WHY do flutes turn flat in the cold weather?! Help please!

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Oddman answered
Even though the flute shrinks by a very small amount, tending to make it more sharp, the speed of sound in cold air has a larger effect. The speed of sound is lower in cold air, so a given wavelength (defined by the flute's fingering) will correspond to a lower pitch.

Apparently, a flute goes flat by about 14.6 cents between 25 C and 20 C. It is down 75.7 cents at 0 C.

Speed of sound is approximately proportional to the square root of (absolute) temperature.

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