The open end of a cylindrical pipe is poorly represented by a load impedance
In general, the acoustic properties of the end of the wind-instrument bore are characterized by a non-zero and complex valued load impedance and this impedance can be expressed as a lumped traveling-wave reflectance, as given by the bracketed term of Eq. (32).
Figure 9 represents the digital waveguide implementation of plane-wave pressure propagation in a cylindrical tube terminated by the reflectance
Thermal and viscous boundary layer losses are neglected in this model.
Digital waveguide implementation of plane-wave propagation in a cylindrical tube, neglecting viscothermal losses.
The waveguide structure of Fig. 9 can be further simplified by limiting observation of physical pressure to the input of the tube.
Then, by linearity and time-invariance, the digital filter representing
can be ``pushed'' through the lower delay line to its output and a single delay line used for the simulation, as shown in Fig. 10.
Simplified digital waveguide implementation of plane-wave propagation in a cylindrical tube using a single delay line and neglecting viscothermal losses. The pressure observation point is constrained to the entryway of the bore.
In general, a digital waveguide model with a single observation point can be implemented using one delay line as long as it is possible to ``tap'' into and out of any point on the delay line.