Why does Emilia rush to Othello's quarters?

In act 5, scene 1, Iago's plan leads to both Roderigo and Cassio being stabbed in a scuffle. Roderigo is dead at Iago's hands; Cassio is merely wounded. At the end of the scene, Iago tells Emilia, "run you to the citadel / And tell my lord and lady what hath happen'd."
The following scene, then, finds Othello and Desdemona in their bedchamber, with Othello preparing to murder his wife. Emilia's voice is heard from outside the bedchamber: "O good my lord, I would speak a word with you!" Othello, having known beforehand of Iago's plan, thinks she is coming to tell him that Cassio has been killed.
When Othello lets Emilia into the outer chamber, she explains to him that Roderigo, not Cassio, has been killed. This gives her an opportunity to hear Desdemona, already smothered, crying faintly from within—"that was my lady's voice"—at which point Emilia recognizes that Othello must have attacked his wife and begins to probe as to why Othello did it and who gave him the information that Desdemona was "false as water."