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Acoustic Propagation
Acoustic PropagationConsider a longitudinal sound wave traveling along a direction in a fluid, the acoustic disturbance propagation causes medium particle displacement in form of oscillation, and the medium particles return to its former state after the disturbance has passed. The fluid in most common engineering acoustic system can be assumed as an idea gas, and obey the perfect gas law. That is or or or or where
P is pressure In equilibrium state, the perfect gas equation is still valid under the sound propagation process. To simplify the problem, the fluid medium is assumed to be homogeneous and isotropic that properties of the medium are same everywhere. The medium is also assumed to be perfect elastic for the sound wave propagation with no energy loss. The fluid is also assumed as an inviscid fluid with no drag force. As the fluid medium is in equilibrium, the gravitational effects on sound propagation can also be neglected. Since the acoustic oscillations are very small, the temperature gradients due to the oscillation is very small also. Nearly no heat can be transferred to other medium particle during the sound propagation process. Therefore the wave propagation process can be assumed to be adiabatic and reversible, an isentropic process. For adiabatic process, the relation of pressure and density is: or where
P is pressure The relationship of pressure and density due to sound wave is nonlinear, but this nonlinearity effect is usually negligible when comparing with the sound perception of ear. When the fluctuations of medium particle are small, e.g. less than 100dB, the acoustic properties can be assumed linear. Acoustic FluctuationAt initial equilibrium ambient state, the medium is assumed to be homogeneous and quiescent. The physical properties are independent of position and time. The initial medium velocity also equals to zero ( ) and the physical properties are defined as: At the acoustic static, assuming there is no mass entering or leaving the system for the sound propagation, the acoustic disturbance will alter the physical properties of medium and can be defined as: where
is the acoustic pressure variations The acoustic fluctuation is a function of traveling distance and time. The fluid returns to its former equilibrium state after the disturbance has passed. Besides, the representation of corresponding volume or specific volume of medium are: where
V_{o} is the initial volume of medium ©sideway ID: 100900017 Last Updated: 9/14/2010 Revision: 1 Ref: References
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