The words noose, nous sound the same but have different meanings and spellings. Why do noose, nous sound the same even though they are completely different words?
The answer is simple: noose, nous are homophones of the English language.
A loop formed in a rope by means of a slipknot so that it binds tighter as the rope is pulled. Also called running noose.
A snare or trap.
To capture or hold by or as if by a noose.
To make a noose of or in.
Philosophy The rational part of the individual human soul.
Philosophy Reason and knowledge as opposed to sense perception.
Philosophy The principle of the cosmic mind or soul responsible for the rational order of the cosmos.
Philosophy In Stoicism, the equivalent of Logos.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").