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Analyzing a Wave Function

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data
    The wavefunction of a transverse wave on a string is
    [itex]\psi[/itex][itex]\left(x,t\right)[/itex]=[itex]\left(30.0 cm\right)[/itex]Cos[itex]\left[\left(6.28 rad/m\right)x - \left(20.0 rad/s\right)t\right][/itex]

    Compute the (a) frequency, (b) wavelength, (c) period, (d) amplitude, (e) phase velocity, and (f) direction of motion


    2. Relevant equations
    1. v = w / k
    2. T = 2[itex]\pi[/itex] / kv
    3. f = 1 / T
    4. [itex]\lambda[/itex] = v / f


    3. The attempt at a solution
    Question seems kind of trivial... I just want to double check if my understanding is right.

    From the equation:
    A = 30.0 cm
    k = 6.28 rad/m
    [itex]\omega[/itex] = 20.0 rad/s

    e) Using equation (1), v = (20.0 rad/s) / (6.28 rad/m) = 3.18 m/s

    c) Using equation (2), T = 2[itex]\pi[/itex] / (6.28 rad/m * 3.18 m/s) = 0.31 s/cycle

    a) Using equation (3), f = 1 / (0.31 s/cycle) = 3.23 Hz

    b) Using equation (4) [itex]\lambda[/itex] = (3.18 m/s) / (3.23 cycles/s) = 0.98 m

    d) Amplitude is given = 30.0 cm

    f) since [itex]\varphi[/itex]=(kx - [itex]\omega[/itex]t) is equivalent to the phase in the given function, the direction of motion is in the +x direction

    P.S I know that there's more than one way to solve this
     
    Last edited: Sep 18, 2011
  2. jcsd
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