Why does the length of an antenna, relative to the wavelength, matter?
So why does the relative length of antenna to wavelength matter?


A monopole antenna (for instance) can be "short" and it will pick up a signal that is proportionately smaller AND look like an impedance that is highly capacitive to the receiver. The "resistive" part of the signal will also be very small too: -



Picture taken from here

This is a good thing for crystal radios because at (say) a length of 0.05\$\lambda\$ it can reactively tune with a coil and produce a decent Q factor in order to give good selectivity in the crystal radio.

On the other hand, for a transmitting antenna, this is problematic because you have to do two things: -


Counteract the capacitance (about 1000 ohms at 0.05\$\lambda\$) with a series inductor in order to be able to drive a decent current into said antenna
Drive a really low value resistor (the transformed impedance of free space at the electrical terminals of the antenna). It's also hard to find sub-1-ohm coax!


So, transmitting antennas are chosen to have a length that makes the electrical interface simpler. For instance, at 0.25\$\lambda\$ the impedance is purely resistive at about 37 ohms. You could even choose a length that is a bit short of 0.5\$\lambda\$ and get a resistance of over 2000 ohms with no reactive part.

If you go to bigger antenna lengths then you get a repeated pattern: -



Picture taken from here

The base of the graph is in MHz with a quarter wave being at 2.5 MHz. The reactive part of the impedance is blue and the resistive is red with both being in ohms along the y-axis. There are some discrepancies in the amplitudes between the two pictures but this isn't the point - the point is that antenna length affects impedance greatly and it steps and repeats as you go from an electrically short antenna to an electrically long antenna.

Regarding the antenna pattern, a dipole looks like this with the antenna vertical and at the centre: -



Picture taken from here