Abstract
When modeling a brass instrument such as the trumpet, an estimate of the pressure at the player's lips is essential, since the resulting force drives the oscillations of the lips which are needed to produce a musical tone. In most work to date, the calculation of the force on the lips has relied on values of the pressure derived from the Bernoulli equation, even though that relation assumes steady flow in contrast to the pulsating flow caused by vibrations of the lips. This paper uses a quantitative application of the Navier-Stokes equations to calculate the flow through a model of vibrating lips attached to a toy model of the trumpet. The results are used to explore when the Bernoulli equation can and cannot be used. The Bernoulli equation is found to fail badly during significant portions of each oscillation cycle of the lips. The reasons for this breakdown are elucidated.
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