Respuesta :
Answer:
[tex]E_{y} (x,t)[/tex]= 10 cos (1.15 10⁻¹¹ x - 3.427 10¹⁵ t)
Explanation:
The general equation of a traveling wave on the x-axis is
[tex]E_{y}(x,t)[/tex] = E₀ cos (kx -wt)
the amplitude of the wave is E₀ = 10 V / m
the wave number is
k = 2π /λ
indicate the value of λ = 550 nm = 550 10⁻⁹ m
we substitute
k = 2π / 550 10⁻⁹
k = 1.15 10⁻¹¹ m⁻¹
angular velocity is related to frequency
w = 2πf
the speed of light is related to the wavelength and frequency
c = λ f
f = c /λ
we substitute
w = [tex]2\pi \frac{c}\lambda }[/tex]
w = 2π 3 10⁸/550 10⁻⁹
w = 3.427 10¹⁵ rad / s
we substitute in the electric field equation
[tex]E_{y} (x,t)[/tex]= 10 cos (1.15 10⁻¹¹ x - 3.427 10¹⁵ t)
Let's test the value of this wave for t = 0 at the point x = 0, the wave is worth
Ey (0,0) = 10
which corresponds to its maximum positive value, therefore this is the expression of the traveling wave
