Improperly secured pipes behind walls may be the cause of the plumbing noises you’ve described. Since water supply pipes are made of metal, they transmit sound waves. As water flows through the system, it flows over obstructions and around turns, creating eddies in the water. These can be rhythmic depending on the speed of the water. When they reach a certain pitch, they cause the piping to begin vibrating in harmonic reaction to the wave created inside the pipe. In order to quiet your noisy water pipes, you’ll have to remove the offending part or debris that's causing the water to fluctuate. If the pipes are accessible, you can strap them with plastic clamps so they can't bang against the structure. If your piping is metal and runs through the joists or studs, then the problem may be expansion and contraction. As soon as either hot or cold water runs through pipes, they expand or contract, causing vibration and noise.
Another problem is water hammer. This happens when you have high water pressure. Water moving in one direction does not want to stop flowing. When you shut off a faucet, the water still has some force, which has to be absorbed, causing the pipe will flex. If the pipe is near wood, it will bang against the wood. You can stop this plumbing noise problem by installing water hammer arrestors on the offending water lines.