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Bell


    The bell is a very important part of the trumpet. The size of the bell, how sharply it is flared, and the diameter and taper of the bell throat influence tone, intonation, and response.  Scientifically, the bell brings the frequencies closer together in order to play a constant pitch. The bell raises the frequencies of the standing waves and the frequencies of the low pitched resonances. The longer waves, deeper notes, are not able to follow the entire flare of the bell thus reflect earlier than shorter waves.  By shortening the length of the instrument for the long waves, their frequency is increase while the shorter waves are left unaltered but can still travel the length of the bell.  


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https://www.flickr.com/photos/spow/3169940604/
http://www.amromusic.com/step-up-trumpets

If the sound waves are short enough they are almost entirely radiated out of the bell,.
This makes it easier to play higher notes louder than lower ones.