That depends on what you mean by "work." The length, as Kiteman said, determines the note -- specifically, the length is half the wavelength of the fundamental frequency.
If you want a particular note, then you need to make it the right length or it won't "work" the way you want it to.
If you're trying to build a flute, with finger holes to generate different notes, then you need to get both the length and the spacing of those holes correct.
Look up a basic text or article on "woodwind instrument making" via Google. Such articles should include the basic physics you need for standing waves in air.
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There is a range of lengths that will work, outside of which you end up with something like a dog whistle (too small) or you don't get any vibration (too large). The pitch is affected by the ratio of width to length, but higher notes can't be produced with larger diameters (think flute v tuba).
I believe that that pitch (fundamental) is determined by the length (by definition, the longest dimension), while the distribution of overtones (harmonics) and secondary frequencies is driven by the width. That is, resonators with different widths -- flute vs. clarinet, for example -- will have different "quality" even when playing exactly the same note.
No the length affects the pitch of the note that is played
No - the length just affects the note.
The longer the whistle, the lower the note.