Re: [Harp-L] Waxing Rivets for Overbends [oops!]

["Vern Smith" <jevern@xxxxxxx>]

Hi Bobbie et al,

Karman vortices are a function of the velocity of the air moving past an 
object (like a reed) and the width of the object.

If the object is a flat plate (and a reed is) then the frequency = 0.18 x 
velocity of the air / width of the object.

We can get an idea of the velocity of the air through the slot by the 
difference in pressure in the chamber from pressure in the room.   If you 
are really blowing/drawing hard, this can be as much as 10 inches of water. 
This corresponds to a velocity through the slot of about 212 feet / sec. 
Plugging this velocity and the reed dimensions into the Karman frequency 
equation above yields a frequency of about 5724 hz which is far above the 
pitch of the highest reed.  Unfortunately, this picture is vastly 
oversimplified.

The video is of a flat plate in a free air stream...but that doesn't occur 
in a harmonica.  When the reed is in the slot no vortices are shed because 
the flow can't pass the reed.  Then the velocity is constantly changing 
because on the downswing the relative velocity is lower and on the upswing 
it is larger.   I don't know for sure, but I think that it takes some time 
for the vortices to build and they are not suddenly just there when the reed 
comes out of the slot.  I am with Turbodog that Karman vortices are 
unlikely suspects to cause squealing.

A more likely suspect IMO is vibration of the reed in a higher/different 
mode.  The next higher mode for the reed is with a node at the base, then a 
loop, another node about two-thirds of the length out and another loop at 
the tip. This would produce a frequency at approximately 3x the reed 
fundamental.  Or the reed might vibrate in a twisting mode. In either case, 
any nail polish, wax, or other gunk applied to the reed would absorb more 
energy at higher frequencies and tend to suppress the higher modes.

A way to test for twisting mode could work.  Polish the tip of a reed to a 
near-mirror sheen.  Reflect a laser pointer beam off of it onto a screen 
such as a white wall or piece of paper.  Blow the reed normally and observe 
the pattern swept out by the beam.  Then make it squeal.  If the squealing 
pattern is wider than the normal one, then reed twisting is responsible.

One could use FEA to locate the next higher mode or twisting mode of 
vibration analytically.  Then if those modes were prominent in the spectrum 
of the squealing reed, then that's  evidence pointing to higher-mode vibes. 
Another thing that could be done is to view a sqealing reed while 
illuminated by a stroboscope.

Then there is whistling.  Air forced through a small orifice (the slot) from 
a resonant chamber (your embouchure) can whistle.  In the immortal words of 
Lauren Bacall, "You know how to whistle don't you? Just pucker up and blow." 
;o)

Vern
Visit my harmonica website: http://www.Hands-Free-Chromatic.7p.com