Whistle physics

[ThorntonRose]

I was showing a workmate my whistles, and he wondered why the holes are different sizes. Does anyone have any information on the physics and math of whistles?

[Phlebas]

Try this.... http://www.geocities.com/SoHo/Museum/4915/INDEX.HTM

Phlebas

[chas]

I'll give a stab at this -- I haven't studied the physics of whistles specifically, but can't resist a physics question.

The whistle is a resonant cavity, with the fundamental wavelength being about half the length of the tube (there's a small correction for the bore diameter, and the tube length is from near the fipple blade). You change notes by changing the effective length of the cavity. This is done by letting air escape from the cavity, setting up an "anti-node". The node is at the other end, near the fipple blade, and, with no holes open, the anti-node is at the end of the tube, a point of maximum amplitude in the sound wave. The effective length is related to the hole position, the hole diameter, and the bore diameter. The larger the hole, the closer the antinode will be to the hole position (for higher notes, the lower holes also will have some effect on the pitch). The volume of the note also is related to the hole diameter.

So in the design, one must determine what's a comfortable reach between holes and what differences in volume can be tolerated. An extreme example of making a very comfortable reach with a very low volume is the Jubilee low whistle, which is designed to have a comfortable reach even down to low-A and without a piper's grip. The second (E) note is very soft on all their whistles, because the E hole must be very small to make the reach comfortable without the piper's grip.

So the differences in hole diameter for most whistles arise from the half-step in the middle of the scale, keeping the volume constant from note to note, and making a comfortable reach, which really doesn't come into play except in the lower whistles.

Charlie

[dkehoe]

I can't resist the physics part either. Chas, you almost got it right. there is is fact a node at both ends. Opening a whole causes the node to move up the pipe. When you play the second-octave D, you open the top whole to cause a node in the middle of the pipe.

Now- you want some real physics? Try to explain how the fipple works. The best explanation I've found is from the organ pipe people, and this is recent stuff. Check out this: http://www.nmol.com/users/wblocker/

[WyoBadger]

I know how the fipple works--you blow in the pointy end.

Tom

[Daniel_Bingamon]

A whistle could be built with all of the toneholes set to the same size but the spacing would be uncomfortable. (Except for some of the low whistles - the spacing could turn out impossible to reach unless you have very long fingers)