Theory
An unflanged pipe end reflects part of the plane wave with the exact reflection coefficient of Levine and Schwinger (1948); a flanged end follows the baffled-piston impedance. Both describe the plane mode only and radiate into the outside air at its own temperature (Insertion loss: outside air temperature). They are applied to the stored scattering matrices of the muffler and of the reference pipe, so the choice needs no new solve.
Above the first non-plane cut-on of an outlet a higher mode reaches the pipe end, which these terminations do not describe: the insertion loss is not shown above the lowest such cut-on of the muffler's outlets and of the reference pipe's outlet, and a band is shown as "-" from the first band whose upper edge lies above it. The radiation domain, computed by finite elements when the outlet card asked for it, describes every mode and has no such limit.
An anechoic outlet is not offered: with an anechoic source nothing would reflect and the insertion loss would equal the transmission loss. Older projects that stored it are evaluated as an unflanged pipe end.
Equations
| where | meaning | unit |
|---|---|---|
| Highest frequency at which the insertion loss is shown | Hz | |
| Speed of sound in the outlet | m/s | |
| Outlet radius (from the outlet's computed modes) | m | |
| First zero of , 1.8412 | - |
Default and rule
- Default
- Unflanged pipe
- Rule
Unflanged pipe.
- Source
Unflanged pipe: Levine and Schwinger (1948). Flanged pipe: the baffled-piston radiation impedance. The cut-on is taken from the outlet's own computed modes.
Valid range unflanged | flanged | radiation domain (when the run computed one)
Plane-wave range
Above the outlets' first cut-on only the radiation domain gives the insertion loss.