A whining sound coming from a faucet is usually caused by a loose washer.
If there is not a loose washer, the problem is caused by air and the air needs to be pushed out of the pipes.
Turn on the water faucet. While it’s on, turn off the main water valve. When the main water valve is turned back on, any air in the pipe will have been flushed out.
If the whining continues the problem might lie with the valves under the sink.
To check this, turn the main water off and take the valves apart, check for any problem and then reassemble.
If these steps don’t solve the problem, a professional plumber should be called.