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Beat Frequency for a Laser!

  1. Sep 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A laser emits a monochromatic beam of wavelength [tex]\lambda[/tex] , which is reflected normally from a plane mirror, receding at speed [tex] v [/tex]. What is the beat frequency between the incident and reflected light?


    I know that the [tex]f_{beat} = |f_2 - f_1|[/tex].

    When the wave hits the plane mirror it has frequency
    [tex]f_1 = \frac{v_0}{\lambda}[/tex].
    Then, when it bouces off due to the doppler effect the wavelength becomes:

    [tex]\frac{\lambda_1}{\lambda} = 1 - \frac{v}{c}[/tex].
    Furthermore then,

    [tex]f_2 = \frac{v}{\lambda_1} = \frac{v}{\lambda - \frac{\lambda v}{c}} = \frac{v*c}{\lambda*c - \lambda*v}[/tex].


    So if i then find [tex]f_{beat} = |f_2 - f_1| = |\frac{v c}{\lambda c - \lambda v} -\frac{v_0}{\lambda}| [/tex] This result does not match the book result which is:

    [tex] f_{beat} = 2*(\frac{v}{c})*v_0[/tex].

    I was wondering if anyone could help me with this problem on what I have done wrong.

    Thanks!
     
  2. jcsd
  3. Sep 18, 2009 #2

    tiny-tim

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    Science Advisor
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    Hi Hells_Kitchen! :smile:

    (what's v0? :confused: Do you mean ν0 ?)

    I don't understand your formula for f2. :redface:

    Hint: the image of the laser (on the other side of the mirror) is receding at a speed of … ? :smile:
     
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