How did Frodo get a second sword?

[Alatáriël Lossëhelin]

I imagine that at some point when Sting had become Sam's, Sam gave his Barrow sword to Merry. But his is nowhere stated.

Sam left his Barrow sword with Frodo's body when he thinks Frodo is dead. It was Sam's sword that the Mouth of Sauron brought to the Black Gate, along with Frodo's cloak & mithril vest. Merry had his own Barrow sword that he used to stab the Witch King. Frodo lost his Barrow sword at the Ford of Bruinen.

Then the leader, who was now half across the Ford, stood up menacing in his stirrups, and raised up his hand. Frodo was stricken dumb. He felt his tongue cleave to his mouth, and his heart labouring. His sword broke and fell out of his shaking hand.