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Finding the wavelength when given the length and frequency (resonant air columns)

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    i'm doing a lab and i have a chart which requires me to find the wavelength. The chart looks like this:

    Frequency(f) Period (T) Length (l) Wavelength (lambda)
    512 ? .15 ?

    2. Relevant equations
    the equation is basically what im looking for

    3. The attempt at a solution
    I think that L1=1/4 (lambda), and every time you go up a length is goes up (3/4, 5/4 etc.) Is this correct? Because then i could just sub in the length and solve for lambda.
  2. jcsd
  3. Dec 13, 2009 #2
    Sorry my chart didnt turn out the way i wanted, its supposed to say frequency = 512, period is unknown, length is .15, and wavelength is unknown
  4. Dec 13, 2009 #3
    It depends on whether or not the pipe is open at both ends or just open at one end. (The one where you hold the tuning fork - or whatever you use to set the air in motion)
    If the wavelengths for subsequent harmonics (higher frequencies) are given as lambda= 1/4, 3/4, 5/4 etc times L, then this is true for a pipe that is closed at one end.
    So yes. In that case, the wavelength can be found from the length of the pipe and the frequency of its vibration.
    I assume you are using different driving frequencies to find different resonances in the same pipe. It's not 100% clear what you are doing, so I'm guessing a little.
    There are a couple of other experimental considerations which may or may not be relevant to your investigation, depending on the level you are at. If your teacher has not mentioned them, it probably won't matter. It's worth checking, though.
    a) is the speed of sound in the tube, the same as that in free air?
    b) there is something called an "end correction" which may be important.
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