General Physics of the Trumpet

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To understand the physics of trumpets, we need to understand the physics of sound. At its basic level, all sounds are waves which require an initial source of vibration. For the trumpet, the vibrations occur from the players lips vibrating at a high speed. As anyone who has ever played a brass instrument will tell you, merely blowing into the instrument does nothing. The sound occurs by buzzing into the mouthpiece. As Glazner, Timpani, and Reed, from the Trumpeter’s Fanfare said, The mouthpiece simply gives the lips a place to vibrate, and harnesses the vibrations.”  Once the wave is produced, it travels down the length of the tube until it reaches the bell. The flared bell of the trumpet harnesses the wave produced by buzzing, and serves as a node of the wave.
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The flaring at the end leads to a sudden drop in resistance, which causes the wave to travel back to the lips changing their shape so that they match the pitch of the trumpet. A standing wave is formed, and because of the way the trumpet is shaped, some energy in the form of sound is released. This excess energy is the sound we hear the trumpet producing.
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Notes sound different from one another because they represent different frequencies and therefore a different numbers of nodes. Higher notes have higher frequencies and lower notes have lower frequencies. For higher notes, the node at the end of the instrument moves further into the bell. Because of this, more energy is released. This makes the higher notes sound louder and are consequentially harder to play. In addition to pressing the valves, you have to adjust your tongue and embouchure on the mouthpiece to create these different notes.