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Simple standing wave question- not exactly sure why I can't get answer?

  1. Mar 12, 2008 #1

    ~christina~

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    [SOLVED] simple standing wave question- not exactly sure why I can't get answer?!

    1. The problem statement, all variables and given/known data

    A particle fingering flute sounds note with frequency of 880Hz at 20 deg celcius(343m/s => sound wave speed) The flute is open at both ends.

    a) find the air column length

    b) find the frequency the flute produces at begining of football game when ambient temp is -50.0C and muscician has not had time to warm up flute.

    answers supposed to be=> a) 0.195m and b) 841m
    2. Relevant equations
    [tex]f= n\frac{v} {2L} [/tex]

    [tex]v= f*\lambda [/tex]

    3. The attempt at a solution

    a) find the air column length

    I really did try to do this and what I did was I got
    v= 343m/s
    f= 800Hz

    [tex]342.91m/s= 800Hz \lambda[/tex]
    [tex]\lambda= 2L [/tex]
    L= 0.206875m=> not the answer in the book?!

    b) find the frequency the flute produces at begining of football game when ambient temp is -50.0C and muscician has not had time to warm up flute.
    [tex]v= 331 \sqrt(1 + 20^oC/273^oC)= 299.1567m/s [/tex]
    based on L before:
    L= 0.206875m

    [tex]f= v\lambda= 288.15e69/0.41375= 723.0378[/tex]=> why isnt' this matching the book answer??

    Please help...
    it's really a simple problem I think.

    THANK YOU
     
    Last edited: Mar 12, 2008
  2. jcsd
  3. Mar 12, 2008 #2

    tiny-tim

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    A what?? :confused: … is it electron-ic? … :smile:
    Hi christina!

    You've used 800 instead of 880 - does that help? :smile:
     
  4. Mar 12, 2008 #3

    ~christina~

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    um no, I don't think so since they don't say anything about that.

    yes that helps for the first part but I can't figure out what's wrong with the second part...I plugged in the number (found in a)to find the wavelength but then it came out ot 767Hz for the frequency.:frown: I can't figure out what's wrong with the second part.

    b) find the frequency the flute produces at begining of football game when ambient temp is -50.0C and muscician has not had time to warm up flute.
    [tex]v= 331 \sqrt(1 + 20^oC/273^oC)= 299.1567m/s [/tex]
    based on L before (corrected):
    [tex]\lambda= 0.389670m[/tex]

    [tex]f= v\lambda= 288.15e69/0.389670[/tex]= 767.717Hz[/tex]

    Thanks tiny-tim
     
    Last edited: Mar 12, 2008
  5. Mar 12, 2008 #4

    tiny-tim

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    Hi!

    I don't follow any of this.

    Where does the difference between -50º and +20º come in? :confused:

    (btw, do you Americans really play football at -50ºC?)
     
  6. Mar 12, 2008 #5

    ~christina~

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    Um...they say that the temperature is -50º so wouldn't that play a part here because if that didn't matter wouldnt' the frequency be the same as in the original question?

    I don't know about football though.
     
  7. Mar 12, 2008 #6

    ~christina~

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    I found out that the temperature was -5C not -50C so that's what was wrong...slaps forehead*

    Thanks for your help tiny-tim.:smile:
     
    Last edited: Mar 12, 2008
  8. Mar 12, 2008 #7

    Hootenanny

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    I believe that your using the wrong equation, or at least plugging the wrong numbers in. See here for more information.
     
  9. Mar 12, 2008 #8

    ~christina~

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    I was plugging in the wrong number for the temp (-5(right) vs -50 (wrong number))
     
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