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!

Homework Help: Waves on a 3-piece string

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution


    The 4 main equations are equations (1), (2), (7) and (8).
    But I can't seem to isolate A5 alone as solving equations (7) and (8) will make A5 disappear..


    I got the relation between A1, A2, A3 and A4 but still no A5..
  2. jcsd
  3. Apr 18, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Did you use that the incoming wave has unit amplitude?
  4. Apr 19, 2013 #3
    Despite that, the equations 7 and 8 have a exp term, how do i get rid of that to find just the amplitude A5?
  5. Jun 5, 2013 #4
    I have recently given it another go:


    I've ended up with these 4 equations. The question wants us to find A5.

    But surely A5 must be exponential? in order to make the resultant term on the RHS of equations (3) and (4) non-exponential. Also, when I tried to express A5 in terms of A1, A2, A3 or A4 I can't, cause equations (3) and (4) sort of make A5 ' cancel out '

    I'm not sure how to go about doing this.
  6. Jun 5, 2013 #5
    Here's the typed out question:

    A semi-infinite string of mass per unit length p1 lies along the negative x-axis and is attached at x=0 to a second string of length a, with mass per unit length p2, lying along the positive x-axis. The end of this string at x=a is attached to a third (semi-infinite) string of mass per unit length p3 which lies along the positive x-axis. The combined string is under tension F.

    A wave of unit amplitude, frequency w and wavelength λ1 travelling from negative towards positive x is incident at the joint x = 0. Write down expressions for the waves propagating in these three regions:

    I: x<0
    II: 0<x<a
    III: x>a.

    What are the boundary conditions that need to be satisfied at x = 0 and x = a? For the case of a = λ2, the wavelength of the propagating wave in region II, find the transmitted amplitude T3 in region III, in terms of p1, p2 and tension.
  7. Jun 5, 2013 #6

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    You forgot to put ##a=\lambda_2 \; (=2\pi/k_2)## in some of those equations, and I think there should be a k1 in there somewhere. I'm also a bit concerned about the signs in there.

    But it's only exponential in a constant ratio, so why does that matter?

    You can cancel A5 that way - but only to get a relation between A3 and A4 ... but that does not make A5 unfindable, you just have to use a different substitution.

    It helps to change notation to something simpler ... i.e. put p,q,r in place of k1,2,3 respectively, and put z=exp[-ik3a] or whatever that turns out to be. Then make A=A2 and B,C,D=A3,4,5. Now it should be easier to track the variables - notice that p,q,r and z are all constants?

    Once you've checked your algebra, you have only to row-reduce the matrix of coefficients of A,B,C,D.
    Last edited: Jun 5, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted