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!

Wave speed on a string of non-uniform linear mass density

  1. Feb 9, 2016 #1
    1. The problem statement, all variables and given/known data

    Consider a long chain of mass m and length L suspended from a tall ceiling. Like any string if one end is disturbed waves will travel along the string. However, the tension in the string is due to its own weight and is not uniform. As such the speed of the wave will be different at each point of the string. Determine the speed of the wave as a function of a location of the wave on the string.


    2. Relevant equations

    Force (F) = mg, Linear mass density (μ) = m/L, Wave Speed (V) = √(F/μ)


    3. The attempt at a solution

    I began this problem by relating the three relevant equations above as follows;
    Wave Speed (V) = √((mg)/(m/l)) = √(g/l), however, I am now stuck on how to relate this as a function of the location of the wave on the string. My initial thought would be to relate this to the velocity of a particle on a string in the following fashion but even this seemed off √(g/l) = -ω A sin (kx - ωt + φ0)
     
  2. jcsd
  3. Feb 9, 2016 #2

    RUber

    User Avatar
    Homework Helper

    Let's say you call the bottom of the chain x = 0, so that x relates to the height. μ should be a constant, mass per unit length of the chain.
    Your tension (F) on the chain at height x: F(x) = x μ g .
    I think the position of the wave on the string is just referring to the position x.
     
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: Wave speed on a string of non-uniform linear mass density
Loading...