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Homework Help: Transverse wave question

  1. Oct 9, 2011 #1
    [itex][/itex]1. The problem statement, all variables and given/known data
    A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of 80 m/s. At t = 0, the string particle at x = 0 has a transverse displacement of 4.2 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 18 m/s.
    It asks to solve for f,λ,[itex]y_{m}[/itex],k,ω, and [itex]\phi[/itex] in the wave formula

    2. Relevant equations

    y(x, t) = [itex]y_{m}[/itex] sin(kx ± ωt + [itex]\phi[/itex])

    3. The attempt at a solution
    Since it says at t and x = 0 the displacement is 4.2cm and stopped moving i assumed that meant that it had reached its max displacement. I then used [itex]u_m=ωy_m[/itex]
    for the max transverse speed and solved for ω, which i put into the formula
    f=[itex]\frac{ω}{2\pi}[/itex] which gave me [itex]0.00367s^-1[/itex], and solving for wavelength using [itex]λ=\frac{v}{f}[/itex] gave me 21827m which doesn't seem right, i'm pretty sure i'm doing something wrong, any help would be appreciated.


    Oh and btw i converted all the cm to m before calculating.
  2. jcsd
  3. Oct 10, 2011 #2
    You wrote,

    u_m=ωy_m (why can't I copy and paste your formulas intact? Oh well)

    Did you mix units, the displacement was given in cm and the velocity in m/s ??? We want everything in cm or m.
  4. Oct 10, 2011 #3
    Yes i converted 4.2cm to 0.042m, then divided 18m/s by 0.042m to get a very large ω value of 428.6
  5. Oct 10, 2011 #4
    Ok, i calculated again and i think i switched the denominator with the numerator in something. Seems to be more reasonable now.
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