THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

18.10 Wind Instruments 537Figure 18.23. Two types of vibrating reed generator.wherem r = mass of reedQ r = quality factor of reed resonancex = position of valve relative to its seatx 0 = equilibrium position of valveω r = angular frequency of reedp b = blow pressurep = acoustic pressureγ gr = geometric factor for the exposed reed facesγ be = Bernoulli force factor based on internal flowin the narrow part of valve gapU = flow velocity.In the air-reed instruments, a steady stream of air does the activation by flippingin and out of the pipe or cavity at the resonant frequency of the system, as shownin Figure 18.24. This steady stream of air thus becomes an alternating flow, andbecause of the nonlinear nature of the exciting force, a number of the resonantelements in the system are excited, thus yielding a series of overtones that add tothe fundamental tone. The whistle and flue organ pipe, each consists of a cavity,a closed or open pipe coupled to an air reed that is activated by a steady airstream. The air stream entering the pipe vacillates between moving to the insideof the pipe and moving to outside of the pipe. Upon entering the pipe, the airstream compresses the air in front of it, as depicted in Figure 18.24 at θ = 0 ◦ . Thepressure inside the pipe builds up to the equilibrium point, and no more air will