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Oscillating String - Transverse Speed, what am I doing wrong?

  1. Aug 29, 2011 #1
    A string oscillates according to the equation
    y´ = (0.654 cm) sin[(π/4.0 cm-1)x] cos[(24.2π s-1)t].
    What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.24 cm when t = 1.13 s?
    Give your answers in centimeter-based units.

    I only need help with part d, the other parts I have gotten right.
    Here's my attempt at solving:

    u = ∂y´/∂t = (0.654 cm) (24.2π s-1) sin[(π/4.0 cm-1)x] (-1) sin[(24.2π s-1)t]

    Then, plugging in x and t:

    u = (-0.654 cm) (24.2π s-1) sin[(π/4.0 cm-1)(1.24 cm)] sin[(24.2π s-1)(1.13 s)]

    u = -32.9 cm/s

    When I plug this solution in, I am told that it is not the correct answer. Even when I tried neglecting the negative sign. I am not sure how my calculations are wrong, but I would love to be enlightened!
     
    Last edited: Aug 29, 2011
  2. jcsd
  3. Aug 29, 2011 #2

    vela

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    Your method looks fine. I get a different number. Are you sure your calculator is in radian mode?
     
  4. Aug 29, 2011 #3
    Oops! I looked at the equation again and it's π/4.0 cm-1, not 4.0π. That is what I used to get the result I did. I have gone back and edited my original post to reflect this. I hope that when calculated with π/4, you get the same thing as I do.

    EDIT: Okay, apparently my method was right, but there is something wrong with my calculator. Just plugged in the numbers to Wolfram and received 36.4 cm/s which is the right answer.

    Final Edit: Yes, I must have been using parentheses dumb or something. Just plugged it into my calculator again and got 36.4 cm/s. I feel dumb now, but I got the right answer after all! :)

    Thank you for your help!
     
    Last edited: Aug 29, 2011
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