300 meters!
AM radio stations broadcast on radio waves hundreds of meters long. In the United States, the waves on the AM dial range from about 176 to 555 meters (579 to 1,821 feet). The explorer shows a wave 300 meters (984 feet) long, the wavelength of a station broadcasting at about 1,000 kilohertz, near the middle of the dial.
Radio waves, like light, are electromagnetic waves, and they have the longest wavelengths of any. A wave's wavelength is the distance from one crest to the next. Its frequency is the number of crests that pass a point each second, counted in hertz. Radio stations are named by frequency: a station at 1,000 kilohertz sends out a million crests a second. Dividing the speed of light, about 300,000 kilometers per second, by the frequency gives the wavelength.
In the United States, the rules of the Federal Communications Commission (FCC) set the AM broadcast band at 535–1,705 kilohertz. Stations are assigned 117 frequencies, from 540 to 1,700 kilohertz in steps of 10 kilohertz. Those frequencies match wavelengths from 555 meters down to 176 meters. A 300-meter wave has a frequency of 999 kilohertz, next to the 1,000-kilohertz channel.
The International Telecommunication Union (ITU), which coordinates radio use worldwide, groups radio frequencies into numbered bands. Band 6, labeled MF, runs from 300 to 3,000 kilohertz, and the ITU calls its waves "hectometric waves". A hectometer is 100 meters, and the waves in this band are between 100 meters and 1 kilometer long. The whole AM band falls inside it.
AM stands for amplitude modulation, a way of placing sound on a radio wave. The station sends out a carrier wave at its own frequency. The sound signal makes the carrier's amplitude, the height of its crests, rise and fall, while its frequency stays the same. A radio tuned to that frequency picks up the wave and turns the changes in amplitude back into sound.
FM, frequency modulation, changes the frequency of the carrier instead, and keeps its amplitude constant. Stray radio noise adds to a wave's amplitude, so an AM receiver takes the noise as part of the signal. An FM receiver can ignore changes in amplitude, which makes FM less affected by noise.
The most efficient length for a straight antenna is half the wavelength of the waves it sends. With waves hundreds of meters long, AM stations need very large antennas. For the explorer's 300-meter wave, half a wavelength is 150 meters (492 feet), almost as tall as the Washington Monument.
The long waves have an advantage. They can travel over and around large obstacles such as buildings and hills, the way ocean waves pass around large rocks. FM and television signals are received best with a clear line of sight to the antenna, so their much smaller antennas are placed high up on tall towers.