Calculating standing waves, given a fruequency? :O

AI Thread Summary
To design a tube closed at one end for a fundamental frequency of 440Hz, the wavelength must be four times the tube's length. The correct formula to use is that the speed of sound in air equals frequency multiplied by wavelength. The speed of sound is approximately 343 m/s, so using the equation v = fλ, the wavelength for 440Hz is calculated as λ = v/f. This results in a tube length of approximately 0.39 meters, as the length is one-fourth of the wavelength. Understanding these relationships is crucial for accurately calculating standing waves in closed-end tubes.
SFSKabam
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Homework Statement


"Design a tube closed on one end so that it's lowest frequency standing wave is 440Hz. (i.e. determine the length of the tube."


Homework Equations


Um...I was unsure.
I thought maybe...I might use w=2(pi)f...and the function 2A sin (kx) cos (wt), but I epically failed on it.


The Attempt at a Solution


My solution was rather embarrassing, and it acquired me 0/10 points on my exam, thus I went online trying to get help (from Wiki and the sorts), then I found this site, thought I'd try it. :)
The attempt was as follows...
w = 2(pi)f = sqrt(g/L)

I then squared both sides to get (2(pi)f)^2 = g/L

Then simplified to L = g/(2(pi)f)^2) --Hence epic fail, for, come to find out, sqrt(g/l) is for pendulums. --

And now I'm lost. -.-
 
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Its really rather more simple than that. A tube closed at one end will have a fundamental frequency, where the wavelength is 4 times the tubes length.
 
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