Riding Lawn Mower running very loud
Things that might be the issue here:

1) Muffler is rusted out and no muffling as it should.
2) The gasket between the engine and the muffler is missing or compromised.
3) There are other loose bolts, perhaps the head bolts or the spark plug.  Either of which can allow compression to leak out and be quite loud.

I suspect you'll have some success with your replacement muffler.