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Waves and phase difference

  1. Feb 21, 2013 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=199171.jpg

    Its part B ii) and iii) that I'm stuck on.


    2. Relevant equations

    Apparently for stationary waves, the phase difference between two particles = m(pi), where m is the number of nodes between the particles. This is according to my textbook here:

    attachment.php?attachmentid=199178&d=1361482568.jpg



    3. The attempt at a solution

    So following that info above from my textbook, for B ii), it should be 1 * (pi) = (pi) or 180 in degrees, 1 * (pi) follows from there being only one node between particles O and B. But I got it wrong, the answer at the back is 225 degrees.

    and for B iii), I'm even more confused, I done: 2 * (pi), because theres two nodes between particles O and C. So I had the answer as 2(pi) or 360 degrees. But I'm wrong, the answers at the back has it as 0

    so whats going on here? :confused:
     
  2. jcsd
  3. Feb 21, 2013 #2

    PeterO

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    Firstly part 3.

    You stand beside someone - each facing North - and you are about to each start rotating on the spot. The angle between the directions you are facing will be your phase difference.
    Now you start first, and your friend will start rotating soon. You actually rotate through 360 degrees before your friend joins in the spinning.
    What will be the angle between the directions you are both facing when you are both rotating [at the same speed]?
     
  4. Feb 21, 2013 #3

    PeterO

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    I am assuming you got B (i) correct

    Compare points A and B of the wave.

    When A is at its lowest point, how would you describe the position of B?
    When A is at its mean position, how would you describe the position of B?
    When A is at its highest point, how would you describe the position of B?

    Edit: Just re-read your post, and the answer in the back of the book (225) is wrong - never happens for a standing wave - your answer was correct.
     
  5. Feb 21, 2013 #4
    0 degrees.

    I see your point, and I can sort of understand why particle C is at 0 degrees relative to particle O. But whats up with the explanation and equations given in my textbook?

    phase difference = m(pi), is this wrong?




    Yeah I got part B i) as 180 degrees which is the same as the answers at the back, I used the m(pi) equation, and just did 1 * (pi), because theres only one node between A and O

    1) When A is at its lowest point, how would you describe the position of B?
    2) When A is at its mean position, how would you describe the position of B?
    3) When A is at its highest point, how would you describe the position of B?

    1) same as shown on the diagram
    2) B would be in mean position as well. When A is in mean position, that curved part where its sitting on in the diagram would become straight (horizontal)
    3) B would be just below A


    errr I'm confused
     
  6. Feb 21, 2013 #5

    PeterO

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    I was kind of hoping for:

    1) When A is at its lowest point , B is at its lowest point.
    2) When A is at its mean position, B is at its mean position.
    3) When A is at its highest point, B is at its highest point.

    in other words, B is in phase with A, so if A is 180 degrees of of phase, so is B.

    With standing waves, when comparing any two points, they are either In phase, or 180 degrees out of phase - there are no other comparisons.

    When looking at the original diagram, every point on the loop that includes O is about to move down. Every point on the loop including A & B is about to move up. Every point on the loop including C is about to move down [in phase with O!].

    The phase difference of two points on any wave will never be more than 360 degrees out of phase - in fact 360 degrees out of phase is in phase.

    So is you slavishly use that m(π) formula, you have to repeatedly subtract 2π until the answer is less than 2π.
     
  7. Feb 21, 2013 #6
    yeah that makes sense, but what is the point of that m(pi) formula? seems a bit pointless, even misleading to me

    and also, what if I get asked to compare a particle on a loop and a particle on the exact point of the node?

    the particle on the node would constantly be stationary while the other particle goes up and down, so how would you describe the phase difference between them? is it even possible?
     
  8. Feb 21, 2013 #7

    PeterO

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    I don't think there is a phase difference between a node and any other point.
    Not that the node is in-phase - just that the term phase has appropriate connection to a node.
     
  9. Feb 21, 2013 #8
    Thanks a lot for all the explanations
     
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