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Energy and Power of a wave traveling along a string

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Two wires are made of the same material but
    the second wire has twice the diameter and
    twice the length of the first wire. When the
    two wires are stretched, and the tension in
    the second wire is also twice the tension in the
    first wire, the fundamental frequency of the
    first wire is 500 Hz.
    What is the fundamental frequency of the
    second wire?
    Answer in units of Hz


    2. Relevant equations
    [itex]l_{2}[/itex] = 2[itex]l_{1}[/itex]
    [itex]r_{2}[/itex] = 2[itex]r_{1}[/itex]
    [itex]τ_{2}[/itex] = 2[itex]τ_{1}[/itex]
    [itex]f_{1}[/itex] = 500 Hz


    3. The attempt at a solution
    From the help of others, I got the answer but there is one confusing part.
    He said that [itex]\mu_{2}[/itex] = 4[itex]\mu_{1}[/itex], but obviously that's not what I got in the below equations. [itex]v_{2}[/itex] = [itex]\sqrt{.5}v_{1}[/itex] So it was Would you explain how this is so?

    [itex]v_{2}[/itex] = [itex]\sqrt{\frac{τ_{2}}{\mu_{2}}}[/itex]
    = [itex]\sqrt{\frac{2τ_{1}}{m_{2}/2l_{1}}}[/itex]
    = [itex]\sqrt{\frac{4τ_{1}l_{1}}{m_{2}}}[/itex]
    = 2[itex]v_{1}[/itex]
     
    Last edited: Dec 4, 2011
  2. jcsd
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