Deep in the somber second act of Tchaikovsky’s opera “The Queen of Spades,” an old countess suddenly turns curmudgeonly critic. The culture, she complains, isn’t what it was when she was young, in the glory days of 18th-century Russia.

“They don’t know how to dance or sing,” she sniffs at the new generation. “Who dances or sings today?”

Well, there’s at least one easy answer to that question: the soprano Lise Davidsen, who made a radiant debut at the Metropolitan Opera in “The Queen of Spades” on Friday evening . Singing with confidence, power and purpose, with both freshness and maturity, Ms. Davidsen, just 32, staked a precocious claim to the great Wagner and Strauss roles that require equal parts youthful flexibility and sheer strength.