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Homework Help: Period, frequency, wavelength, and velocity of a light wave

  1. Dec 1, 2013 #1
    1. The problem statement, all variables and given/known data
    A light wave has a frequency of 6 x 1014 Hz. A) What is its period? B) What is its wavelength in a vacuum? C) When the light wave enters water, its velocity decreases to 0.75 times its velocity in vacuum. What happens to the frequency and wavelength?

    2. Relevant equations
    c = λf

    v = c/n

    T = 1/f

    3. The attempt at a solution

    I understood how to do parts A and B.

    For A, since we know the frequency, we can take the equation for period, T to find the answer:

    T = 1/f = 1/(6 x 1014 Hz = 1.67 x 10-15 sec.

    For B, we know that c = 3.0 x 108 m/s in a vacuum and we're given the frequency so wavelength is found by taking the equation:

    λ = c/f = (3.0 x 108 m/s)/(6 x 1014 Hz) = 5 x 10-7 m.

    For part C, however, I got confused.

    I believe we can use the equation:

    v = c/n

    We're told that velocity decreases by 0.75 times in a vacuum so I think that v then would be:

    v = 0.75c

    So from here, we have to relate it to the equation c = λf.

    So would we use the equation:

    0.75c = λf to find wavelength since we already what f is? Can we assume that f does not change but that wavelength would?

    To get wavelength then, we'd take:

    0.75c/f = λ?
  2. jcsd
  3. Dec 1, 2013 #2
    Yes, the frequency of the wave will remain constant.
  4. Dec 1, 2013 #3
    So for finding the wavelength then, how exactly do you use the information of v being reduced to 0.75 times its original velocity to find the new wavelength in water then?
  5. Dec 1, 2013 #4
    The new velocity will will be 3/4 the original velocity c. You know what c is, so compute the new velocity. Furthermore, you know what the frequency is. That's two out of three variables. You can solve for lambda.
  6. Dec 1, 2013 #5
    Oooh! Ok got it. I wanted to verify my understanding when we were told that the velocity was 0.75 times its original velocity in water. Got an answer of 3.75 x 10^-7 m, which makes sense as an answer. Thanks!
  7. Dec 1, 2013 #6
    Perfect. Since the velocity decreased by a factor of 3/4, the wavelength does also. This can be verified by multiplying your wavelength result you attained previously.
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