How air change the pitch of wind instruments?

The pitch of a wind instrument is determined by the length of the air column inside the instrument. When you play a note on a wind instrument, you are setting up a standing wave inside the instrument. The length of the standing wave is equal to the distance between the mouthpiece and the first open tone hole.

When you change the temperature of the air inside the instrument, you are changing the speed of sound in the air. This causes the length of the standing wave to change, which in turn changes the pitch of the note that you are playing.

Hot air travels faster than cold air. This means that when you play a wind instrument in warm weather, the pitch of the notes will be higher than when you play in cold weather.