Swamped

You set up the metronome so that, over time, it will make the disruptive noise you found before. Your captor doesn't seem to know enough about sounds to notice this until it starts happening.

It's likely he'll be able to work out that the metronome timer is the cause, so you set it up to make it hard to remove without affecting functionality. Since he doesn't know acoustics like you do, this should be enough to force him to negotiate with you if he wants to fix the problem.

Once you're done, you send it off with a note that it should be working now.

And then it's not long before the fateful cup of tea comes in.

You know exactly what the point of this tea is, and you can't afford to drink it. But if your host realizes you haven't, he'll probably take more drastic measures.

So how can you get rid of it without alerting him?