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30 September, 12:14

The y component of the electric field of an electromagnetic wave traveling in the + x direction through vacuum obeys the equation Ey = (375 N/C) cos[kx - (2.20 * 1014 rad/s) t]. What is the wavelength of this electromagnetic wave? (c = 3.0 x 108 m/s)

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  1. 30 September, 14:10
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    Given that,

    Ey = 375•Cos[kx - (2.20 * 10¹⁴t) ]

    Speed of light

    c = 3*10^8m/s

    What is the wavelength?

    Generally,

    The wavelength of electromagnetic wave is give as

    Ey = Emax•Cos (kx-wt)

    k = 2π/λ

    w = 2πf

    Ey = Emax•Cos (2πx/λ-2πft)

    Comparing this to the wave equation given,

    We notice that,

    2πx/λ = kx

    Also,

    2.20 * 10¹⁴t = 2πft

    t cancels out

    2.20 * 10¹⁴ = 2πf

    f = 2.20 * 10¹⁴ / 2π

    f = 3.5 * 10¹³ Hz

    Since we are given that

    c = 3*10^8m/s

    Then, using relationship between c, v and λ.

    c = fλ.

    λ. = c/f

    λ. = 3*10^8 / 3.5 * 10¹³

    λ. = 8.57 * 10^-6m

    λ. = 8.57 μm

    The wavelength of the electromagnetic wave is 8.57 micro meter (8.57 μm)
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