.Re = 0.8216 * a;
/* determine the frequency-dependent end correction (15a) */
d.Re = d.Re / (1 + pow(0.77 * ka,2) / (1 + 0.77 * ka));
/* determine the modulus of the reflection coefficient (15b) */
modR = (1 + 0.323 * ka - 0.077 * pow(ka,2)) / (1 + 0.323 * ka
+ (1 - 0.077) * pow(ka,2));
/* calculate the imaginary part of the end correction */
d.Im = log(modR) / (2 * k);
/* calculate the impedance (9) */
Z = multz(j, multz(Z0, tanz(multz(real(k), d))));
return Z;
}
TransferMatrix tubeMatrix(double f, double c, double rho, double L,
double a, double alphacorrection) {
complex Zo, jkL, A, B, C, D;
/* check for zero length segment */
if(L == 0.0)
return identitym();
Zo = charZ(c, rho, a);
jkL = multz(j, multz(waveNum(f, c, a, alphacorrection), real(L)));
A = coshz(jkL);
B = multz(Zo, sinhz(jkL));
C = divz(sinhz(jkL), Zo);
D = A;
return createTransferMatrix(A, B, C, D);;
}
TransferMatrix coneMatrix(double f, double c, double rho, double L,
double a1, double a2, double alphacorrection) {
complex k, kL, kx1, kx2, theta1, theta2, sintheta1, sintheta2;
complex A, B, C, D;
double S1, S2, x1, x2, a;
double rhoc = rho*c;
/* check for zero length segment */
if(L == 0.0)
return identitym();
/* calculate apex distance for both ends of conical section
based on similar triangles */
x1 = L/(a2/a1 - 1.0);
x2 = x1 + L;
a2 = a1*(1.0 + L/x1);
/* calculate areas of each end based on given radii */
S1 = M_PI*a1*a1;
S2 = M_PI*a2*a2;