I believe that part was doing a sound quality test to ensure the data rate could be reached. If the line quality was bad it would connect at a slower rate since it was based on frequency.
It's a specific 56K protocol. There were a few different types of 56K modems and they did the last part of the handshake differently. One did the "boing boing" and another common one had more of an ascending tone at the end of the handshake.