Hi,
I recently bought a used 2005 V50. The car runs fine, but after the first 15 km or so off the lot a constant low-pitched ringing noise (like a tone from a keyboard almost) from under the car (I don't think the engine area) appeared. It is now there constantly whenever the engine runs. The sound is low (at 60km/h it cannot be heard over the engine noise) and is not influenced by speed, engine revs, increased fan speed or other factors that I have been able to identify as of yet.
I have not had the AC on.
Any ideas?

Have you ever thought of stopping the car, grabbing a broom stick and beat the catalytic converter? If you hear loose parts here, thats probably the cause, it happens a lot to people doing short runs with the car.

Also follow the exhaust pipe and check the heat shields are not nearly touching the exhaust or body. They are just thin metal plates that can easily be moved out the way by hand and can make the "tinkling" sound you describe