The phrase "air of exasperation" is correct and usable in written English.
It can be used to describe a general atmosphere or demeanor that conveys frustration or annoyance.
Example: "When she entered the room, there was an unmistakable air of exasperation among the team members who had been waiting for her decision."
Alternatives: "sense of frustration" or "atmosphere of annoyance".
Dr. Smalley's final response has an air of exasperation.
"Here's the bottom line," he told me, with an air of exasperation.
Eileen's characteristic amalgam of irony and jauntiness is very difficult to separate out, but the air of exasperation is undisguised.
On an episode of "This Week with George Stephanopoulos," Pence, with an air of exasperation, said, "Hoosiers don't believe in discrimination.... Anybody that's been in Indiana for five minutes knows that Hoosier hospitality is not a slogan, it's a reality.
At branches of Laiki Bank and the Bank of Cyprus in the Cypriot capital, Nicosia, where lines had virtually disappeared over the last three days, there was an air of exasperation, anger and anxiety on Thursday as people hoped that money would still be in the machines by the time it was their turn to make a withdrawal.
Soutine's most celebrated and penetrating picture of his benefactor, completed in 1929 and now in the Metropolitan Museum of Art, shows her seated with a slight but unmistakable air of exasperation in an ocelot coat over a long dress, the skirt in rich folds, her lips pursed in impatience, her hands calling attention to a small, proud waist.
With an air of wounded exasperation, Fuentes responded: "Young man, this is a literature class.
"If these species are to survive," he writes, with an air of wounded exasperation, "they will need something more imaginative than an online petition".
"In the book version of The Snowman, there's no Christmas, there's nothing Christmassy in Fungus, and Father Christmas is anti-Christmas," he says with an air of mild exasperation.
Completely fed up with her job and her employer, she always has an air of complete exasperation about her.
It will also be the sense of frustration in the air, maybe even of exasperation, and likely too a whiff of foreboding about the whole situation.
