Question: How do I turn off the stupid noise my modem makes when it is trying to connect to the internet?
Answer: The only way to stop the modem making that noise is to not use the modem since that noise is its communicating down the phone line to establish a connection. Once the connection is established the modem will automatically disconnect the speaker so that the rest of the communication can be done in silence. If you were to turn off the speaker before the connection is established then you will have no way of telling if the modem is working or not or if someone answers the phone at the other end and wants to abuse you for calling the wrong number.
This article written by Stephen Chapman, Felgall Pty Ltd.