1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Qustion on sinewave

  1. Dec 18, 2011 #1
    If the expression forsinewave is y=Asin(ωt±α)
    then α is the phase angle.
    But what is time displacement looking at that expression?
    Thank you
     
  2. jcsd
  3. Dec 18, 2011 #2

    Mentallic

    User Avatar
    Homework Helper

    Time displacement? I assume you mean how long it takes for the sine wave to repeat a cycle, or its [STRIKE]frequency[/STRIKE].

    All sine waves repeat every [itex]2\pi[/itex] units. So what we're looking for is

    [tex]wt_1+\alpha+2\pi[/tex]

    to be equal to

    [tex]wt_2+\alpha[/tex]

    and we want to find t2 in terms of t1, t2>t1

    So equating each expression and simplifying:

    [tex]wt_1+\alpha+2\pi=wt_2+\alpha[/tex]

    [tex]wt_2=wt_1+2\pi[/tex]

    [tex]t_2=t_1+\frac{2\pi}{w}[/tex]

    So clearly from this, we can see that the time it takes from the first point in a cycle (t1) to the next (t2) takes [itex]2\pi/w[/itex] time.

    Also to get a more intuitive understanding of this, just think about the length of a complete cycle for sin(x), then sin(2x), sin(x/3) - which is the same as sin(1/3*x) etc.


    edit: meant to say period, not frequency.
     
    Last edited: Dec 18, 2011
  4. Dec 18, 2011 #3
    Thank you for your really good explanation.
    But I am not sure this is the answer to the question I was given. I am not sure.
    Can frequency and time period T be called time displacement? Is it not about that phase angle?
    Thanks any way
     
  5. Dec 18, 2011 #4
    Is it ω that is worrying you?
    ω is an 'angular velocity' it is the number of cycles (given in radians) completed per second
    1 cycle is 2∏ radians and therefore ω = 2∏/T where T is the time for 1 cycle.... the time period

    So T = 2∏/ω

    and frequency f = 1/T = ω/2∏

    Hope this helps
     
  6. Dec 18, 2011 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You haven't given the definition of "time displacement". If you write[tex]
    sin(\omega t \pm \alpha) = \sin(\omega(t \pm \frac \alpha \omega))[/tex] is it the [itex]\pm\frac \alpha \omega[/itex] you want? (Notice that is a question; I'm just guessing here).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook