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Homework Help: Fundamental frequency

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    A stretched wire vibrates in its fundamental mode at a frequency of 400Hz. What would be the fundamental frequency if the wire were half as long, with twice the diameter and with four times the tension?


    2. Relevant equations

    fn = nV / 2L where n is the harmonics number. f1 is the fundmental frequency.

    i think i should be using
    V= Sqrt(T/u)

    3. The attempt at a solution

    how do i start? this is what i got...

    since it gave 400Hz... then i think i should use...

    fn = nV/2L -----> 400Hz = V/2L

    therefore V= 400 * 2L

    using V= Sqrt ( T/u) ---> 400*2L= Sqrt( T/U) ----

    i am stuck here...i have a hunch that i need to find something it term of something that play back the two equation..afterwhich it will cancel out something..then i can get the value...dunno where to go from here...any hel thanks??
     
  2. jcsd
  3. Sep 29, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    dimensions

    Hi hemetite! :smile:

    This is a dimensions question …

    write out the formula for the fundamental frequency, f1

    then see whether f1 is proportional to T, to 1/T, to √T, or what?

    same for L and d. :smile:
     
  4. Sep 29, 2008 #3
    k...let me struggle..abit...i seems to smell something already...hopefully it is not burnt... :)

    physic is just so challenging.... what a rush...!
     
  5. Sep 29, 2008 #4
    here what i get...

    these are the formulas...

    for fundamental frequency...n=1

    so,

    f= V/2L --------- 1

    lamba = 2L ------- 2

    v= lambda * f -----3

    v= sqrt (T/ (m/L) ------4

    ---------------------------------------

    using 3 ..... v= (2L) 400Hz
    so if we wire of 1/2 as long so
    v= (1/2) (2L) 400Hz = 400L

    put these into 1

    f= V/2L = 400L/2L =200Hz

    these is 1 of the answer...i have to get for 2 more right for the change for D and T?

    .....i see the question like 3 condition combine into 1?...or..3 mini quesiton or 1 big question?
     
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