Normal water hammer is a one time thunk or boom related to a fast closing valve such as the dishwasher, washer, and toilet. It can be fixed with replacement of the toilet ballcock, a hammer arrestor added to the pipes next to the valve, or an old fashioned air chamber (not recommended) which get water logged over time and don't work.
You probably have a loose faucet washer somewhere that blocks part of the flow and moves back and forth in the flow creating the constant hammering sound or a valve was operated and was left half open or the washer got stuck half open when it was opened back up or stuck cause the stem broke. Look for a valve that you haven't used much such as the main valve that was closed and reopened for a recent repair or a stop valve under a sink. With hot water, a bad washer can expand and maybe do the same thing and occasionally newer nipples in the hot water that have the little ball to stop rising heat can stick and cause problems. A likely culprit could be a toilet ballcock valve even though they are unrelated to where it happens. You have to replace those. Fluidmaster is best recommended brand depending upon your brand of toilet. It could also be a prv valve or the meter valve. Any of those is where I would start first.
Because the noise resonates throughout the house, it is hard to trouble shoot the bad valve. Start where you hear it or with the faucet you turn on first but it could be another valve somewhere else that the particular faucet you turn on starts the flow of water through. Its a process of taking apart valves, checking, and replacing bad washers, stems, seats, and cartridges, etc. Have fun crawling in and out of your crawlspace and chasing after valve parts if you can't hire it done. Sometimes it could be a loose screw holding the washer though. If you take a faucet apart, use some "silicone" faucet grease (not regular faucet grease) to help them work better in the future. Sounds like a good time to R & R the stems and seats buy yourself years of future peace and quiet and no drips.
Post back with what you find out. You will have to pic through your budget and save for this if you don't like the noise. I posted this just a few days ago to another question but expanded a little further with this one.