... brick'¹

Spot the quote, poetry pickers.

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... positive²

Why so?

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... $rp=f(r+ct)$³

Why did we not do this for one-dimensional waves?

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... wake⁴

So three dimensional acoustics is easier than two dimensional.

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... amplitude⁵

In practice, we only ever refer to the `amplitude' of a sound: `loudness' has a particular technical meaning related to our perception of noise.

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...Marsh⁶

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... noise⁷

This is a lie. The truth appears in §4.3.

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... factor⁸

which explains the footnote on page .

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... system⁹

A very good introduction to this area--and the basis of this section--is DOWLING, A. 2000, ``Vortices, sound and flames--a damaging combination'', Aeronautical Journal, 104(1033):105-116.

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...$\theta=0$¹⁰

Why does this make no difference to the answer?

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... problem¹¹

Don't ask me how I know, I just do, OK?

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... unrealistic¹²

``Everything should be made as simple as possible, but not simpler,'' Einstein.

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... time¹³

For more information, you might like to look at Chapman, C. J. 1990, ``The spiral Green function in acoustics and electromagnetism'', Proc. R. Soc. Lond. A, 431:157-167.

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...$2\pi$¹⁴

Why?

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... noise¹⁵

``In or near the plane of rotation the noise has peculiar and indescribably unpleasant physiological effects.'', E. J. H. Lynam, Preliminary report of experiments on a high tip-speed airscrew at zero advance, Aeronautical Research Committee, Reports and Memoranda, 596, 1919.

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... Powell¹⁶

``Theory of vortex sound'', Journal of the Acoustical Society of America, 36(1):177-195.

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... sound.¹⁷

If you must know, it should read $\partial^{2}\rho/\partial t^{2} -c_{0}^{2}\nabla^{2}\rho = \nabla\nabla T_{ij}, T_{ij} = \rho v_{i}v_{j} + p_{ij} - c_{0}^{2}\rho\delta_{ij}$.

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