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ditto whiteboard. this is ever so much easier to understand visually.

1) a radio wave is a sine wave, before you modulate it.

2) a sine wave is a two dimensional representation of a three dimensional concept. A sine wave is the path of a rotating point traveling along a line. A sine wave is:

a coil spring
a notebook spiral
a screw thread
the path of one tip of a propeller

represented in two dimensions

a term used in conjuction with sine waves is PHASE ANGLE. the phase angle is the position of the rotating point at any given moment. by convention, phase angle 0 is where the rotating point crosses the middle going up.

on a paper graph, phase angle 90 is the most positive point and phase angle 270 is the most negative point. difference = 180 degrees = 1/2 wavelength.

on a physical object like a notebook spiral, any two points 180 degrees apart are as far apart as they can be on that object.

An antenna that is 1/2 wavelength long is sized to intercept the maximum voltage change across the radio frequency sine wave. the largest dimension.

longer antennas develop inverted signals along the too-long portion which reflect off the ends and subtract from the signal.

shorter antennas do not intercept the full voltage difference across a 1/2 wavelength.

1/4 wave antennas are 1/2 wavelength antennas, in a roundabout way. the ground plane creates a virtual 1/4 wave counterpart to the antenna. you will burn up a transmitter using a 1/4 wave antenna without a ground plane.

a 1/4 wave antenna produces one half of the output of a 1/2 wave antenna in the same location.

you can make a 1/2 wave antenna by mounting two 1/4 wave antenna connectors back to back, feeding one with the center conductor and the other with the ground lead. antennas on the mounts, of course.

Yagis are 1/2 wavelength antennas with reflectors and directors.

Dishes are 1/2 wavelength antennas with reflectors.