1. Limited time only! Sign up for a free 30min personal 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!

Wave Equation for a Progressive Wave

  1. Jul 27, 2016 #1
    1. The problem statement, all variables and given/known data
    In some places, the wave equation is y=Asin(wt-kx) and in other places they have y = Asin(kx-wt) and they treat them as if they are equal. How are they equal? They also had y=-Asin(wt-kx). What is the difference between all 3?

    2. Relevant equations
    As above

    3. The attempt at a solution
     
  2. jcsd
  3. Jul 28, 2016 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The third one is equal to the second one, because ##\sin(-x)=-\sin x##.
    The first one is almost the same as the other two, with the only difference being a phase shift of 180 degrees (half a cycle), because ##\sin(x+180^\circ)=-\sin x##. In many calculations phase does not matter. Where it does, it would be important to pick one of the above and stick with it throughout the calculation.
     
  4. Jul 28, 2016 #3
    In the book I have, I was reading up on the equation of a standing wave with a reflection at a fixed end.
    This is what they said: Consider a stretched rop fixed at O, and consider a point P, at a distance x from O.
    Let O receive (from the right) an incident train of waves of equation: yo = A sin wt
    Being a fixed end, O receives simultaneously a reflected wave (to the right) of the form: y'o= -A sin (wt)
    which results in O having zero displacement at all times.
    Point P receives reflected waves with a time lag. The equation of its displacement becomes: y1= - Asin(wt-kx)
    Simultaneously, P receives the incident waves ahead of O. The equation is: y2= A sin(wt+kx)
    The resultant displacement of P is y=y1+y2
    So y=2Asin (kx) cos (wt)

    In a video I saw, he was using the incoming wave as y1= A sin (kx-wt) and y2= A sin (wt+kx)
    And the answer is obviously going to be the same.

    What I didn't understand was in the book, they took the upside down reflection equation as - A sin(wt-kx). Does the minus sign in this case come from the negative amplitude of the upside down reflected wave? Why didn't the video take this into account?

    I do know that A sin(wt-kx) is when the wave is travelling in the positive x-direction and A sin(wt+kx) is when the wave is travelling in the negative x-direction.
     
  5. Jul 28, 2016 #4

    pasmith

    User Avatar
    Homework Helper

    Sine is an odd function : [itex]\sin (kx - \omega t) \equiv - \sin(\omega t - kx)[/itex].
     
  6. Jul 28, 2016 #5
    Thanks pasmith. Could you please take a look at the post#3?
     
  7. Jul 30, 2016 #6
    n the book I have, I was reading up on the equation of a standing wave with a reflection at a fixed end.
    This is what they said: Consider a stretched rop fixed at O, and consider a point P, at a distance x from O.
    Let O receive (from the right) an incident train of waves of equation: yo = A sin wt
    Being a fixed end, O receives simultaneously a reflected wave (to the right) of the form: y'o= -A sin (wt)
    which results in O having zero displacement at all times.
    Point P receives reflected waves with a time lag. The equation of its displacement becomes: y1= - Asin(wt-kx)
    Simultaneously, P receives the incident waves ahead of O. The equation is: y2= A sin(wt+kx)
    The resultant displacement of P is y=y1+y2
    So y=2Asin (kx) cos (wt)

    In a video I saw, he was using the incoming wave as y1= A sin (kx-wt) and y2= A sin (wt+kx)
    And the answer is obviously going to be the same.

    What I didn't understand was in the book, they took the upside down reflection equation as - A sin(wt-kx). Does the minus sign in this case come from the negative amplitude of the upside down reflected wave? Why didn't the video take this into account?

    I do know that A sin(wt-kx) is when the wave is travelling in the positive x-direction and A sin(wt+kx) is when the wave is travelling in the negative x-direction.
     
  8. Jul 31, 2016 #7

    mukundpa

    User Avatar
    Homework Helper

    I think a lot of confusion is there. I simply understand it by putting x = 0 and t = 0 as well as I think the phase decreases in the direction of wave motion. Thus

    y = A sin (wt - kx) wave moving in positive x direction and initially wave displacement (y) at origin is zero and increasing in positive y direction with time.
    y = A sin (wt + kx) wave moving in negative x direction and initially wave displacement (y) at origin is zero and increasing in positive y direction with time.
    y = A sin (kx - wt) wave moving in negative x direction and initially wave displacement (y) at origin is zero and increasing in negative y direction with time.
     
  9. Jul 31, 2016 #8
    Wrong .

    Wave represented by y = A sin (kx - wt) moves in positive x direction .
     
  10. Jul 31, 2016 #9

    mukundpa

    User Avatar
    Homework Helper

    May be, but I think at a particular moment (t = constant) if we increase x the phase angle increases and as per I think with at a moment of time phase angle decrease in the direction of wave motion. Please let me now how you thinks that it is moving in positive x direction. .
     
  11. Jul 31, 2016 #10
    Sorry I do not understand your point .

    Here is some food for thought for you . If you believe y = A sin ( wt - kx ) travels in positive x-direction , then what makes you think that y = A sin (kx - wt) moves in negative x-direction .

    What is the difference between y = A sin ( wt - kx ) and y = A sin (kx - wt) ?
     
  12. Jul 31, 2016 #11

    mukundpa

    User Avatar
    Homework Helper

    Thanks but where is the food? I need it. :smile: I do not believe, I try to make logic and try to understand. In first equation x is negative and with increase in x the phase angle (wt - kx) decrease while in second x is positive and with increase in x phase angle (kx - wt) increases (considering snapshot at time t)
     
  13. Jul 31, 2016 #12
    y=Asin (kx +wt) or A sin (wt+kx) travels in the negative directiion and
    y=A sin(kx-wt) or y = A sin(wt-kx) travel in the positive x direction
     
  14. Jul 31, 2016 #13
    Correct .
     
  15. Jul 31, 2016 #14
    Your logic is flawed .

    When you take a snapshot at time t , you basically fix 't' . And as soon as you do that the wave is not moving anymore . Now , you cannot determine whether the wave is moving in positive or negative direction . Both waveforms look same .
     
    Last edited: Jul 31, 2016
  16. Aug 1, 2016 #15

    mukundpa

    User Avatar
    Homework Helper

    Thanks for your comments. I will try to learn more about it.
     
  17. Aug 1, 2016 #16
    "If it is cosine A(wt-kx), a crest is at wt-kx=0. This means that at t= 0 the crest is at x=0 and at a later time t, it is at x= k/w*t. This is the same equation that holds for a body moving along the x axis with uniform velocity v=k/w in the positive direction (from left to right)."

    I found this on another post by a scientific adviser on the forum. I don't understand the part where he says at a later time t, x =k/w *t
    how did he get this??
     
  18. Aug 1, 2016 #17
    I get it he wrote v as k/w when it should be w/k then it follows because w=2pi (f) and
    k =2pi/lambda so v= 2pi f / 2pi/lambda which gives v= f (lambda) so yeah.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Wave Equation for a Progressive Wave
  1. Progressive wave (Replies: 1)

Loading...