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Coke bottle on another planet, involving harmonics and speed

  1. Dec 1, 2012 #1
    Number4-1.png

    This is what I tried doing, but I ended up getting an answer that isn't listed above

    1. frequency = speed/wavelength

    2. On Earth

    480 Hz = (343 m/s)/wavelength
    wavelength = 343 / 480
    wavelength = 0.714 is the wavelength for the Coke bottle

    3. On Earth 2

    Since they already gave me frequency on Earth 2, and I already solved for wavelength, all I have to do is plug in those numbers to solve for speed on Earth 2.

    frequency = speed/wavelength
    (520 Hz) = speed/0.714
    (0.714)(520) = speed
    371.58 m/s = speed
     
  2. jcsd
  3. Dec 1, 2012 #2
    Wait...I think first i have to find the harmonics...
     
  4. Dec 1, 2012 #3

    gneill

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    Staff: Mentor

    You're dealing with a fundamental frequency on Earth, but a harmonic on Earth 2. What harmonics can a closed-bottom cylinder produce?
     
  5. Dec 1, 2012 #4
    n = 1, 3, 5, 7

    So...

    On Earth 2:

    520 = 5*104 (fifth harmonic of 104 Hz)
     
  6. Dec 1, 2012 #5
    You still there?
     
  7. Dec 1, 2012 #6

    gneill

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    Staff: Mentor

    Still here. You should confirm which harmonics can be produced by a closed-end pipe.
     
  8. Dec 1, 2012 #7
  9. Dec 1, 2012 #8

    gneill

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    Staff: Mentor

    So, when the problem states that "a second available harmonic of 520Hz is available", which one do you think they're referring to?
     
  10. Dec 1, 2012 #9
    312/3 = 3*104 (second available harmonic of 104)
    520/5 = 5*104 (third available harmonic of 104)
     
  11. Dec 1, 2012 #10

    gneill

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    Staff: Mentor

    Why 104? The frequencies will go: 520, 520/3, 520/5, 520/7,...

    The second one is 520/3, right?
     
  12. Dec 1, 2012 #11
    Ohh!

    that's right, because I was thinking the whole time the the numbers HAD to be integers...

    Yeah that's what I meant to say!

    But what next though?


    Do I then do:

    1. frequency = speed/wavelength

    2. On Earth

    480 Hz = (343 m/s)/wavelength
    wavelength = 343 / 480
    wavelength = 0.714 is the wavelength for the Coke bottle

    3. On Earth 2

    Since they already gave me frequency on Earth 2, and I already solved for wavelength, all I have to do is plug in those numbers to solve for speed on Earth 2.

    frequency = speed/wavelength
    (173.3 Hz) = speed/0.714
    (0.714)(173.3) = speed
    123.76 m/s = speed?
     
    Last edited: Dec 1, 2012
  13. Dec 1, 2012 #12
    Is 123.9 the answer to this problem?
     
  14. Dec 1, 2012 #13

    gneill

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    Staff: Mentor

    You'll have to show your work; I can't verify a guess :smile:
     
  15. Dec 1, 2012 #14
    I just did :eek:

    frequency = speed/wavelength
    (173.3 Hz) = speed/0.714
    (0.714)(173.3) = speed
    123.76 m/s = speed
     
  16. Dec 1, 2012 #15

    gneill

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    Staff: Mentor

    I have a problem with the length of column (bottle) that you're using (Think about a coke bottle over 70cm tall!). While the error has fortunately cancelled out along the way, I can't in good conscience say that your answer is altogether correct :smile:

    On the web page that you found, take a look at the table partway through that shows the column length \ wavelength relationship for the various harmonics. Note that the fundamental is NOT the same length as the column.
     
  17. Dec 1, 2012 #16
    What what??

    You mean

    Wavelength = (4/3)*L
    Wavelength = (4/3)*(0.714)
    Wavelength = 0.952????
     
  18. Dec 1, 2012 #17
    I'm so confused now...
     
  19. Dec 1, 2012 #18

    gneill

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    Staff: Mentor

    On Earth 1, the fundamental is 480Hz, speed 343m/s. Wavelength is then 0.715m. That's fine. But the bottle has length L = λ/4, so L = 0.179m. The length is assumed not to vary between planets (same bottle).

    So take that bottle length and the harmonic 520Hz and use the appropriate length versus wavelength relationship to find the speed (since v/f = λ, and λ = (4/3)L for this harmonic).

    Sorry, gotta go now to an important meeting with a pint of something refreshing :wink:
     
  20. Dec 1, 2012 #19
    Earth 1

    Step 1) Find wavelength
    Fundamental frequency on Earth 1: 480 Hz
    Speed on Earth 1: 343 m/s.
    Wavelength on Earth 1: λ = v/f, which is 343/480 = 0.715 m

    Step 2) Find the length of the bottle
    The bottle has length L = λ/4
    L = (0.715 m)/4
    L = 0.179 m

    The length is assumed not to vary between planets (same bottle).

    Earth 2

    Step 3)
    Take that bottle length (L = 0.179) and find the second available harmonic of 520 Hz.

    Since the bottle is a close-ended cylinder, n = 1, 3, 5, 7 and the frequencies will go: 520, 520/3, 520/5, 520/7. The second available harmonic of 520 Hz is 520/3 = 173.3
    According to: http://www.physicsclassroom.com/class/sound/u11l5d.cfm

    Step 4) To find speed, use v = λf (speed = wavelength*frequency). λ for the second available harmonic of 520 Hz will = (4/3)L

    λ = (4/3)(0.179)
    λ = 0.239

    So,

    v = λf
    v = (0.239)(173.3)
    v = 41.3 m/s
     
  21. Dec 1, 2012 #20
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