The word tough is pronounced /tʌf/. The word though has a completely different pronunciation, that is /ðəʊ/.
Is there a reason why the latter would not be pronounced /ðʌf/?
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There is no reason that a word spelled though shouldn't be pronounced /ðʌf/ in principle. However, with regard to the English word we are actually talking about, the problem is the other way round. Words are primarily a progression of sounds. The spelling is a means of representing that series of sounds.
So, in a way, the question might be phrased: "Why do we represent the word /ðəʊ/ similarly to the way we represent the word /tʌf/?". The answer is very complicated. The short answer to the question is that English doesn't have a good correspondence between the sound and the spelling of words - because of the history of the language, the history of printing, and the fact that certain words change their sounds depending on stress.
I've heard some native English speakers say that they can pronounce any new word they see without having heard it before, but they can't. A simple way to show that this claim isn't true, is to take the Original Poster's letter cluster : -ough
This can have nine different pronunciations in English. Here are some example words and pronunciations:
What this shows is that we use -ough to represent all kinds of different sounds in English. There's no way for a speaker who hasn't seen a particular -ough word before to know what the pronunciation of the word will be. There is no principled way to justify this in modern English. It's mostly down to historical accident.
I'm afraid that I don't know the historical reasons why the current English word /ðəʊ/ is spelled the similarly to /tʌf/, but I'm sure someone here can help. What I do know is that there's little intuitive rhyme or reason for the spelling of a lot of English words. So, to kind of answer the Original Poster's question more directly, if there was a homograph of the word though, it might well be pronounced /ðʌf/!
The two words have totally different histories. Without going into the English line of development it is possible to show this by comparison with German.
though/although is related to German doch/jedoch. http://www.etymonline.com/index.php?allowed_in_frame=0&search=though&searchmode=none
tough is related to zäh, Bavarian zach /tsa:ch/.http://www.etymonline.com/index.php?allowed_in_frame=0&search=tough&searchmode=none