Longman Dictionary of Contemporary English - sigh

~1 v 1 to breathe in and out making a long sound, especially because you are bored, disappointed, tired etc  ("Well, there's nothing we can do about it now," she sighed. | sigh heavily/deeply)  (Frankie stared out of the window and sighed deeply.)  (He sighed with despair at the thought of all the opportunities he had missed.) 2 if the wind sighs, it makes a long sound like someone sighing  (The wind sighed in the trees.) 3 sigh for sth to be sad because you are thinking about a pleasant time in the past  (Emilia sighed for her lost youth.) ~2 n an act or sound of sighing + of  (She settled down in her chair with a long sigh of relief.) breathe/give/heave/let out a sigh of relief  (We all heaved a sigh of relief when we heard they were safe.)