Flushing the toilet in the basement making a loud noise,if I turn on the faucet when I ;m flushing the toilet no noise any suggestion?Thanks.

You either have a loose washer in the toilet stop valve that is vibrating or a defective seal in the tank fill valve (or ball cock). Opening the faucet changes the water pressure slightly and the defective part does not vibrate.
Suggest replacing the seal in the tank fill valve. If you still get the noise, replace the stop valve under the toilet.