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Finding the harmonics of a flute

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    A flute is essentially a pipe open at both ends.
    The length of a flute is approximately 66.3 cm.
    The speed of sound in the flute is 342 m/s.
    What is the first harmonic of a flute when
    all keys are closed, making the vibrating air
    column approximately equal to the length of
    the flute? Answer in units of Hz.

    What is the second harmonic? Answer in
    units of Hz.

    What is the third harmonic? Answer in units
    of Hz.

    2. Relevant equations

    I found the equation for fundamental frequency in an open-ended tube online: f=v/2L.

    3. The attempt at a solution

    f=v/2L
    f=342/2x.633
    f=270.142

    However, my assignment says this is wrong. I searched some more and found that harmonics are multiples of the fundamental frequency (f, 2f, 3f, etc.). I'm sure this is relevant, I'm just not sure how - finding 2f gave me an incorrect answer as well.
     
  2. jcsd
  3. Jan 18, 2009 #2
    Look at the units of your equation:
    On the right side you have v/(2*L) [=] (L/T)/(L) [=] T
    so the answer comes out in "per second". What does this mean? It means that the frequency you have calculated is in radians/sec, not in Hz. You need to then adjust the value to put it into Hz.

    Does anybody teach unit checking these days? I sure see a lot of unit errors!
     
  4. Jan 18, 2009 #3
    How do you convert something from radians/second to oscillations/second? I understand how the units cancel, but I'm still unsure of what to do to get the correct answer.
     
  5. Jan 18, 2009 #4
    2 PI radians = 1 oscillation.

    So if you have an answer in Radians / second (R/sec), convert to Oscillations / second (Osc/sec) by multiplying:

    (R/sec) . (Osc / Radian) = Osc / sec.

    In this case, you'll get your answer times (1 Osc / 2 PI Radians) -- or: Your answer divided by 2 PI. Do you get the right answer now?
     
  6. Jan 18, 2009 #5
    Nope, not the right answer =\

    270.142/6.283185307=42.9944. Tried that and it wasn't correct. Any ideas on what I'm doing wrong? Did I mess up multiplication somewhere?
     
  7. Jan 18, 2009 #6

    LowlyPion

    User Avatar
    Homework Helper

    Try recalculating with the .663 that is given in the problem.
     
  8. Jan 19, 2009 #7
    ...I hate myself -.- I tend to go through my problems and look over them, rather than rewrite them. Unfortunately this can make me miss stupid mistakes like that.

    Thanks a lot for the help.
     
  9. Dec 9, 2011 #8
    flutes are closed ended columns so the tube is equal to 1/4 of the wavelength so it would be

    4X66.3 in metres so 4X0.663 = 2.652 that is the wavelength

    to find the frequency it is speed/wavelength which is 129.7hz so assuming variants in atmospheric pressure will occur this frequency can be reguarded as C which is 130hz with a wavelength of 264cm
    so to check 264/4=66.3 the length of the tube.

    so the harmonics are 1st 130hz
    2nd 260hz
    3rd 390hz
    4th 520hz

    i think thats right im pretty sure thats how it goes
     
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