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Homework Help: Transverse Wave

  1. Nov 19, 2008 #1
    1. The problem statement, all variables and given/known data
    A transverse wave on a string is described by the wave function
    y = (.120m) sin(pie/8 + 4pie(t))

    (a) Determine the transverse speed and acceleration of an element of the
    string at t=0.200s for the point on the string located at 1.60m
    (b) What are the wavelength, period, and speed of propagation of this wave?


    2. Relevant equations
    Part (a)
    Velocity = -wA cos(kx-wt)
    Acceleration = -w^2A sin(kx-wt)

    Part B
    Wavelength = k = 2pie/lambda
    Period = 1/f
    Speed = f(lambda)
    w = 2pief
    f = w/2pie = 2.0 rad/s

    3. The attempt at a solution

    Part (a)
    V = -(4pie) (.120m)cos(pie/8 + 2.51) I don't know what to do from here
    A = -(4pie)^2 (.120m) sin(pie/8 + 2.51) I don't know what to do from here

    Part (b)
    Wavelength = pie/8 = 2pie/lambda = 16m
    Period = 1/2.0 s^-1 = .5s
    Speed f(lambda) = (2.0s^-1)(16m) = 32m/s

    If anyone can help I would appreciate it.
    Thanks,
    Kevin
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 19, 2008 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Hi,

    Is that supposed to be
    (.120m) sin((x)pie/8 + 4pie(t))
    ?
    (An "x" is needed for this to be a wave.)

    Just plug the numbers into your calculator, using radian mode for the sine calculation. And again, please check if it should really be
    (x)pie/8

    You got the right answer. However, what you wrote here is bad "math grammar". It says (among other things) that
    Wavelength = pie/8
    which is wrong. pie/8 is actually "k", which as you know is different than wavelength.

    A better way to write this out would be something like this:

    Wavelength:
    k = pi/8 m^-1 = 2pi/lambda
    lambda = 2pi / (pi/8 m^-1) = 16 m


    Your period and speed calculations look correct.
     
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