Frankly speaking no standing waves. Waves always travel. In air travel the
pressure pulse. When the two waves travel in opposite directions they
interfere. See: http://en.wikipedia.org/wiki/Kundt's_tube
"The sound generator is turned on and the piston is adjusted until the sound
from the tube suddenly gets much louder. This indicates that the tube is at
resonance, which means its length is a multiple of the wavelength of the
sound wave. At this point the sound waves in the tube are in the form of
standing waves, and the amplitude of vibrations of air are zero at equally
spaced intervals along the tube, called the nodes."

Between the nodes are places where the amplitude is doubled. So the places
with doubled amplitude are standing. Pressure pulse travel.
In antennas is electron gas. The first place where the doubled amplitude
(amplitude means voltage or electron density) appear is end of the radials.
The next is halve wave apart from the end. Such places radiate strong
electric waves. They are the source of radiation.
Of course the next source is weaker because some part of energy is radiated.
But such is stronger than the trawled source (normal voltage pulse)

If antenna has only one source it is omnidirectional. If two or more is
directional because the waves from different sources interfere.

The halve wave dipole has the two sources. The next two appear than a
dipole is longer than the wave length.
So that what R. Clark wrote is obvious: "[* What is this proportional and
proportionate mean? For a dipole of
0.05 WL to a dipole of 0.5WL, the far field change for that 10:1
variation is negligible. However, for a dipole of 0.5WL to a dipole
of 1.25WL, the far field change for that 2.5:1 (a smaller proportion)
variation is very noticeable.]

The above is the antenna with the Helmholtz' pressure wave.
Could anybody describe the antenna with the Heavisde's TEM waves?
In a few words. Do not send mi to library.
S*