Resonant Lengths in open and closed colums

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Resonant lengths for closed and open air columns follow specific mathematical patterns applicable to musical instruments. For closed-ended columns, the formula is Ln = (2n-1)Vf/4, while for open-ended columns, it is Ln = nv/2f. Here, Ln represents the resonant length, n is the harmonic number, v is the speed of sound in the medium, and f is the frequency of the sound wave. The speed of sound in air can be calculated using the formula v = 331.3 + 0.606*(temperature in degrees Celsius). Understanding these formulas is essential for analyzing sound behavior in different column types.
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Is there a pattern for resosnant length for closed and open air coloums. Does this apply to instruments.
 
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Yes and yes.

Your question is too vague to offer any more information.
 
What is the pattern

can u tell me the pattern
 
For a closed-ended column it's:

Ln = (2n-1)Vf
4

For an open-ended column it's:

Ln = nv
2f


Ln: which resonant length your finding.
n: the number corresponding to which resonant length is being found
v: theoretical speed of sound in the particular medium you are using. in air, you can find this with the formula: v = 331.3 + 0.606*(temperature in degrees celcius)
f: frequency of the soundwave in the column.

Hope this helps :smile:
 
Sorry, the "4" and the "2f" are the denominators of the equations
 

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