The noise you are hearing is the modem sending computer data over the telephone line to establish a connection with another computer at the dialed destination. The noise from the modem's speaker normally stops after the connection is successfully negotiated.
Depending on the software you are using, the speaker volume in your modem can be lowered or completely shut off. For example, America Online and Netzero have user-applied settings that can set the volume before you begin dialling.
Some modems, like the 3Com / USR Sportster series have a physical speaker volume knob that you can rotate to adjust the speaker volume.
In addition, there are control strings that the above applications apply to you modem. If your particular internet service doesn't provide these settings, you can manually set them yourself through a terminal interface connecting to the modem.
Tom Glenchur
December 2004