Refraction and shielding of sound from a source in a jet

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Abstract
In typical jet-noise measurements one is almost always interested in the pressure in the far field as kR → ∞. The purpose of this paper is to show that this limit is singular in the sense of matched asymptotic expansions. The inner solution (kfixed, R→ ∞) is given by geometric acoustics, whereas the outer is given by the so-called acoustic-shielding solution (k fixed, R→ ∞). A suitable composite solution is also constructed.Now jet-noise measurements are always made at fixed and finite values of R (typically 50 jet diameters) and from these measurements one would like to infer the value of pR at R = ∞, where p is the acoustic pressure. One interesting and somewhat unexpected result of this paper is that the value of pR at infinity cannot be inferred from these measurements above a certain frequency. In other words, in order to obtain accurate estimates of pR at infinity for higher and higher frequencies, one has to be further and further away from the jet!

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