Numerous sources say that LW length shouldn't be a multiple of λ/2 for any frequency in interest. This will cause the antenna to have a high impedance at this frequency. Since the coax cable impedance is 50 Ohms, we will get a high SWR. I get this part.

What I don't get is **why** the antenna will have a high impedance in this case and low impedance otherwise. It is my understanding that it has something to do with standing waves and voltage nodes. However when I tried to investigate this question further I've found only a lot of formulas, and since I'm not a mathematician this is where I stuck.

Could you please explain why the antenna works this way as if I was 10 years old? Or maybe name a book or article that does this.