Answer:
a) the propagation direction is x, b) E₀ = 125 N / C²
, c) B = 41.67 10⁻⁸ T
,
d) f = 4.95 10¹¹ Hz, e) λ = 4.42 10⁻³ m, f) the speed of light
,
Explanation:
The equation they give for the sine wave is
E = 125 cos (14.2 10² x - 311.2 10¹¹ t)
This expression must have the general shape of a traveling wave
E = Eo cos (kx - wt + Ф)
we can equal each term between the two equations
a) the propagation direction is x, since it is the term that accompanies the vector k
b) the amplitude is the coefficient before the cosine function
E₀ = 125 N / C²
c) to find the amplitude of the magnetic field we use that the two fields are in phase
C = E / B
B = E / c
B = 125/3 10⁸
B = 41.67 10⁻⁸ T
d) the angular velocity is
w = 311.2 10¹¹ rad / s
angular velocity and frequencies are related
w = 2π f
f = w / 2π
f = 311.2 10¹¹ / 2π
f = 4.95 10¹¹ Hz
e) the wavelength is obtained from the wave number
k = 2π /λ
k = 14.2 10² rad / m
λ = 2π / k
λ = 2π / 14.2 10²
λ = 4.42 10⁻³ m
f) the speed of an electromagnetic wave is the speed of light
g) what is a transverse wave
