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The wave of 2 strings

  1. Oct 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Two strings are stretched tautly parallel to each other. The length of one is L1 and the length of the other is L2(>L1). When both are simultaneously made to undergo fundamental vibration, beats can be heard at a frequency n. The waves in both strings travel at the same speed. Let us denote the fundamental freqency of the string with length L1 as f1.
    Find the ratio ##\frac{L_2-L_1}{L_1}##

    2. Relevant equations
    The answer is ##\frac{L_2-L_1}{L_1}=\frac{n}{n-f_1}##

    3. The attempt at a solution
    I have some equation about wave in two strings:
    ##L_1=\frac{v}{2f_1}##
    And
    ##L_1=i_1\frac{v}{2n};L_2=i_2\frac{v}{2n}##
    But I cant solve as answer.
    And What does
    "When both are simultaneously made to undergo fundamental vibration, beats can be heard at a frequency n" mean?
    Thanks for helping .
     
  2. jcsd
  3. Oct 8, 2016 #2

    gneill

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    Staff: Mentor

    Look up "beat frequency".
     
  4. Oct 8, 2016 #3
    The beat frequency means F=|f1-f2| but it is definition or must prove?
     
  5. Oct 8, 2016 #4

    gneill

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    Staff: Mentor

    You can take it as given.
     
  6. Oct 8, 2016 #5
    I want to prove this equation:
    If we have 2 wave: ##y=Acos(2\pi f_1t)## and ##y'=Acos(2\pi f_2t)##
    We have
    $$x=y+y'=2A(cos(\pi (f_1- f_2)t)cos(\pi (f_1+f_2)t)$$
    But why we dont use f=f1+f2 ?
     
  7. Oct 8, 2016 #6

    gneill

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    Staff: Mentor

  8. Oct 8, 2016 #7
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