General:
* Quiet
* Stillness
* Hush
* Soundlessness
* Mutism
* Tranquility
* Peace
* Serenity
* Calm
More specific:
* For a person: Quietude, reticence, taciturnity
* For a place: Solitude, remoteness, isolation
* For an absence of sound: Soundlessness, dead air
* For a deliberate act: Secrecy, suppression, suppression of sound
The best synonym to use depends on the specific meaning you want to convey. For example, "tranquility" suggests a peaceful and serene silence, while "suppression" implies that the silence is intentional.