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!

Two waves Interfereing resulting waves interferes with another wave

  1. Apr 28, 2008 #1
    [SOLVED] Two waves Interfereing...resulting waves interferes with another wave

    1. The problem statement, all variables and given/known data
    Two traveling sinusoidal waves given by

    Y1(x,t) = 3.87 sin (2.00x - 40.0t) and Y2(x,t) = 3.87 sin(2.00x - 40.0t + 120deg.)

    interfere. The resulting wave interferes with

    Y3 ( x, t) = 3.87 sin ( 2.00x- 40.0t)


    2. Relevant equations





    3. The attempt at a solution

    i am confused...do i add the two first waves together, then add that wave with the third wave? do i need to change my degrees to radians?
     
  2. jcsd
  3. Apr 28, 2008 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Welcome to PF!
    Sounds good to me!
    I shouldn't think so.
     
  4. Apr 28, 2008 #3
    alright so i guess i need to know how to add waves...
     
  5. Apr 28, 2008 #4

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    There are some rather obvious trig identities that you should be using here. Do you have a table of trig identities? If so, can you find one in which two sine functions are being added together?
     
  6. Apr 28, 2008 #5
    i have my physics book which doesn't go to sinusoidal waves
     
  7. Apr 28, 2008 #6

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Try looking for the angle-sum identity for sine. If you can't find it in your physics text, try a mathematics text or alternatively have a look on the internet :wink:
     
  8. Apr 28, 2008 #7
    thnx... you mean like

    sin(A+B) = sinAcosB + cosAsinB

    i don't understand how that applies to the waves adding tho
     
  9. Apr 28, 2008 #8

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sorry, my bad! I meant sum to product formulae :redface:
    Well, your waves are sinusoidal functions aren't they?
     
  10. Apr 28, 2008 #9

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I'm talking about trig identities that come from a typical course in College Algebra and Trigonometry or Precalculus. Surely such a math course would be a prerequisite for your physics course?
     
  11. Apr 28, 2008 #10
    ynet(x, t) = y1(x, t) + y2(x, t)

    = Asin(wt - kx) + Asin(wt - kx + f)

    = [2Acos 1/2(theta)]sin(wt -kx + 1/2 f).
     
    Last edited: Apr 28, 2008
  12. Apr 28, 2008 #11

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    And what is "theta"?
     
  13. Apr 28, 2008 #12
    originally its 120 so...theta would be 60 for the first two interference and 30 for the 2nd interference?
     
  14. Apr 28, 2008 #13
    sry i don't why the f's are f's they should be thetas
     
  15. Apr 28, 2008 #14

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Right. And it doesn't matter if you call them all f's or thetas, as long as they are the same symbol.

    So there is your formula for adding two sinusoidal waves with the same amplitude and frequency, but different phase angles.
     
  16. Apr 28, 2008 #15
    ok so now i have a few more questions about the reamaing part of the problem.

    its ask for
    amplitude:
    2ym cos 120/2 = 2*3.87*cos 60 = 3.87 (interference of 1+2)
    2ym cos 60/2 = 2*3.87*cos 30 = 6.70(interference of resultant and 3)

    correct?

    Phase = 120/2 = 60 (interference of 1+2)
    60 / 2 = 30 (interference of resultant and 3)

    wavelength = i need help here...isn't it lambda?
    defined as 2pi/k

    frequency
    defined as w = 2piF ; F is frequency?
    defined as w = 2pi/T ; since f = 1/T
    so F = 1/T

    period:


    wave number
    this is k right?
     
    Last edited: Apr 28, 2008
  17. Apr 28, 2008 #16
    i have 715 deadline please help
     
  18. Apr 28, 2008 #17

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You are correct on all counts.
     
  19. Apr 28, 2008 #18
    period

    what about the period
     
  20. Apr 28, 2008 #19
    so does that mean the final wavelength will be just pi?

    so does that mean final frequency will be 6.36?
    period:

    that mean k= 2?
     
  21. Apr 28, 2008 #20

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Those are all correct. And since you got the frequency, you can easily get the period.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Two waves Interfereing resulting waves interferes with another wave
  1. Wave interference? (Replies: 9)

Loading...