I'm still not clear about what you're hearing. Roku does have a sound that plays when it boots up, and you get the "bouncing ROKU" logo on the screen. Is that the "startup tone" you're talking about?
And as for a "shutdown tone," Roku doesn't automatically shut down. If you have Bandwidth Saver enabled, and you don't interact with the remote for four hours, the app will stop playing and device will return to the Home screen, but that's it. The Roku won't shut down. There's no shutdown routine, manual or otherwise, for Roku.
When you reboot the Roku via the menu, there's no special tone. The only sound is the same tone you get when you press OK to launch an app. There is no "shutdown tone." That's why I'm not sure what it is you're hearing.
DBDukes Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution." Note: I am not a Roku employee.