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!

Waves on a cylinder

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution


    Not sure what they mean by general superposition of solutions...Do i use D'alembert's solution whereby I assume initial velocity = 0, and therefore:

    z = z(θ-ct) + z(θ+ct)
  2. jcsd
  3. Apr 10, 2013 #2
  4. Apr 10, 2013 #3


    User Avatar
    Homework Helper
    Gold Member

    Why are you restricting k to positive integers only?

    I don't understand the assumption of zero initial velocity.
    You want to construct a specific superposition of solutions for ω2 that will create a "node" at θ = π/3.
  5. Apr 10, 2013 #4
    i'm not sure how to create that superposition do i use A1*exp(kθ-ωt) + A2*exp(k+ωt) or something?
  6. Apr 10, 2013 #5


    User Avatar
    Homework Helper
    Gold Member

    What are the two values of k corresponding to ω2?

    Superimpose two waves with those values of k. Note that you do not want to change the sign of the ωt term in the exponential. After forming the superposition, you will be able to factor out a common factor of e-iωt.

    You might want to review the concept of "standing waves"on a string.
  7. Apr 11, 2013 #6
    The '-ωt' term involves the velocity of the wave, so you must superimpose:

    A1*ei(-kx-ωt) + A2*ei(kx-ωt)

    so that the waves destructively superimpose.
  8. Apr 11, 2013 #7

    Is this correct??
  9. Apr 11, 2013 #8


    User Avatar
    Homework Helper
    Gold Member

    That looks good to me. You want to limit the value of n such that you don't repeat the same positions on the cylinder.
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: Waves on a cylinder
  1. Hamiltonian Cylinder! (Replies: 2)

  2. Cylinder floating (Replies: 3)

  3. Cylinder with piston (Replies: 16)