I had always assumed that there was just one word for a row of grass or other cereal crop as it falls as it’s mown, or a broad area of land, also used by extension for a broad area of anything (swathes of the English-speaking population use swathe and not swath), but then swath started cropping up in both the newspaper and the current affairs magazine I read regularly (which do not share a publisher, although some journalists write for both).
To me, personally, “swath” sounds wrong when I read it (this is where I find out not everyone hears the words in their head, like when I found out that not everyone gets earworms (uninvited music playing in your head). I’ve always pronounced the word to rhyme with “bathe”, with the “a” that’s in “cave”, presumably because I first saw it written as “swathe” and applied the rule that an “e” at the end of a word lengthens the vowel. “Swath” reads to me with a harder “the” and the “shortened”, so like the beginning part of “gather” (this is hard without using linguistic pronunciations symbols!) although I suppose you could read it with the same vowel as “bath” or even “swatch”.
As the dictionaries I consult for this series (primarily Oxford and Merriam-Webster) both say you can use either swathe or swath, I’m guessing that which you use depends on which you first saw and read and thus the way you pronounce it. I’d love to know which you use and how you pronounce it!
Oh, and if you like this kind of stuff, I can highly recommend Kory Stamper’s new book “Word by Word: The Secret Life of Dictionaries”. I’ve not finished it yet, but, oh, it’s just marvellous. There’s a photo on my book review blog here and a review will appear on the blog in due course.