56K modems do NOT operate at 56K bits per second. The name "56K" is more marketing than technical reality. Most 56K modems conform to the ITU V.90 standard. This standard defines an asymmetrical transmission system that provides for faster downloads (from server to client) than uploads (from your home client to the server). This is convenient since most users typically send a short web page name to the server and receive a whole screen of data from the server. The transmission speed in both directions is limited by the signal quality of the line. The Shannon formula determines the maximum rate of data transmission based on the signal to noise ratio on the phone line. If you live near your telephone central office and have a good clear line, you can upload data at a maximum rate of 31.2 Kbits per second. The maximum download speed is also limited by the quality of the phone line. If you had an ideal phone line with no noise, you would be able to download at 53Kbits per second.
To send data at greater than 31.2 Kbits per second, the server has to have a digital connection to the phone company. By eliminating the analog to digital conversion on the serverís side, the server can send a digital bit stream to the phone company at up to 56K bits per second. When this digital data arrives at your local telephone exchange, it is converted to analog using the normal codec (coder - decoder) that is used to convert digital voice to analog signals for your phone. The data is sent at the maximum speed your phone line can handle. When you first make a modem connection, the first 12 seconds or so are used to measure the signal to noise ratio on the line and negotiate transmission parameters. Because there is usually a minimum background noise, the signal to noise ratio can be improved by increasing the strength of the signal. This is somewhat analogous to shouting above the noise. The Federal Communications Commission (FCC) limits the maximum signal strength to avoid crosstalk where a strong signal on one wire is picked up by physically adjacent wires. This limits the maximum speed to 53K bits per second.
In practice, you are doing well if you can achieve over 45 Kbits per second with your 56K modem. Your instructor once bought a cheap 56K modem that was very optimistic. It would frequently connect at 52 Kbits per second. This would be nice except that it generated so many transmission errors that almost nothing could get through. My telephone line is not of sufficient quality to support 52 Kbits per second. I replaced the cheap modem with another 56K modem that usually connects at 31.2 Kbits per second, but generates very few transmission errors.