3 meters!
FM radio stations broadcast on radio waves about 3 meters (10 feet) long. That length is the wave's wavelength: the distance from one crest of the wave to the next. FM stands for frequency modulation, the method these waves use to carry sound.
Radio waves are electromagnetic waves, the same kind of wave as light, and radio stations make them with electric currents in wires and circuits. A wave's frequency is the number of crests that pass a point each second, counted in hertz. All radio waves travel at the speed of light, about 300,000 kilometers per second, so a wave's length is that speed divided by its frequency. The higher the frequency, the shorter the wave.
In the United States, federal rules set aside 88–108 megahertz for FM broadcasting, divided into 100 channels. One megahertz is a million crests per second. The International Telecommunication Union (ITU), which coordinates radio use worldwide, gives slightly different limits for different parts of the world: the FM band starts at 87, 87.5 or 88 megahertz and ends at 108 megahertz.
Those frequencies give wavelengths of 2.78–3.45 meters, and a station at 100 megahertz sends out waves 3.00 meters long. The ITU calls all frequencies from 30 to 300 megahertz, with wavelengths of 1–10 meters, "metric waves", or very high frequency (VHF). FM radio falls inside this band, and so do some television channels.
A radio station sends out a carrier wave at its own frequency, such as 105.1 megahertz. To carry sound, the station changes that wave. In AM, short for amplitude modulation, the sound changes the strength of the wave. In FM, the sound shifts the wave's frequency up and down while its strength stays the same.
The shifts are small. In the United States and Western Europe, the frequency can move at most 75 kilohertz, or 75,000 crests per second, either way. A receiver tuned to the station turns those shifts back into sound.
FM is less troubled by static than AM. Electrical noise adds to a wave's strength, not to its frequency. An AM receiver hears that noise as part of the sound, but an FM receiver can ignore changes in strength and listen only for changes in frequency.
The most efficient length for a straight antenna is half the wavelength. For 3-meter FM waves, that is about 1.5 meters (4.9 feet). AM waves are hundreds of meters long, so broadcasting them well takes very large antennas.
Wavelength also affects where a signal can reach. Long AM waves can bend over and around large obstacles, such as buildings and hills. FM signals are received best along a clear line of sight, so FM antennas are placed high up, often on very tall towers.