1.

a. The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength (/4) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 68.0 m high, what frequency does it broadcast most efficiently?

b. Is this in the AM or FM band?

2.

a. What is the wavelength of 96.0-MHz radio waves used in an MRI unit?

b. If the frequencies are swept over a 1.00 range centered on 96 MHz, what is the range of wavelengths broadcast?

3. TV-reception antennas for VHF are constructed with cross wires supported at their centers, as shown in the figure below. The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for particular channels and find them to be 2.05 and 0.701 m long, respectively. What are the frequencies for these channels?

4.

a. Lunar astronauts placed a reflector on the Moon's surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns?

b. What percent accuracy is this when the Moon is at a distance of 3.8710⁸ m from Earth?

5. Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed back into sound on a speaker inside the astronaut's space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut's voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.45 s, what was the approximate distance to the Moon, neglecting any delays in the electronics?

6.

a. The electric field of an electromagnetic wave is given by; E=2.10 10² sin(2.70 10⁶ (x-3.0 10⁸ t)) where everything is in SI units. What is the wave's frequency?

b. What is the amplitude of the magnetic field associated with the TEM wave?

7.

a. The components of the electric field in an electromagnetic wave traveling in vacuum are described by E_x=0, E_y=0, and E_z=573 sin(k x - 1.6710¹⁰ t) V/m, where x is in meters and t is in seconds. Calculate the frequency of the wave.

b. Calculate the wavelength of the wave.

c. Calculate the amplitude of the magnetic field of the wave.

d. Calculate the intensity of the wave.