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!

Energy and rate of energy transmitted by a given wave function

  1. Oct 28, 2009 #1
    1.
    The wave function for a wave on a taut string is given below, where x is in meters and t is in seconds.

    y(x, t) = (0.300 m) sin(11πt - 3πx + π/4)​

    (a) What is the average rate at which energy is transmitted along the string if the linear mass density is 75.0 g/m?

    (b) What is the energy contained in each cycle of the wave?


    2.
    y(x,t) = Asin(kx-wt+phi)
    E^ = (1/2)uw2A2^
    P = E^/T = (1/2)uw2A2v
    k = 2π/^
    v = w/k
    w = 2π/T = 2πf

    A=amplitude, phi=phase contstant
    E^=total energy in one wavelength, u=linear mass density, ^=wavelength
    P=power, T=period,
    k=wave#
    v=velocity
    w=angular frequency, f=frequency


    3.
    given: y(x,t) = (0.300 m) sin(-3πx + 11πt + π/4), therefore A = 0.3m, k = -3π, w = -11π, phi = π/4; u = 75g/m

    (a)
    P = (1/2)uw2A2v and v = w/k
    therefore:
    P = (1/2)(75g/m)(-11π)2(0.3m)2(-11π/-3π)
    P = 37.5*121π2*0.09(11/3) = 14660.2709

    P = 14660.27W

    (b)
    E^ = (1/2)uw2A2^ and k = 2π/^ so ^ = 2π/k
    therefore:
    E^ = (1/2)(0.075kg/m)(-11π)2(0.3)2(2π/-3π)
    E^ = 0.0375*121π2*0.09(2/-3) = -2.6655038

    E^ = -2.67J
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Energy and rate of energy transmitted by a given wave function
  1. Rate of energy (Replies: 1)

  2. Energy in a wave (Replies: 1)

Loading...