Shinkansen question

Just bought tickets for the Shinkansen departing from Hakone to Osaka. I bought a “non reserved” ticket. I was in a bit of a hurry due to my bus running late, and so very quickly got on the train and into a reserved section. I tried to ask someone where the non reserved section was but didn’t have much time before the train took off and I sat in a reserved seat.

A lot of the seats in these sections are empty rn, but I’m assuming someone is going to walk through each section and check our tickets during the route, right?

Sorry if this is a stupid question, this is my first time riding Shinkansen