Noise after flushing toilet

Thank you for your suggestions. We will try them and see if anything can help.

One more thing we've noticed after closer observation -- if we flash the tank so it's almost empty, the rumbling noise in the pipes are much less and even sometimes disappear.

Recently we've changed the handle. It broke because it was plastic and we changed to the metal one. Do you think it could cause the problem?

Also, our friend thinks that our vent pipe maybe stuck with something. When we first heard the noise, we had a snow on our roof. After snow has melted, the noise disappeared for some time but re-appeared a week ago or so. Any idea?

Thank you for any thoughts.

You can help tell the difference between the two.

Fill a bucket with a couple of gallons of water and dump it into the bowl.

That will cause the toilet to "flush".

If you hear the sound then it is from the drain/vent system.

To check the fill valve turn the stop valve off. And then flush the toilet. Wait until it finishes.

Then turn the stop valve back on and all the tank to refill. Do you hear the noise them. If so it is in the fill valve. But fill valve usually make more of a squealing sound.

I fixed a big paper clip on the rod and the rumblings disappeared instantly.

Have drained the system and it still persists, there are no loose pipes. Please help!
The pipe that rumbles is located just before the hot water tank.