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!

Standing waves on a circular plate.

  1. May 16, 2012 #1
    Suppose I have a rigid circular metal plate that takes sound X microseconds to cross. What frequency would I have to vibrate that plate to get standing waves that form seven concentric circles? The obvious answer is 14X but I'm not sure.

    BTW, this is not homework.
  2. jcsd
  3. May 16, 2012 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    Don'y forget that standing waves have two antinodes per wavelength.
  4. May 16, 2012 #3
    It's not so obvious in several respects.
    First, if x is a time, the frequency cannot be 14x.
    Second, the answer depends on the boundary conditions (free edge, clamped edge, etc).
    And then the answer depends on the plate's thickness too (not only diameter).
    For a plate with clamped edges, the mode with 1 nodal circle has a frequency given by
    where c is the speed of longitudinal waves, h is the thickness and a is the radius.
    Your x would be 2a/c, I suppose (you didn't say which way is the sound going in X seconds) so you can eliminate either c or a from the formula but still have h dependence.
    For the mode with two circular nodes:
    f_02 is 3.89 f_01.
    I don't have the value for f_06 but you can see that the relationship between mode frequency is not harmonic (integer multiples).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook