Superposition Question

  1. A transverse wave of frequency 40 Hz
    propagates down a string. Two points 5 cm apart are
    out of phase by p/6. (a) What is the wavelength of the
    wave? (b) At a given point, what is the phase
    difference between two displacements for times 5 ms
    apart? (c) What is the wave velocity?

    for a.) I use theta=(sπx)/λ
    solving for λ I get λ=.6m

    Please help me on part b and c, and check to see if I did part a correctly.
  2. jcsd
  3. chroot

    chroot 10,351
    Staff Emeritus
    Science Advisor
    Gold Member

    For part b, you can figure out the phase difference by looking at the frequency of the wave. The frequency is 40 Hz, so the wave has a period T = 1/40 Hz = 0.025 s. The time period 50 ms is thus 0.050 / 0.025 = 2 periods, exactly. If the point on the string executes exactly an integer number of periods in 50 ms, then its phase difference between the beginning and end of that 50 ms period is zero.

    For part c, you know the frequency, 40 Hz, and the wavelength, 0.6 m. You can find the velocity with

    [tex]v = \lambda \cdot \nu[/tex]

    Does this make sense?

    - Warren
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