Gwyneth Paltrow will join performers including Vampire Weekend, Ellie Goulding, Chromeo and the Naked and Famous at the Music to Know Festival presented by Bing in East Hampton on Aug. 13 and 14. Sources said she’ll perform a short acoustic set in the event’s VIP room on Aug. 13. Paltrow kicked off her singing career playing an alcoholic country crooner in the movie “Country Strong” and with appearances on Fox’s hit “Glee.” Reps for the festival and Bing had no comment. Paltrow’s rep said, “She’s been invited but nothing is confirmed yet.”