When I was closing a chest, I opened my inventory immediately after, while my crosshairs were still over the chest, and before the chest closing animation had finished. When I closed my inventory, the sound the chest makes when it closes played. I tested this with both single and double chests, and both work. Additionally, trapped chests also do this.

Steps to Reproduce:
1. Open a chest.
2. Close the chest by pressing 'E'.
3. Quickly tap 'E' again to open your inventory before the chest's closing animation can complete.
4. Close your inventory by pressing 'E'. You should hear the sound of a chest closing.