How will playing a trumpet in warmer weather affect the pitch? Why?
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The sound of a trumpet originates in the column of air inside it. As the trumpeter blows from the mouthpiece to the open end of the trumpet, the air column begins to vibrate in and out of the mouthpiece and open end creating a standing wave. The vibration of the air column produces the sound. Every one of the piston valves when engaged lengthens the air column hence lowering the pitch.
At a higher temperature but same atmospheric pressure air has a lower density, therefore there are lesser air molecules in the same length of air column. For the same amount of energy blowing the trumpet, lesser air molecules vibrate faster or at a higher frequency which increases the pitch making it sounds sharper .