Question

Your local AM radio station broadcasts at a frequency of f = 1100 kHz. The electric-field component of the signal you receive at your home has the time dependence E(t) = E0 sin(2πft), where the amplitude is E0 = 0.62 N/C. Radio waves travel through air at approximately the speed of light.
a) At what wavelength, in meters, docs this station broadcast?
b) What is the value of the radio wave's electric field, in newtons per coulomb, at your home at a time of t = 3.1 μs?

Answer 1

Answer:

(a) 272.73 m

(b) 0.338 N/C

Explanation:

frequency, f = 1100 kHz = 1100 x 1000 Hz

E(t) = Eo Sin(2πft)

Eo = 0.62 N/C

(a) Velocity of light, c = 3 x 10^8 m/s

wavelength, λ = c / f = (3 x 10^8) / (1100000) = 272.73 m

Thus, the wavelength is 272.73 m.

(b) at t = 3.1 microsecond = 3.1 x 10^-6 s

E = Eo Sin (2 π ft)

E = 0.62 Sin (2 x 3.14 x 1100 x 10^3 x 3.1 x 10^-6)

E = 0.62 Sin (21.4148)

E = 0.62 x 0.5449 = 0.338 N/C

Thus, the electric field at t = 3.1 microsecond s 0.338 N/C.