The frequency of the lowest note played on a flute at room temperature (20^oC) is 262 Hz. What would be the frequency of the same note when the flute is played outside in the winter and the air temperature in the flute is 0^oC?

Speed of sound at T = 20°C = 293 K: 

v = 20.1 x √293 = 344 m/s

Speed of sound at T = 0°C = 273 K: 

v = 20.1 x √273 = 332 m/s

The speed of sound is lower by a factor of (332 / 344) = 0.965. The frequency is reduced to:

f = 262 Hz ⋅ 0.965
f = 253 Hz