🚀 go-pugleaf

Eric Gallun has correctly and simply described the basic truths you
seek: that the length of a resonant pipe is ideally one quarter
wavelength. Also that some tuning and tweaking is customary.

Here's one more nit you might not need. For fluid-mechanical reasons,
the effective length of the pipe is greater than its actual length.
Therefore, the pipe should be slightly shorter than quarter-wave
calculations would indicate.

Why, you ask?

Because some of the gas at the end of the pipe moves as a unit with the
gas in the constricted pipe. This makes the effective length of the pipe
greater than it's actual length and gives rise to the celebrated "end
effect". (which has nothing to do with the battle of Armageddon)

How much should you reduce pipe length to allow for the "end effect"?

About 0.6 times the pipe radius.

So, if the pipe radius is 1.5 inches, the pipe may be cut about 0.9
inches shorter than a calculated quarter wavelength.

Interestingly, this correction is frequency independent.
-- 
David Lubman in Westminster, California
Always happy to put a little fizz into "fizzics"
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thomasr wrote:
> 
> Could someone tell me how long to cut a one-inch pipe to get middle C?
> 
> I am trying to make a set of pipes to use as primitive brass instruments
> for a chidren's music class.  I understand that I should operate on the
> following formula:
> 
>        x is do
> 7/8 of x is re
> 4/5 of x is mi
> 2/3 of x is so
> 3/5 of x is la
> 
> But I don't know any formula for setting do.
> Could anyone give me such a formula, or tell me where to find a chart?