Vibration in tube leading to sinks when water is turned on

Help -- I have a 15 year old home. A new problem has just arisen. When I turn on the sink (sometimes cold water only), a loud low-pitched noise can be heard. If I touch the metal tube under the sink that carries water between the local shut off valve and the faucet, I can feel that tube vibrating strongly (which I think creates the noise). The noise and vibration stop immediately when I turn the water off.

If I remove the aerator from the faucet and let the water come out as quickly as possible (turning the faucet all the way on), there is no noise or vibration. If, having removed the aerator, I reduce the water flow by not turning the water all the way on (so that it approximates the water flow I get with the aerator), the vibration occurs again. Replacing the aerator with an aerator from a different sink gives me the same results (vibration and noise).

One other symptom. When I turn the water on, on that sink, the flow is initially very strong, and there is no noise, but the flow reduces to about half of what it was within 2-3 seconds, after which the noise is heard.

Can anyone explain what is happening and how this can be fixed?

Thank you.

This vibration is caused by the pressure change as the water goes from the 1/2" copper pipe, thru the undersink shutoff valve, and into the 3/8" supply line that carries the water to the faucet. The cutoff valves are 15 years old and are likely getting coroded on the inside. The first thing that I would do is replace the "metal tubes" with flexible braided supply lines. If that doesn't fix the problem you may also want to change the undersink shutoff valves. The pressure decrease is caused by pressure buildup in the waterlines that balances after 2-3 seconds. If you are going to mess with this at all I would change out the supply lines and undersink valves in one shot and be done with this problem.