The physical principles responsible for the sound we hear from musical instruments have been the subject of study since ancient Greek times. As the physical sciences developed, wave motion was used to explain the behaviour of water and light in addition to the production of audible sound. Frequency analysis techniques were developed illuminating the sensations of pitch and tone. The arrival of accurate microphones and sound reproduction equipment allowed quantitative experimental measurement of the resonance characteristics of musical instruments. With the invention of the computer, numerical methods became available for predicting the properties of musical instruments, to confirm the accuracy of the wave motion theory and to analyse how suggested changes in an instrument would effect the playing properties.
This work concentrates on brass musical wind instruments. The sounds we hear from such instruments result from wave motion caused by rapid compressions and expansions of the air inside the tubing. We begin with a qualitative explanation of the acoustic behaviour of air columns. This discussion will show how a quantity called the input impedance can provide information on the playing frequencies of brass musical instruments. This quantity, along with the internal profile, will be investigated both experimentally and theoretically in the body of work which follows.