Some Stochastic Considerations in Theoretical Formulation of Acoustic Intensity Method Using Two Microphones

The theoretical formulation of the cross-spectral density formula based on finite difference approximations is examined in light of certain stochastic considerations. General expressions for mean square errors involved in estimating acoustic pressure and particle velocity for determining acoustic intensity are derived. It is shown that estimation of particle velocity using finite difference approximation is, in particular, not satisfactory even for very small microphone spacings. The results presented in this paper indicate the necessity of evolving more rigorous and stochastically sound estimation procedures for determining acoustic pressure and particle velocity.