Can a metal sheet roof be vibrated at audio frequencies? So I'm renting a cheap place for now due to certain circumstances. Problem is outside noise is excessive because there is no ceiling and the roof is only a metal sheet... Lately I play white noise to get some peace but it's not as effective as I want it to be... So I was wondering if I built my own speaker (come) to attach to the metal roof an play white noise, would the whole roof become some giant speaker emitting white noise in turn blocking outside noise since the roof is the main culprit for noise coming in, the walls are fairly thin.
I know this is a weird physics question but I need my peace to work on my projects, so I'd appreciate any information
 A: Yes, you could make a big surface like your metal roof radiate sound. If it's effective, or how effective, depends on the details such as density, thickness, total area and geometry.
Regarding the cancellation of external noise, I doubt it. Maybe you could add some layers, like a thick curtain, to add disipation for medium or high frequencies. For low frequencies there's not much you can do, maybe a sound trap with a Helmholtz resonator un s corner.
A: If you plan to stay there for long it's probably best to add a ceiling inside the metal sheet.  In-between put a thick layer (20cm or more) of sound absorbing material such as Rockwool.
If you use the right material it'll act as a heat insulator in winter.  Living spaces lose most heat through the ceiling.
A: Ah, white noise to drown out sound disturbance, I've done that too.
(I went as far as going to a place that usually sells hearing aids. They have that goo that is injected in the  ear canal and then solidifies in a minute so you get a mould of the ear canal. I had those moulds used to make thingies in which standard earbuds fit. They sell that product to people who want to use earbuds to listen to music. In my case I used the earbuds to play white noise. I still keep those thingies, in case I ever have to share a cabin with someone who snores.)

You describe trying to contact-transfer white noise vibration to a metal roofsheet. I think that is not worth giving it a try. Very unlikely to be succesfull, I think.
What remains is trying to set up sound absorption. There's actually a lot of information available about affordable ways to achieve sound absorption. (A lot of people want to start a youtube channel, and an echo-y room is unpleasant to hear. So you get people filling that need for information on how to absorb sound.)
There is for instance the guy with the channel DIY perks.
He made a video about sound absorption modules that were designed to be effective and affordable.
[Later edit]
Overlooked an earlier video from DIY perks:
The title claims: high performance sound panels for $5
Ironically, because of the way Matt tested: his design is optimal for absorbing sound, not for scattering sound, as is preferable for recording studios. But it's taylor made for you: you want all the absorption you can get. The 5$ price is very optimistic. Matt uses many layers of (old) towels. If you can get your hands on boatloads of old towels: great. But if you need to buy the towels new the cost is going to add up, I think.
A: It is easy to turn a metal roof into a gigantic loudspeaker or radiating surface, as follows:
There are miniature speaker drivers you can buy which, when placed on a tabletop and driven with an audio signal, will turn the whole tabletop into a loudspeaker. If you attach one of these to a metal roof, the metal roof sheet will indeed become a speaker cone. it will be a fun experiment to see if your roof can be driven with white noise, but a better alternative may be this:
Imagine driving the roof with the recorded sound of rain falling on a metal roof. Now it sounds like it is raining, which (IMHO) is soothing! Try this and report back to us the result!
