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Standing waves of current/voltage occur along the length of the antenna.  That is voltage values at each point on the antenna is dependent on the distance from the center of the antenna.  Voltage along the length will be like a  Sin π x/L  curve from  x = -L/2 to +L/2.  L is the total length of the antenna.

    A dipole antenna is a pair of two conductor rods (usually hollow cylindrical or square tubes).  They are placed end to end in a straight line with an air gap in between.  When alternating current / voltage is applied in between the two open ends in the center, there are electro magnetic radiation waves that are emitted by the rods.  The emissions take place from the  point of connection,  then from each far end of the conductor rods.  Each rod is of length nearly L/2.

The electric field is along the length of the rod.  The direction of propagation will be perpendicular to the length of the rod.  There will also be some signal transmitted in direction parallel to the length of the rod.

When the length of the antenna L is equal to λ / 2   ie., c / 2 f   then the antenna resonates properly.  The length matches with phase difference of π between the two ends of the antenna.  Then maximum voltage difference from the wave in air will be collected by the receiver. 

When a small AC current/voltage is applied between the two rods, the electrons in the two rods always flow towards the higher voltage side.  The extreme far ends of the antenna are separated by the largest voltage difference.  There is an electric field along the length of the rod.  The electrons alternately flow in and out of the rods.  The high (charge density) at the two far ends sends waves with the electric field intensity on the wave proportional to the voltage at that end.

The wavelength of the radiation will be around 4 times the length of one rod.  This is in case of a half-wave dipole antenna.
If these rods are vertically mounted, then the waves are transmitted in the horizontal plane parallel to the ground all around the space.  The waves are more horizontally directed than in  the vertical direction.

The radio waves (meter waves) microwaves are transmitted and received using these antennas.

The matching wave length of the wave emitted will be:  λ = c / f = 2 L  nearly
               L = length of the antenna.
               f = frequency of signal emitted
               c = speed of light

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The standing wave along the length of antenna is propagated in air in time at the frequency f of the source of current applied.