🚀 go-pugleaf

In article <246@mindlink.bc.ca> Gordon_Wong@mindlink.bc.ca (Gordon Wong) writes:
>In the classic resonant air column experiment where a tuning fork is struck
>over a graduated cylinder, the tube length is varied in some matter, to
>cause a reinforcement of the sound of the tuning fork. These reinforcements
>occur at L = WL/4 (fundamental); L = 3/4*WL (1st overtone); L = 5/4*WL
>(2nd overtone); etc ... [Note: L = length of column; WL = wavelength]
>Supposedly, the idea of this experiment is to measure L, then use that
>measurement to determine the wavelength, then to calculate an accurate value
>for the speed of sound.

First, you must worry about the end correction, because the air motion at 
the end of a tube does not correspond to the idealization of the boundary 
condition used in deriving the formula relating L and \lambda. 

The end correction causes the "effective length" of the tube to be 
less than its actual length by about 0.6 of a tube diameter. 

Reference: Home Experiment 5.15 on page 257-8 of "Waves: Berkeley Physics 
Course - volume 3" by Frank S. Crawford Jr.  (You might find HE 5.16 
and 5.18 of interest as well.)  His description of the Helmholtz 
resonator -- aka Whiskey-bottle resonator -- Home Experiment 4.15 
on page 218-9 is excellent also.  

Since it is easy to get different diameter cardboard tubes (e.g. 
wrapping paper sometimes comes on large diameter tubes), you 
can test this formula by comparing lengths for same tuning 
fork and different diameter tubes.  

There are many ingenious problems suggested in this book, including 
one about the phase sensitivity of your brain-plus-two-ears system 
(Home Experiment 5.17) and some other nice ones for the bathtub. 

>My question: Which (the fundamental, the 1st overtone, or the 2nd overtone)
>would yield the more accurate value for the wavelength; or does it matter?

Good question.  Your experiment should help you answer it. 

My question: it is fall, so the air temperature is changing.  Is this 
measurement accurate enough to sense the change in the speed of sound 
with changing air temperature?

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)