sigh
verb
[ sʌɪ ]
• emit a long, deep audible breath expressing sadness, relief, tiredness, or similar.
• "Harry sank into a chair and sighed with relief"
sigh
noun
• a long, deep audible exhalation expressing sadness, relief, tiredness, or similar.
• "she let out a long sigh of despair"
Origin:
Middle English (as a verb): probably a back-formation from sighte, past tense of siche, sike, from Old English sīcan .