Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave Function in specific range

  1. Oct 22, 2011 #1
    I obtained the following from a book.

    Question is:

    Periodic Sawtooth described by the following;

    f(x) = x/2∏ for 0<x<2∏
    f(x+2∏) = f(x) for -∞<x<+∞

    The solution is:

    If x = 0
    y = 0

    If x = 2∏
    y = 2∏/2∏ = 1

    If x = 4∏
    y = f(2∏+2∏) = 2∏ = 1

    Can anyone explain to me why when x = 4∏ y = 1 ? I'm not clear on that bit.

    I would just think if you're putting x = 4∏ into the 2nd equation in the question you would get y = f(4∏+4∏) = f(8∏)

    I know a full rotation is 2 ∏, so I can see how 8∏ would be the same as 2∏, but then how did they go from 2∏ to 1 in the part above which I have emboldened?

    Thank you
  2. jcsd
  3. Oct 22, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You were given f(x) = x/2∏ for 0<x<2∏. Your function is not defined at x = 0 or at x = 2∏. So you don't have f(0) = 0 and f(2∏) = 1. The value of a function like that at the two end points is irrelevant in calculating things like the Fourier Series so they are usually left undefined. If you insist on defining f(0)= 0, then you have no choice but to also choose f(2∏) = 0 if you want the function to be periodic.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook