page_title: Physics of whistles
section_title: Circular-saw whistle
hierarchical_section_title: Physics of whistles / Dipole-like whistles / Circular-saw whistle
caption_attribution_description: English: Circular saw blades
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: An edge tone occurs when a jet impinges on a fixed surface. A trailing edge tone occurs when an exterior flow passes over a trailing edge. There is a whistle that is a combination of an edge tone and a trailing-edge tone and might be called a wake-edge tone. It occurs in rotating circular saws under idling conditions and may be called the circular-saw whistle. Under load conditions, blade vibration plays a role, which is not addressed here.
  There have been several studies of the fundamental sound generating mechanisms of this whistle.
  A drawing of typical blade construction is shown in the figure on the right. Research has shown that the sound field is dipole with the primary axis perpendicular to the blade plane. The sources are fluctuating forces acting on each cutting blade. Bies determined that the characteristic speed was the blade velocity RΩ, and the characteristic dimension was the tooth area. Other researchers used blade thickness as the characteristic dimension. Cho and Mote found that the Strouhal number St = fh/U was between 0.1 and 0.2, where h was the blade thickness. Poblete et al., found Strouhal numbers between 0.12 and 0.18. If the edge tone is relevant, perhaps the characteristic dimension should be the gap between the blades.
  The researchers deduced that the fluctuating force was proportional to U², but the sound power was found to vary from U4.5 to U6.0. If the measurement bandwidth is broad and the measurement distance is out of the near field, there are two dynamic factors (Strouhal number and dimensionless force), that can cause the exponent to be less than 6. Both the Deltameter and hole tone data show the Strouhal number is a weak negative function of Reynolds number, which is squared in the sound power equation. This would result in a reduced speed exponent. This factor is not likely to explain the large reduction in exponent however.
  The blade geometry was highly variable in the tests, so it is likely that the negative dependence of the dimensionless force on Reynolds number is the major factor. This whistle has two features that separate it from the other whistles described here. The first is that there are a multiplicity of these dipole sources arrayed around the periphery, that most likely are radiating at the same frequency, but incoherently. The second is that blade motion creates a steady, but rotating, pressure field at each blade. The rotating steady force creates a rotating dipole field, which has an influence in the geometric near field. The feedback is class I (hydrodynamic), and there is no indication that stages other than stage 1 occur.
caption: Part of saw blade
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