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How long should I cut my pipes?

Cathy Highet and Erick Gallun erick at sirius.com
Wed Aug 20 21:06:37 EST 1997

thomasr wrote:
> Could someone tell me how long to cut a one-inch pipe to get middle C?

I will assume that this pipe is open at the end as you referred to
primitive brass instruments.
The frequency of middle C is about 262 cycles/sec.
The speed of sound (at 68 degrees F) is about 344 meters/sec.

Thus, you want the pipe to resonate at 262 cycles/sec when a blast of
air is sent down it.  

This means that the wavelength of the sound wave should be
velocity/frequency or 344/262 or 1.3 meters.  My physics book tells me
that the length of an open tube is equal to 1/4 of the wavelength of its
fundamental frequency.  

Thus, a tube of .325 meters (i.e., about 12.8 inches) should be a good
start.  As you noticed, I have made a number of approximations and
cavalier roundings along the way, so some tuning will be necessary.

Hope this is helpful (and correct :)

Best of Luck.

erick gallun

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