Urbaniak started his music education during high school in Łódź, Poland. When he was in Warsaw he took violin classes from Tadeusz Wroński. He first performed with a Dixieland band and later with Zbigniew Namysłowski. Later he was invited to play with Andrzej Trzaskowski and toured the United States in 1962 with the Andrzej Trzaskowski band. He has played in various festivals and clubs in Newport, San Francisco, Chicago, Washington, D.C., and New York City, and more.