Air in the lines gives off a vibrating or prolonged noise, accompanied by water coming out of the faucet in spurts. To rid air from your lines to your kitchen sink, allow water to flow to push out the air pockets. If you've been working on your sink, you may only need to open the tap all the way to push out the air. However, if the noise comes after you've worked on plumbing in other areas of the house, you'll need to flush all the lines. To do this, open all your taps, flush your toilets and run anything attached to a water supply line until you no longer hear the air noise.
If you hear a series of bangs or a single thump when you shut off a valve or when a washer switches cycles, the problem is water hammer. Water hammer refers to the noise produced when water bangs against itself as the water changes speed as it travels along the pipe. You'll often hear the noise when you shut off a valve, the dishwasher or washing machine cycle changes or if you shut off a tap quickly. Because water hammer can damage your pipes, this problem should be looked at by a plumber.
If the water flows well, but produces a continuous tapping sound, your water meter may be too small. Check with your water provider for options to replace your water meter. Rapid noises that sound like drums can stem from a broken valve. Broken valves are a serious issue that need to be addressed by a professional plumber.
A clunking noise that lasts for only a minute when you turn on the water is usually caused by water flowing into pipes of different temperatures. Insulating your pipes, especially those near an outside wall, can help reduce this problem. If your pipes aren't securely attached, they can squeak or thump against a wall. Solve the problem by installing pipe-holding brackets available at most hardware stores.