Diameter vs length

Hi,

Here are some questions for the whistle makers out there. If you were to make a series of three whistles, one in the key of D, and the other two in C and Bb, could you do it by keeping the overall length the same as the D whistle any get the other two keys by just increasing the bore diameter? If you can’t, why? Is the pitch dependent upon the length only? What would just increasing the bore size of a whistle do to he pitch while keeping the length the same?

I would never try it, but I’m just curious.

Regards,
Paul N.

“Diameter vs length” …i’m really trying to be mature …really, i am. :smiley:

Yeah, and then there’s the other current topic, “finger vs mouth vibrato”…

okay, I’m stopping now.

hehe… now my damn leg is shaking and I can’t make it stop!!!

Okay, I’m done too …someone give the OP a serious answer to his question …preferably something without bird puns.

This morning I woke up with a woodpecker. Whoops! Wrong thread.

If you were to make a series of three whistles, one in the key of D, and the other two in C and Bb, could you do it by keeping the overall length the same as the D whistle any get the other two keys by just increasing the bore diameter?
No

If you can’t, why?
The pitch of the bell note depends mostly on the length.
Why? You ask too many questions (which is the cop out for I don’t have time to explain, and you probably wouldn’t understand even if I could explain, which I probably couldn’t beacause in the end it would probably be one of those things like: Why do things fall? Because of gravity. What’s gravity? Its what makes thing fall… (I know - that is bad grammer - the World won’t end, or will it?)

Is the pitch dependent upon the length only?
No

I was about to toss off answer the last question from the top of my head, but this can be dangerous - so I put the opened up the spreadsheet and put some numbers in and… a wider bore whistle needs to be slightly shorter, and as I was considering these numbers I remembered that I had two A whistles that I played yesterday with very similar construction but different bores and they confirmed my calcs. So…

To answer the last question in the style of my proceeding answers:
What would just increasing the bore size of a whistle do to he pitch while keeping the length the same?
The pitch would be flatter.

I would never try it,
Why not?
but I’m just curious
It is good to be curious, but truthfully why do you want to know?

I’ll now return you to the previous programming - a serious reply ratio of 20% is plenty!

One more feeble attempt to be serious, since it is a good question:

Pitch is determined essentially by the length of the wave of the fundamental note. So, using totally bogus numbers for the example, if the length of the sound (sine) wave for the bell note on a D whistle is 9 inches what we’re talking about is the length of the wave, not the length of the tube. The tube will be a bit shorter than the9 inches, and how much shorter will be determined by the diameter of the tube. The wave will be longer since it will include the offsets from still (Giving that sort of “S on its side” sort of shape. In a very non mathematical way the length of the wave is equal to the length of the tube plus some factor for the diameter of the tube. Since the wave will be free to vibrate in a “bigger” S with a bigger diameter tube than with a small diameter one the length of the tube with a bigger diameter will be slightly less than that of the small diameter one.

Now, that is NOT a totally accurate description of the issue, but it is a way I’ve been able to think about it. I think it follows from this that a larger diameter tube will, all other things constant, sound a bit louder (besides being a bit shorter) because the amplitude of the wave will be greater. So, why aren’t whistles bigger in diameter? Because diameter also affects the sound quality by changing the overtones of the note, and also affects the placement of holes for notes other than the bell tone.

I’m out on a limb here because I haven’t paid much attention to those aspects of the physics of sound since college days…a LONG time ago.

So, someone correct or amplify this please. Don’t just take it a gospel. I know there are lots of folks out here that can do a much better job of being precise about what is happening.

There is also the very important question of the second octave. The narrower the bore, the easier it is to overblow. (To the point where you cannot really play te fundamental any more, but only overblow, Tabor pipes, among some others, work on this principle.) So, even if you could increase the bore to the point where it drops by a tone, it would be so fat that you could only play one octave.
However, if you are hell-bent on having three whistles in one, you can make one with eight fingerholes. You will need to plug up the unwanted ones at the top if playing in the lower pitches, but would also have to put up with the fact that each setup would play in a different mode, with only one possible in the normal major scale. It would be identical to playing a six note series on the white keys of a piano, starting with te appropriate notes.

One big correction to cboody:
The length of a whistle or flute from mouth hole/window to bottom end is slightly less than half the wave length of the fundamental frequency.

Visualise it as half a wave vibrating inside the tube, like from first node to middle node (think of a sinus curve from 0 to 180 degrees, or just the upper part of it). Only those nodes are not exactly at the ends, but a little further out. The vibrating air column does not stop precisely at the ends, but extends a bit further.

My understanding is (and I hope I will be corrected if wrong):

The distance that it extends from the ends of the tube depend partly on the diameter of the tube (hence a shorter whistle for a wider tube). Note also that I said ends plural. The vibrating air column extends out of the window by the blade, and out of the highest open tone hole. How far it extends depends on the geometries of both. Complicated, innit?

Well, I’m not sure I am reading anything different between what Hans posted, and Cboody’s explanation to start with, but Yuri makes an excellent point concerning being able to get two full octaves in diatonic scale (and in tune with each other) from the whistle.

Even if you could pull this off through a series of “give and takes” in the designs of the whistles, the playing characteristics of the three whistles would be radically different, and their respective tones would likely be undesirable.

Just my tuppence worth, on a subject I’ve expressed some practical interest in … that is to say I’ve actually made (and play) some relatively wide-bore whistles, so I can post some “real” numbers as examples.

All numbers are “eyeballed” with a tape-measure, so may be +/- a mm or so.

For reference, a “normal” D whistle (12mm brass) is 265mm long from “window” to end … it’ll play 2 octaves without any real effort.

A “normal” C whistle, both Feadog (14mm tube) and Clarke Sweetone (tapered), are 292mm long from “window” to end … they’ll both play 2 octaves without any real effort. I’ve re-drilled my Sweetone to play in D with a low-C, ie a seven-hole whistle … it works :slight_smile:

A seven-hole whistle in D (+low-C) made from 18mm bore (20mm o/d) plastic conduit has a much “purer” tone than any of the above, though this factor is partially mouthpiece dependant, it is 285mm long from “window” to end … it’ll play an octave D-d then on up to “a” … plus the low C, obviously. A “vent-hole” under the LH thumb (recorder style) can help with the higher notes, basically it means you don’t have to blow so hard to get the higher harmonics, so they are of a more similar volume to the lower notes.

A seven-hole whistle in D (+low C) made from tapered 22-20mm bore bamboo has an even “purer” tone than any of the above. This “pureness of tone” is due mostly to the loss of high harmonics, it’ll only just play up to the f# above high d, but sounds beautiful … if a little quiet. It is 255mm from “window” to end, so overall is about the same length as the “normal” D whistle.

A Fitchhorn “Song Flute” (looks similar to a “Tonette”) will play as a “D+low C” instrument with a slight tweak of the fingerholes, (low B if you stop the “bell” with your knee or whatever). It is approx. 25mm o/d, 210mm long from “window” to end, and relies on a LH thumb-hole for the high d. It has no usable high harmonics so can possibly be considered as an ocarina.

I hope these numbers may help demonstrate the extents available, and their limitations … to precis :

Short and fat, lovely “pure” tone but limited range.
Long and thin, lots of “chiff” and wide range (over two octaves, with practice)

The difference is half a wave length:



It is significant to me to get at least the most basic physical facts right.

The frequency of the lowest note and the speed of sound in air determine primarily the length of the tube. Differences in bore diameter and window design are secondary factors, which change the tube length only a little.

Well this sort of touches on what I had in mind when referring to design. The D would probably require a very narrow bore (a little too narrow to make a good D whistle), the C could probably reamain somewhat standard - perhaps a little shorter with the right mods to the head, and the Bb would likely need to have a conical, stepped, or baffled/shaded bore to attempt to get them to all be the same length - but all of this kind of falls outside of the realm of the original question - especial the conical bore.

It still looks as if you are both describing the same thing from opposite aspects, to me… :laughing:

You are describing the length of the tube, Cboody is describing the length of the wave, and both descriptions seem to mean the same thing, the way they are written - except that as they are written, Cboody’s inclusion of the bore diameter being a factor is a little more accurate.

No, not quite.

cboody equated the length of the tube with ‘a wavelength’ and hans corrected this to ‘half a wavelength’. I am not picking on cboody here, and I am sure hans is not either (the jist of his comments were entirely correct) - just making sure the physical/acoustical facts are recorded.

FWIW there are at least three calculators out there that can perform the math for you. I wonder if it would be instructive to program TWJCalc to draw the end nodes of the vibrating air column, showing how far out the tube they lie… thoughts anyone?

We are describing the same thing from much the same angle. Only cboody’s whistles will be double the length than mine. Maybe for him a wave length goes from highest point to lowest point, whereas for me it goes from highest point to the next highest point. But I think he made just a small mistake in his description, although a mistake which has big effect, as it doubles the length of the tube. I only wanted to correct that. I don’t understand why you don’t get that. :poke:

you can do some simple maths:
speed of sound in air: ca 340.000 mm/sec
C-whistle: ca 300mm
the C on the whistle is ca 523 Hz
the wave length is 340.000 / 523 = 650 mm
which is a bit more than double of 300 mm.
300mm plus end-effect corrections is half of the wave length.

To simplify it, based on the OP question: Length is the main factor determining pitch. The diameter does influence pitch, but to a much lesser degree than length. Note that a ratio of bore length to diameter should be within an optimal amount in order to have a whistle which works ( plays both octaves in tune, at the desired pitch and sounds like a whistle). Changing only the bore diameter will not give much range of pitch.

Hi,
Thanks to all who have gone through the time and trouble to explain this to me. It is much appreciated and it is slowly sinking in.
Regards,
Paul N.

Hans’ point is that the tube length is about half the wavelength - so not an ‘S’ on its side, but half the S, a ‘U’ sort of.

And as long as we are talking about getting the Physics right - while thinking about the wave as an S is useful one (which would be the octave D on a D whistle) should remember that sound waves are longitudinal - that is nothing is physically wiggling (and yes I know that is not a precise scientific term!) perpendicular to the bore, say the way a string vibrates and thus if you push the S shape analogy too far by suggesting that a narrower bore is quieter because the S cannot be as tall is wrong. Now it may be that a wider bore having more volume (of air) that it can support more volume (of sound), in fact given the pressure variation the greater volume in a wider bore would be louder, and I have no desire to figure out the math since: It is undoubtably much more important how the head/mouthpiece/window/blade are configured. To illustrate this consider the whistles that have a variable window width to quiet the the whistle, or do the paper clip thing (partially unfold a paper clip, and insert in the window - instant hushed whistle with the same bore.

Also consider that the harmonic structure of a musical sound can effect the perceived loudness - more edge to the sound and it will cut through a lot!


cboody said

Giving that sort of “S on its side” sort of shape. In a very non mathematical way the length of the wave is equal to the length of the tube plus some factor for the diameter of the tube. Since the wave will be free to vibrate in a “bigger” S with a bigger diameter tube than with a small diameter one the length of the tube with a bigger diameter will be slightly less than that of the small diameter one.

Now, that is NOT a totally accurate description of the issue,

and after saying that it is not an accurate description, the description was used to explain loudness

I think it follows from this that a larger diameter tube will, all other things constant, sound a bit louder (besides being a bit shorter) because the amplitude of the wave will be greater.