This is an excerpt of the full split-phase household power supply webinar held on June 6, 2016. In this excerpt, I explain why antiphase sine waves (meaning 180 degrees out of phase with each other) cancel each other out in a sound mixer but not in a center tapped transformer. Just because an AC voltage can be represented or modeled as a sine wave does not mean all sine waves behave the same way everywhere regardless of the device-- you have to know what you're measuring!

References:

Summing Amplifier Basics

How Sine Waves are Used to Model things in the Real World

Using an Oscilloscope to Understand 120 VAC Household Power Supplies