Final answer:
When you take a saxophone from a warm environment to a cold environment, the pitch of the saxophone will likely decrease due to the decrease in the speed of sound in air with decreasing temperature.
Step-by-step explanation:
Wind instruments like trumpets and saxophones work on the same principle as a tube closed on one end. When you take a saxophone from inside your house (at 76 degrees F) to the outside on a cold day when the outside temperature is 45 degrees F, the pitch of the saxophone will likely decrease.
This is because the speed of sound in air decreases with decreasing temperature. As a result, when the saxophone is taken to the colder outside temperature, the speed of sound in the air inside the instrument decreases. This causes the wavelength of the sound produced by the instrument to increase, resulting in a lower pitch.
It's similar to when you blow a balloon and the sound becomes higher pitch when you release some of the air. The pitch depends on the speed of sound when it leaves the instrument and enters the room or environment, in addition to the length (and valves, finger holes and tubes) of the instrument.