Radio waves are entirely real and physical things even though we cannot see them. It seems simple now that I write it but they are hard enough to imagine in the first place. An AM carrier wave varies in height because they are amplitude modulated. The height varies regardless of the frequency. But the wavelength is constant. For example 820 WNYC-AM has carrier wave with a wavelength of over 1,120 feet. 99.5 FM WBAI, also in New York, has a wavelength of about 10 feet. But because its Amplitude is not modulated, that too is constant. WBAI uses a microwave link between its studio and transmitter. This microwave link at 950 MHz has a wavelength of about 11 inches.
This physical size is behind the design for the "long wire antenna" Each type of long wire is suited to respond best to an even fraction of the full wave. A 1120 foot long wire antenna would be best to receive WNYC-AM. But also impractical inside a Manhattan apartment. At 560 feet it is tuned to the half-wave. At 280 feet the quarter wave. At 140 feet, an eighth and so-on. Great article on Long-wire antennas here.
This same concept applies to the broadcast of the signal. 880 WCBS broadcasts from a tower rigged to output almost a perfect half wave. More info here. There are no AM radio stations that I know of radiating a full half-wave. If you do, please fill me in.