Calculating standing waves, given a fruequency? :O

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SUMMARY

The discussion focuses on designing a tube closed at one end to achieve a fundamental frequency of 440Hz. The correct approach involves understanding that for a tube closed at one end, the wavelength is four times the length of the tube. The user initially attempted to apply the formula for pendulums, which is incorrect. The correct formula to determine the length of the tube is derived from the relationship between frequency, wavelength, and the speed of sound in air.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with the speed of sound in air
  • Knowledge of fundamental frequency concepts
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the relationship between frequency, wavelength, and tube length for closed-end tubes
  • Learn about the speed of sound in different mediums
  • Explore the derivation of wave equations in physics
  • Investigate practical applications of standing waves in musical instruments
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Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone involved in designing acoustic instruments or sound-related projects.

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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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