harry potter - How did Dumbledore detect the "traces of magic" in the Cave?

Albus Dumbledore was able to do things many other wizards/witches could not. He was after all a brilliant Wizard. The best ever? That's up to the individual to decide. He most certainly (in my opinion) was the most clever - he may even have thought so himself ;).

My question is, How did he detect the "traces of magic" in the Horcrux cave?

References to what I'm asking:

“Yes, this is the place,” said Dumbledore.

“How can you tell?” Harry spoke in a whisper.

“It has known magic,” said Dumbledore simply.

-Harry Potter and the Half-Blood Prince - CH. 26 (The Cave)

Then later on...

Dumbledore approached the wall of the cave and caressed it with his blackened fingertips, murmuring words in a strange tongue that Harry did not understand. Twice Dumbledore walked right around the cave, touching as much of the rough rock as he could, occasionally pausing, running his fingers backward and forward over a particular spot, until finally he stopped, his hand pressed flat against the wall.

“Here,” he said. “We go on through here. The entrance is concealed.”

Harry did not ask how Dumbledore knew. He had never seen a wizard work things out like this, simply by looking and touching; but Harry had long since learned that bangs and smoke were more often the marks of ineptitude than expertise.

-Harry Potter and the Half-Blood Prince - CH. 26 (The Cave)

And mostly importantly...

“How did you know that was there?” Harry asked in astonishment.

“Magic always leaves traces,” said Dumbledore, as the boat hit the bank with a gentle bump, “sometimes very distinctive traces. I taught Tom Riddle. I know his style.”

-Harry Potter and the Half-Blood Prince - CH. 26 (The Cave)

I'm assuming he performed some sort of incantation similar to Homenum Revelio but is there proof of what he did to detect these "traces of magic"?

Did his [Elder] Wand (being as powerful as it is) enable him in any way?

EDIT: I should have clarified that I meant did his Elder Wand help?

Answer

Dumbledore "murmured words in a strange tongue." Undoubtedly he was attempting to detect traces of magic -- what else would he be doing? The text clearly does not reveal what Dumbledore says. I personally haven't read, that I can recall, any interview with J.K. Rowling where she reveals what Dumbledore says or what language he is speaking at that moment. Please, anyone, correct me if I am wrong.

Dumbledore speaks English, Parseltongue (or at the very least he understands Parseltongue), Gobbletygook (Goblin), and Mermish. Harry would have known if it were either English or Parseltongue and canon doesn't indicate anywhere that Voldemort spoke anything other than English and Parseltongue. It doesn't seem possible, then, that Voldemort would have protected the cave with Gobbledygook or Mermish. It would seem that the logical conclusion would be that Dumbledore was incanting some sort of revealing spell that Harry simply didn't know.

You quoted:

‘Yes, this is the place,’ said Dumbledore.

‘How can you tell?’ Harry spoke in a whisper.

‘It has known magic,’ said Dumbledore simply.

The very next sentence demonstrates that magic can be sensed and felt. I would imagine this is how Dumbledore knew that that particular spot had known magic.

Harry could not tell whether the shivers he was experiencing were due to his spine-deep coldness or to the same awareness of enchantments.

_{Half-Blood Prince - page 521 - Bloomsbury - chapter twenty-six, The Cave}

Regarding Dumbledore's wand, yes it enabled him:

Dumbledore stepped back from the cave wall and pointed his wand at the rock. For a moment, an arched outline appeared there, blazing white as though there was a powerful light behind the crack.

_{Half-Blood Prince - page 522 - Bloomsbury - chapter twenty-six, The Cave}

He also used his wand to dry Harry's clothes following their swim from the rock to the cave.