Troubleshooting your connection...
Run a cord from your modem to a standard wall jack. Make sure the jack is not a radio jack or a power-outlet jack as non-standard jacks will definitely cause problems. If there is a phone plugged into the modem, unplug it. If there is a line splitter or coupler on the phone cord, remove it and go straight from the jack to the modem, ideally with a cord less then 10 feet long.
If you have another line in the house, give it a try and see if there is a difference. Keep in mind that a dedicated line for your modem does not guarantee it is problem free, so if you have another line typically used for voice calls, give it a try as a test.
Phone line trouble can occur from too many devices, or from a noisy device on a line. Unplug any fax machines, cordless base stations, speaker phones, answering machines, caller id, novelty phones or old phones from their wall jacks. Even if they are turned off, they are part of the telephone circuit. They might not cause a problem that you can hear, but your modem might be affected. If you have another wall jack you can plug into, you might want to give that a try as well. If your problem vanishes after unplugging these devices, plug them back in one at a time to identify the culprit.
Some Phone Companies, when they check out a line and declare it to be sound, mean it is okay for voice calls. It does not mean the quality is good enough for a high speed modem. Ask them to check for noise on the line that could affect a data connection.
Check to make sure your modem has the latest drivers (software) from the manufacturer. Even if you've just bought the modem, it's still a good idea to check. There's no telling how long it's been on a shelf and updates are released all the time. It is very important to have the latest revisions available.
A new initialization string
Sometimes, changing the way your modem is initialized can affect its performance. Contact your modem manufacturer for initialization string suggestions for your particular modem.