g The electric field in a sinusoidal wave changes as E = 125 N>C2cos 311.2 * 1011 rad>s2t + 14.2 * 102 rad>m2x] (a) In what direction does the wave propagate? (b) What is the amplitude of the electric field oscillations? (c) What is the amplitude of the magnetic field oscillations? (d) What is the frequency of the wave? (e) What is the wavelength? (f) What is the speed? (g) What other information can you infer from the equation

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