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It seems like there should be a dimensionless number for wave guide width and frequency vs turn radius, but I have not been able to locate it or understand the proper application of one I am overlooking. I am currently evaluating acoustic waves, but an electrical wave dimensionless number would probably work with some adaptation.

For example, say I have 20khz acoustic radiation traveling down a pipe (wave guide) filled with water at STP. The pipe diameter is 10mm and the radius of curvature of a 180 degree bend is say 100mm.

I anticipate that mathematically it would be very hard to calculate the attenuation/distortion at the other end of the wave guide. A dimensionless number would make it easier to test empirically then use similitude to predict a scaled system with the same value dimensionless number. But perhaps I am oversimplifying and no such number exists.

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  • $\begingroup$ What do musicians do for trumpets? How is the mouthpiece frequency compared to the output frequency? trumpets have several 180 bends... $\endgroup$
    – Solar Mike
    Commented Mar 30 at 16:03
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    $\begingroup$ For RF waveguides everything is scaled to the vacuum wavelength of the EM waves being guided. Dimensions are in "wavelengths", which is essentially a dimensionless number until you select a frequency. I suspect you could do the same thing with sound waves, but you'd have do scale by the wavelength of sound in the medium inside your wavelength (e.g., air at standard temperature and pressure). $\endgroup$
    – TimWescott
    Commented Apr 1 at 3:46
  • $\begingroup$ @TimWescott, Awesome, I will look into this. Thanks! $\endgroup$
    – ericnutsch
    Commented Apr 1 at 9:52

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