The length of so-called
half-wavelength or λ/2
Dipole antennas are, in reality, typically less than λ/2. The input
impedance Z
in of a dipole exactly λ/2 long is 73 + j42.5 Ohms. To achieve
resonance, the dipole is typically shortened to around .47-.48 λ until the
reactive part of the impedance vanishes. The
thicker the
wire or
tubing the dipole is made out of, the shorter the dipole will need to be to be resonant. This is, of course, assuming that the dipole is ideal, i.e. it's perfectly straight and not suspended over some sort of conducting ground (which most are if you live on earth).
Dipoles are not necessarily limited in length to λ/2. In fact, dipoles with lengths of several wavelengths can have very useful radiation patterns and are often used in practice. For example, there are shortwave radio stations that broadcast on multiple frequencies simultaneously using the same dipole antenna (using duplexers, or clever use of tuning stubs). The radiation pattern will be different for each of the transmitted frequencies.