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Waves MC Question - 2 strings, same tension, different μ

  1. Mar 1, 2014 #1
    1. The problem statement, all variables and given/known data

    A long string is constructed by joining the ends of two shorter strings. The tension in the strings
    is the same but string I has 4 times the linear mass density of string II. When a sinusoidal
    wave passes from string I to string II:

    A. the frequency decreases by a factor of 4
    B. the frequency decreases by a factor of 2
    C. the wavelength decreases by a factor of 4
    D. the wavelength decreases by a factor of 2
    E. the wavelength increases by a factor of 2

    2. Relevant equations

    3. The attempt at a solution

    [itex]\lambda_1f= \sqrt{\frac{\tau}{4\mu}}=\frac{1}{2}\sqrt{\frac{\tau}{\mu}}[/itex]
    [itex]\lambda_2f= \sqrt{\frac{\tau}{\mu}}[/itex]
    [itex]\therefore \lambda_1 = \frac{1}{2}\lambda_2[/itex]

    So shouldn't the answer be E since λ2 = 2λ1?
  2. jcsd
  3. Mar 1, 2014 #2


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    That all looks correct to me.
  4. Mar 1, 2014 #3
    Ok thanks. Its weird because the answer key says its D.
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