sigh of relief, (heave) a

A feeling or display of relief that something particularly stressful, unpleasant, or undesirable has been avoided or completed. Everyone in class heaved a sigh of relief after that horrible midterm exam was over. Investors in Europe had a big sigh of relief now that a Greek exit from the Euro has been avoided.

Whew; an expulsion of breath indicating that one is out of a tight spot. Sighing with longing, pain, grief, and numerous similar emotions is common in the English language—especially in poetry—from the earliest days. The word “sigh” comes from Middle English and Old English words meaning exactly the same thing (to expel breath). Heaving a sigh to express intense emotion, especially amatory longing or grief, was current from about 1700 on.