Traditional explanation:
quin tu audi] quin < qui-ne, i.e. why not; properly speaking an encouraging question like Quin tu audis?, i.e. Why do you not listen? Intended meaning intensified imperative Audi! i. e. Listen! > Both elements contracted to one exhortative clause Quin tu audi, i.e. Just do listen ...! or something like that.
Cf. Valerius Flaccus 7, 257: "quin hoc" ait "audi..." (i.e. Nay, listen to this," she says..., transl. J. H. Mozley)