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Simple standing waves problem

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data
    Hello everyone,
    I am stuck with a basic concept.How do we can recognize if a given equation is wave or not?For example we know that the standing waves equation is y=2Acos(kx)sin(ωt). In my text book there is a problem which says that two waves having only different amplitudes are traveling on opposite directions on x-axis. They have asked if the waves form standing waves.


    2. Relevant equations



    3. The attempt at a solution
    First of all i wrote the following equations.
    y1=A1sin(kx-ωt) ; y1=A2sin(kx+ωt)
    i added them and got
    y1+y2= (A2+A1)sin(kx)cos(ωt)+(A2-A1)coskxsinωt

    how do i recognize if this equation represents a standing wave or not??
     
  2. jcsd
  3. Oct 15, 2013 #2
    The standing waves have pretty neat definition.

    I guess, this gives you the answer!!!

    For a given function ##h## to be a travelling wave, it must be of the form ##h(x-vt)##, where v is velocity of wave.
     
  4. Oct 15, 2013 #3
    i was thinking the same but my book says that it forms standing waves and also transports energy
     
  5. Oct 15, 2013 #4
    standing waves in general form pattern in which point of minimum and maximum displacement don't change with time, moreover in general there is no transport of energy over large distance.

    Maybe author of your book wants to make a point!!!

    You can check this out at: http://www.physics.buffalo.edu/claw/Page15/ProjectCLAW-P15.html [Broken]

    Edit: The equation you found can be considered to be superposition of two standing waves. But it won't reproduce pattern characteristic of standing waves!!!!
     
    Last edited by a moderator: May 6, 2017
  6. Oct 15, 2013 #5
    I got it from a simulation at http://www.ualberta.ca/~pogosyan/teaching/PHYS_130/FALL_2010/lectures/lect12/lecture12.html

    if the amplitudes are not equal then the wave formed is a wave both travelling and standing.This wave transmites energy as it is partially traveling.
     
  7. Oct 15, 2013 #6
    Last edited: Oct 15, 2013
  8. Oct 15, 2013 #7
    I meant to say partially traveling.
    thanks for guidance:smile:
     
  9. Oct 15, 2013 #8
    no problem!!!:wink:
     
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