Increasing Airstream Velocity

For a given distance between a slit and an edge, the edgetone frequency increases with airstream velocity, but may break up or down to a different region with changes in the airstream velocity. At a given airstream velocity, a fairly stable tone may be maintained, attributable to a feedback mechanism.

Edgetone Regions

The line labeled Region I below is the main region of operation for edgetone organ pipes. The positive feedback from the interaction of the airstream with the edge holds the pitch relatively steady. It determines a wavelength relationship for the vortex modulated airstream. The expressions below assume a vortex velocity of 0.4 times the airstream speed.

Feedback and Edgetones

The undulations of the airstream, traveling at about 0.4 times the speed of the jet, cause the airstream to dip below the edge. Interaction with the edge causes an increase in pressure, which feeds back to the slit area, tending to force the airstream upward. When this upward deflection reaches the edge, its feedback forces the stream downward at the slit. This positive feedback reinforces an edgetone frequency for which the slit-to-edge distance is a half wavelength, so this frequency will build up and maintain reasonable stability.

The airstream dips below edge, shedding its vortex. Pressure down on airstream causes feedback to slit area where it tends to push the airstream up.

The air column resonance of an organ pipe will tend to alter the free edge tone to match the resonant frequency of the pipe. It is typical for the edge-excited organ pipe to produce the fundamental frequency of the pipe. But considerable effort in design must be spent to make sure that is so. The position of the slit relative to the edge and the distance from the slit to the edge must be chosen so that the fundamental pitch is stable at the airstream velocities produced by the wind chest of the organ. If the airstream velocity is increased, the pipe can go sharp, or even jump to the next harmonic of the pipe. It is common to hear this jump due to airstream velocity with boat whistles, for example. Generally you don't want your organ to do that.

Edgetone Variations With Gap Distance

The frequency of an edgetone produced by a slit and and edge tends to decrease as the gap between the slit and the edge increases. It may break into a different mode as the gap is further increased. For musical instrument use, only Region I is used according to Hall. "Rolling in" with a flute