- Under the previous assumption that the reed can be adequately modeled as a mechanical spring, the motion of which is in phase with the pressure () acting across it, Eq. (22) can be rewritten using Eq. (20) as

where is the pressure necessary to push the reed against the mouthpiece facing and completely close the reed channel. - The flow through the reed orifice is assumed to separate and form a free jet at the air column entrance. In the ensuing region of turbulence, the pressure is assumed equivalent to the reed channel pressure and conservation of volume flow to hold.
- In this case,
*u*=*u*_{d}and we can use Eq. (23) and the relation

to find a set of solutions for various values of . - The approach of McIntyre et al. (1983) is to assume a constant upstream pressure (
*p*_{u}) and obtain solutions for the outgoing downstream pressure*p*_{d}^{+}based on incoming pressures*p*_{d}^{-}. This amounts to finding the intersection of the flow curve and a straight line corresponding to Eq. (24), as illustrated in Fig. 11 below. - However, it is preferable to maintain the dependence on , which allows us to modify the mouth pressure in a time-domain simulation.
- Note that

*p*_{d}^{+}-*p*_{d}^{-}= *p*_{d}^{+}-*p*_{d}^{-}+ [*p*_{u}-*p*_{u}] + [*p*_{d}^{-}-*p*_{d}^{-}]= *p*_{u}- 2*p*_{d}^{-}-*p*_{u}+ [*p*_{d}^{+}+*p*_{d}^{-}]= (25)

where consists of pressure components known or computable from previous values. - We can then find a table of solutions, such as shown in Fig. 12, for the equation
.
- For values of
greater than
*p*_{c}, the reed is closed and the solutions are given by a straight line of slope one, which corresponds to zero flow and pressure reflection without inversion at the junction. - Thus, when the reed is forced against the mouthpiece facing, the air column appears as a rigidly terminated or stopped end.

©2004-2016 McGill University. All Rights Reserved. Maintained by Gary P. Scavone. |