Ring Pro Doorbell - It Dings & Eventually Dongs

Okay, my subject line is the only way I can describe it :) Just installed a new doorbell chime and the Ring Pro Doorbell. I press the Ring Doorbell, and inside the home, the new doorbell will "Ding" - I hear a very slight buzz sound from the doorbell chime, and then about 10 seconds late it goes "Dong" Did not replace the existing (but old - very old) transformer. Looking for suggestions to have a normal sounding chime :) Thanks in advance