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

APPENDIX B. PROGRAM LISTINGS 333
}
return Z;
complex holeInnerRadiationImpedance(double f, Hole hole) {
double t_i;
double Z0 = charZ(hole->c, hole->rho, hole->radius).Re;
double k = (2*M_PI*f)/hole->c;
t_i = innerRadiationLengthCorrection(hole->boreRadius,
hole->radius);
return imaginary(t_i * k * Z0);
}
complex holeSeriesImpedance(double f, Hole hole) {
double a = hole->boreRadius;
double b = hole->radius;
double delta = b / a;
double t = hole->length, t_0 = 0, t_a;
double Z0 = charZ(hole->c, hole->rho, hole->boreRadius).Re;
double k = (2*M_PI*f)/hole->c;
if (strcmp(hole->fingering, "CLOSED") == 0) {
if (hole->key == NULL)
t_0 = b * (0.55 - 0.15 / cosh(9 * t / a) + 0.4
/ cosh(6.5 * t / a) * (delta - 1));
t_a = closedHoleSeriesLengthCorrection(a, b, t - t_0);
}
else
t_a = openHoleSeriesLengthCorrection(a, b);
}
return imaginary(t_a * k * Z0);
TransferMatrix embouchureMatrix(double f, EmbouchureHole h,
double entryratio, complex branchZ) {
TransferMatrix m, riserMatrix, cornerMatrix, innerRadMatrix;
double t_m, t_i, t_a;
double radiusin, radiusout;
complex Z_i, Z_a;
double Z0_hole = charZ(h->c, h->rho, h->radiusin).Re;
double Z0_bore = charZ(h->c, h->rho, h->boreRadius).Re;
double k = (2*M_PI*f)/h->c;
/* calculate the matching length correction */
t_m = matchingLengthCorrection(h->boreRadius, h->radiusin);
/* introduce lossy elements to account for the discontinuity */
m = identitym();
m->B = embouchureSeriesResistance(f, h, entryratio);
m->C = embouchureShuntConductance(f, h, entryratio);
/* calculate the matrix (with losses) for the tube section
comprising the hole and matching length */
radiusin = h->radiusin;
radiusout = entryratio * h->radiusout;
riserMatrix = (radiusin == radiusout) ?
tubeMatrix(f, h->c, h->rho, h->length + t_m, radiusin, 1) :