The problem could be a loose pipe that is vibrating when water flows through it, and thus the pipes make noise inside your walls. You can try to find the noisy water pipes by inspecting your plumbing in open areas of the home to see if there is significant movement of those pipes when someone turns on the faucets. If so, you could secure them to the wood framing with pipe clips or clamps, which should keep them from moving and banging against the structure.
Another problem resulting in noise in water pipes could be water hammer. Water hammer is triggered by fast-closing valves like toilet fill valves and faucets. As water flows through pipes and the valve shuts off quickly, it causes the water to stop abruptly in the pipes. If the pipe is near wood, it will bang against the wood. Adding a water hammer arrestor to the banging pipes could fix the problem, but that can involve cutting and soldering pipes This is a more complex repair, however, and often requires the expertise of a plumber.
It is also possible that your water pressure is too high. This can not only cause pipes to vibrate, but may also lead to long-term damage to your pipes and even your appliances. There are water pressure test gauges you can get to test the pressure yourself, or you can hire a professional plumber like Roto-Rooter to test the pressure for you and, if necessary, fix the problem.