O Brother, Where Art Thou?

Three convicts, Ulysses Everett McGill (George Clooney), Pete Hogwallop (John Turturro) and Delmar O'Donnel (Tim Blake Nelson) escape from a chain gang and set out to retrieve a supposed treasure Everett buried. The three get a lift from a blind man driving a handcar on a railway. He tells them, among other prophecies, that they will find a fortune but not the one they seek. The trio make their way to the house of Wash, Pete's cousin. They sleep in the barn, but Wash reports them to Sheriff Cooley, who, along with his men, torches the barn. Wash's son helps them escape.
They pick up Tommy Johnson, a young black man. Tommy claims he sold his soul to the devil in exchange for the ability to play guitar. In need of money, the four stop at a radio broadcast tower where they record a song as The Soggy Bottom Boys.[a] That night, the trio part ways with Tommy after their car is discovered by the police. Unbeknownst to them, the recording becomes a major hit.
Near a river, the group hears singing. They see three women washing clothes and singing. The women drug them with corn whiskey and they lose consciousness. Upon waking, Delmar finds Pete's clothes lying next to him, empty except for a toad. Delmar is convinced the women were Sirens and transformed Pete into the toad. Later, one-eyed Bible salesman Big Dan invites them for a picnic lunch, then mugs them and kills the toad.
Everett and Delmar arrive in Everett's home town. Everett confronts his wife Penny, who changed her last name and told his daughters he was dead. He gets into a fight with Vernon T. Waldrip, her new "suitor." They later see Pete working on a chain gang. Later that night, they sneak into Pete's holding cell and free him. As it turns out, the women had dragged Pete away and turned him in to the authorities. Under torture, Pete gave away the treasure's location to the police. Everett then confesses that there is no treasure. He made it up to convince the guys he was chained with to escape with him. Pete is enraged at Everett, because he had two weeks left on his original sentence, and must serve fifty more years for the escape.
The trio stumble upon a Ku Klux Klan rally, who are planning to hang Tommy. The trio disguises themselves as Klansmen and attempt to rescue Tommy. However, Big Dan, a Klan member, reveals their identities. Chaos ensues, and the Grand Wizard reveals himself as Homer Stokes, a candidate in the upcoming gubernatorial election. The trio rush Tommy away and cut the supports of a large burning cross. The cross falls on Big Dan, killing him.
Everett convinces Pete, Delmar and Tommy to help him win his wife back. They sneak into a Stokes campaign gala dinner she is attending, disguised as musicians. The group begins a performance of their radio hit. The crowd recognizes the song and goes wild. Homer recognizes them as the group who humiliated his mob. When he demands the group be arrested and reveals his white supremacist views, the crowd drives him out on a rail. Pappy O'Daniel, the incumbent candidate, seizes the opportunity, endorses the Soggy Bottom Boys and grants them full pardons. Penny agrees to marry Everett with the condition that he find her original ring.
The next morning, the group sets out to retrieve the ring, which is at a cabin in the valley, where Everett earlier claimed was the location of his treasure. The police, having learned of the place from Pete, arrest the group. Dismissing their claims of receiving pardons, Sheriff Cooley orders them hanged. Just as Everett prays to God, the valley is flooded and they are saved. Tommy finds the ring in a desk that floats by, and they return to town. However, when Everett presents the ring to Penny, it turns out it wasn't her ring, and she doesn't even remember where she put it. The movie ends with the two bickering and the blind man driving the handcar is seen again.

Question: Which song do the four record at the radio broadcast tower?
Answer: The Soggy Bottom Boys