Antenna Length for Low Frequency Radio Signals - Why so long?
Think of the vibratory modes on a string clamped at both ends.  When you clamp a length of string at both ends, the allowed vibration patterns all have one thing in common; they go to zero at the ends.



So, the length of the string determines the natural frequencies of vibration; the longer the string, the lower the fundamental frequency.

Very roughly speaking, an antenna acts similarly.  For example, the current must be zero at the ends of a center-fed dipole antenna in analogy with the clamped ends of the string.

 

So, for the antenna to resonate at a lower frequency, it must be longer, just as the string must be.