Symbolism, Imagery, Allegory
Silent Nights, Unholy Nights
Creepy, unnatural silence is a sign of Peter Quint's presence in both his first appearance and when he shows up inside the house on the staircase.
In the first of these scenes, the Governess, who's strolling happily outside, notices that everything goes quiet when the mysterious figure appears, even the peaceful sounds of birdsong:
It was as if, while I took in – what I did take in – all the rest of the scene had been stricken with death. I can hear again, as I write, the intense hush in which the sounds of evening dropped. The rooks stopped cawing in the golden sky, and the friendly hour lost, for the minute, all its voice. But there was no other change in nature, unless indeed it were a change that I saw with a stranger sharpness. [...] (3.11)
This is a signal that something abnormal and unnatural is happening—even though she doesn't yet know that he's a ghost yet, she can already tell that he's not meant to be there.
Inside the house, the silence is even more marked; though this close encounter seems more "human and hideous" (9.6), the lack of conversation between the Governess and her nemesis is what really makes it freaky.
Finally, when the Governess actually tries to speak to one of the ghosts (Miss Jessel in the schoolroom, 15.5), the ghost doesn't—or can't—answer.
What to make of these terrible silences? From a symbolic perspective, they so unnerving because they hint at a lack of unresolvability: without speech and communication, there's no way of the Governess—or us—ever knowing why the ghosts are there in the first place, or what their aims might be.