Wasnt Muddy Waters, Howlin Wolf, Jimmy Reed the second "wave" of Chicago blues musicians?

Yes Spence, they were at least the second wave-more likely the third. The "Great Migration" of blacks into the north beginning before World War I, increased dramatically after the war. That was most likely the first wave. What is known as the "Bluebird Blues", "Bluebird Sound", or "Bluebird Period" is what many mean when they refer to the "first wave" of Chicago Blues. It refers to Bluebird records, a subsidiary of RCA that was the main label recording blues in Chicago during the 30's and 40's. Their "race music" talent scout/producer in Chicago was Lester Melrose, who signed and recorded "first wave"people like Big Bill, but also those who's style predates that, like Tampa Red.

Yes, Muddy did come later but he is credited with creating what we refer to today as electric Chicago Blues. Muddy pretty much invented the rock & roll band putting a guitars, bass drums and piano together in a small combo. That's why we refer to Muddy as the King of Electric Blues.

Big Bill Broonzy wasn't playing the electric guitar. He was known more for his folk style.

The problem with your question is that these people arrived to Chicago at different times.

Unless you properly define what "wave" means, I must assume that each individual was their own wave. Muddy wasn't walking hand-in-hand with Reed and The Wolf when they strolled into Chicago.