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16 July, 21:47

The equation of certain traveling waves is y (x. t) = 0.0450 sin (25.12x - 37.68t-0.523) where x and y are in

meters, and t in seconds. Determine the following:

(a) Amplitude. (b) wave number (C) wavelength. (d) angular frequency. (e) frequency: (1) phase angle, (g) the

wave propagation speed, (b) the expression for the medium's particles velocity as the waves pass by them, and (i)

the velocity of a particle that is at x=3.50m from the origin at t=21. os

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Answers (1)
  1. 17 July, 00:20
    0
    A. 0.0450

    B. 4

    C. 0.25

    D. 37.68

    E. 6Hz

    F. - 0.523

    G. 1.5m/s

    H. vy = ∂y/∂t = 0.045 (-37.68) cos (25.12x - 37.68t - 0.523)

    I. - 1.67m/s.

    Explanation:

    Given the equation:

    y (x, t) = 0.0450 sin (25.12x - 37.68t-0.523)

    Standard wave equation:

    y (x, t) = Asin (kx-ωt+ϕ)

    a.) Amplitude = 0.0450

    b.) Wave number = 1 / λ

    λ=2π/k

    From the equation k = 25.12

    Wavelength (λ) = 2π/25.12 = 0.25

    Wave number (1/0.25) = 4

    c.) Wavelength (λ) = 2π/25.12 = 0.25

    d.) Angular frequency (ω)

    ωt = 37.68t

    ω = 37.68

    E.) Frequency (f)

    ω = 2πf

    f = ω/2π

    f = 37.68/6.28

    f = 6Hz

    f.) Phase angle (ϕ) = - 0.523

    g.) Wave propagation speed:

    ω/k=37.68/25.12=1.5m/s

    h.) vy = ∂y/∂t = 0.045 (-37.68) cos (25.12x - 37.68t - 0.523)

    (i) vy (3.5m, 21s) = 0.045 (-37.68) cos (25.12*3.5-37.68*21-0.523) = - 1.67m/s.
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