Trying to diagnose this acceleration problem.

One question did this appeared after you bought the car or did car already had this behavior?

 

How's the fuel economy?

A weak traction battery forces the hybrid system to use the gas engine more. During acceleration, "more" means higher RPM, which means more noise.

This can happen if the battery is simply a bit low or too cold or too hot. If it's happening regularly, it is possible that the battery is worn out.

 

Maybe it's the video/audio, but it didn't sound that loud. That is what mine sounds like.
It's a little hard to hear over the podcasts though.
If this is your first Prius, it will take time to learn and understand the different noises the car makes.
It was pretty strange for me. I wasn't sure what was normal and what wasn't.

 

Almost 50 MPG is very good for a Gen 3, especially a 2010. All Gen 3's are loud, very little sound insulation. The one thing you haven't mentioned is your tires. Make sure they are pumped up to 42 front/40 rear for best MPG. Also, they should be designed for low rolling resistance (LRR). The sidewall should say "Eco" or "Green" or have a leaf image on them for "green economy" tires. If they are worn (not much tread left), they will be louder.

 

how many miles on her? have you cleaned the egr circuit? changed the oil and filter?

cleaned the throttle body? maf?

have you read any of the egr/oil burning/oil catch can/blown head gasket threads?

 

Any clear reason to believe there is anything amiss?

 

only if the acceleration noise is much worse than normal