fuzzyduff

I am an artist, and have begun working on a project based primarily in the origins of the metric system, however my research has led me into theories about potential standardised basic units of measurement suggested in the past. One of these was by Gabriel Mouton in 1670, suggesting that the world should adopt a uniform system of measurement based on the length of one minute of the earth's arc. Despite my high school level grasp of mathematics and physics I've managed to figure out how fast I am spinning here in Banff, Canada (1050.21 km/h) based on how quickly the earth rotates at a fixed point on the Equator (1675 km/h) however I thought it would also be interesting to see also how fast we are moving in comparison to the speed of sound (which is another interest of mine). My question is this: If we are moving at 1.35 x speed of sound at the equator (0 degrees latitude) and 0.85 x speed of sound in Banff ( approx 51 degrees latitude) at what latitude do we on the globe rotate at the same speed as sound?