page_title: Physics of whistles
section_title: Edge tone
hierarchical_section_title: Physics of whistles / Dipole-like whistles / Edge tone
caption_attribution_description: English: edge tone flow
context_page_description: A whistle is a device that makes sound from blowing air. The physical theory of the sound-making process is an example of the application of the science of fluid dynamics. Knowledge of the geometry, dimensions and fluid properties can allow prediction of the properties of the whistle. The principles relevant to whistle operation also have applications in other areas such as fluid flow measurement.
context_section_description: When a rectangular jet impinges on a sharp-edged object such as a wedge, a feedback loop can be established, resulting in a nearly pure tone. The figure on the right shows schematically the circulation of two vortices as they pass the wedge. This simple diagram suggests that there is a force applied to the wedge, whose angle varies as the vortices pass.
  As found in the Aeolian tone, the vertical component (lift) is large and results in a dipole-like sound field at the wedge (shown in the lower figure) and a much weaker horizontal component (drag) at twice the frequency (not shown). The drag component may contribute as part of the driving force for musical instruments (discussed below). A seminal study by Powell of this phenomenon has exposed many details of the edge-tone phenomenon. He showed that this whistle has three stages, and the feedback loop was hydrodynamic (class I). A semi-empirical equation for the frequency, developed by Curle, when converted to Strouhal number, is
  This equation, applicable for h/d > 10, shows the mean speed U of the jet at the orifice as the characteristic speed and the distance h from orifice to the edge as the characteristic dimension. The integer n represents the various vortex modes. It also suggests that dynamic similarity is achieved to a first approximation; one deviation is that the speed at the wedge, which is less than that at the orifice, should be the characteristic speed. A weak negative Reynolds-number effect is likely. The orifice width d also has some influence; it is related to vortex size and lateral correlation of the shedding process.
  The presence of a dipole sound field and a periodic force proportional to U² was confirmed by Powell. Numerical simulations of the edge tone and extensive references can be found in a NASA report. The lower figure on the right may be called a wake-edge tone. If the preferred frequencies of the trailing edge instability match the preferred frequencies of the free edge tone, a stronger dipole sound should arise. There does not appear to be any research on this configuration.
caption: Edge-tone dipole-like flow
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