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Acoustics Fluid Wave Motion

A fluid is rotating with a velocity of , and , where β is a constant and c is the speed of sound and is the density. When can a ray of sound move in a closed circle?

See attached file for full problem description.


Solution Preview

As I do not have the book of Kinsler, I cannot guess which of the possible methods to answer this question he may suggest.

I therefore offer you a method which I think is the simplest: based on the Fermat principle.

The explanations are written in the attached pdf file.

I have written down all the essentials, however, if you feel you need more explanations, you can ask your questions in the feedback.

As required by Brainmass, I past the original text written in plain TEX below.
You do not have to read it since all you need is in the pdf file.

Here is the plain TEX source

centerline{bf Sound ray in a rotating fluid}

We assume that the problem is 2-dimensional, that is the sound rays in

question travel in the plain normal to the axis of rotation
(we have to assume it because of the translational symmetry and so

impossibility of having ...

Solution Summary

This solution describes how to calculate the fluid wave motion of acoustics.