Final answer:
The wavelength of electromagnetic radiation for an AM radio station at 990 kilohertz is approximately 303 meters. The time required for the radiation to propagate from the broadcasting antenna to a radio 2 km away is approximately 6.67 microseconds.
Step-by-step explanation:
To determine the wavelength of electromagnetic radiation for an AM radio station broadcasting at 990 kilohertz, the formula for calculating wavelength can be used.
This formula is λ = c / f, where λ is the wavelength in meters, c is the speed of radio waves which is the speed of light (approximately 3×108 m/s), and f is the frequency in hertz.
First, convert the frequency to hertz by multiplying the kilohertz by 1,000: 990 kHz × 1,000 = 990,000 Hz.
Then plug this value into the formula to get the wavelength: λ = 3×108 m/s / 990,000 Hz ≈ 303 meters.
For the electromagnetic radiation to propagate from the broadcasting antenna to a radio 2 km away, the time required can be found by dividing the distance by the speed of light, since electromagnetic radiation travels at the speed of light.
So the time t = d / c, where d is the distance.
Therefore, t = 2,000 meters / 3×108 m/s ≈ 6.67×10-6 seconds or 6.67 microseconds.