The words know, no sound the same but have different meanings and spellings. Why do know, no sound the same even though they are completely different words?
The answer is simple: know, no are homophones of the English language.
To perceive directly; grasp in the mind with clarity or certainty.
To regard as true beyond doubt: I know she won't fail.
To have a practical understanding of, as through experience; be skilled in: knows how to cook.
To have fixed in the mind: knows her Latin verbs.
Used to express refusal, denial, disbelief, emphasis, or disagreement: No, I'm not going. No, you're wrong.
Not at all; not by any degree. Often used with the comparative: no better; no more.
Not: whether or no.
A negative response; a denial or refusal: The proposal produced only noes.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.