Abstract
In a recent paper (AIAA‐90‐4031), Pierce and Sparrow have suggested that the prediction of the distortion of sonic booms by atmospheric turbulence can be carried out using modification of the Friedlander series theory that gives waveforms as a power series in time relative to wave onset. The present paper explores basic mathematical problems associated with that theory by analysis of a simplified mathematical model. A step pulse in acoustic pressure propagating in the + x direction enters at time t = 0 the region x > 0 in which sound speed c(x) is a random function of position, where this function is drawn from an ensemble with given statistical properties. The wave at any positive x begins with a weak shock that arrives at a time τ equal to the x integral of 1/c and which, for t < τ can be expanded in a power series t > τ. The statistics of the coefficients in this power series are studied with the assumption that the random process c(x) is homogeneous and Gaussian.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
