By applying the wave equation we know that the maximum speed of the element's oscillatory motion is 1716 micrometer / s.
We need to know about wave equations to solve this problem. The displacement of the wave on the y-axis can be explained by the wave equation
y = A cos (kx - ωt)
where y is y-axis displacement, A is amplitude, k is wave number, x is x-axis displacement, ω is angular speed and t is time.
the wavenumber and angular speed of the wave equation can be determined respectively by
k = 2π / λ
ω = 2πf
where k is the wavenumber, λ is wavelength and f is frequency.
From the question above, we know that:
y = 2.00cos (15.7x - 858t)
v = dy / dt
v = d(2.00cos (15.7x - 858t)) / dt
v = -858 x (-2.00sin(15.7x - 858t))
v = 1716 sin(15.7x - 858t) micrometer/s
maximum velocity can be reached when (sinθ = 1), hence
v = 1716 sin(15.7x - 858t)
v = 1716 x 1
v = 1716 micrometer / s
For more on wave equation on: brainly.com/question/25699025
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