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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.
    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


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    Staff Emeritus
    Science Advisor
    Homework Helper


    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

    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:

    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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