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

204 APPENDIX B. PROGRAM LISTINGS
Z_u = unflangedZ(f, c, rho, a);
Z_f = flangedZ(f, c, rho, a);
/* calculate the characteristic impedance */
Z0 = charZ(c, rho, a);
/* calculate complex end corrections for unflanged and flanged
pipe */
d_u = divz(arctanz(divz(Z_u, multz(j, Z0))),real(k));
d_f = divz(arctanz(divz(Z_f, multz(j, Z0))),real(k));
b = a * (1+flange);
a_on_b = a / b;
/* calculate the length correction */
d = addz(addz(d_f,multz(real(a_on_b),subz(d_u,d_f))),
real(0.057*a_on_b*(1 - pow(a_on_b,5))*a));
/* calculate the reflection coefficient (42) */
R_norefl = multz(real(-1), expz(multz(imaginary(-2 * k), d)));
modR_edge = -0.43 * (b - a) * a / pow(b,2)
* pow(sin(k * b / (1.85 - a_on_b)),2);
phaseR_edge = -k * b * (1 + a_on_b * (2.3 - a_on_b - 0.3
* pow(ka,2)));
R_edge = multz(real(modR_edge), expjz(real(phaseR_edge)));
R = addz(R_norefl,R_edge);
/* calculate and return the impedance */
Z = multz(Z0, divz(addz(one, R), subz(one, R)));
return Z;
}
complex unflangedZ(double f, double c, double rho, double a) {
double k = (2*M_PI*f)/c;
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 = 0.6133 * a;
/* determine the frequency-dependent end correction (14b) */
d.Re = d.Re * ((1 + 0.044 * pow(ka,2)) / (1 + 0.19 * pow(ka,2))
- 0.02 * pow(sin(2 * ka),2));
/* determine the modulus of the reflection coefficient (14c) */
modR = (1 + 0.2 * ka - 0.084 * pow(ka,2)) / (1 + 0.2 * ka
+ (0.5 - 0.084) * 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;
}
complex flangedZ(double f, double c, double rho, double a) {
double k = (2*M_PI*f)/c;