I've been looking around for a decent physical explanation of the differences in the phase relationships between acoustic pressure and particle velocity in different types of waves.

Mathematical analyses abound, including those already found on this forum e.g. Why is there a 90˚ phase angle between particle velocity and sound pressure in spherical waves? but I have failed to find an intuitive explanation in terms of the mechanisms.

In a plane wave, most sources seem to agree pressure and velocity is in phase (one source I have read asserts that in a plane wave the phase relationship is either fully in or fully out, see page 13 of http://www.microflown.com/files/media/library/books/microflown_ebook/ebook_2_sound_and_vibration.pdf under the heading 'The far field (plane waves)', and please comment if this is correct, and explain why). If acoustic pressure is the variation in total pressure from ambient, it must include static and dynamic components. It seems to me that, when static pressure, which is a measure of the wave potential energy, is maximum, particle velocity must be minimum (i.e. static pressure and particle velocity must be out of phase). If this is correct, does this mean that in a plane wave the dynamic component of pressure, which is a measure of the wave kinetic energy, is dominant, and this is why sound (total) pressure and velocity can be in phase?

What is happening when the phase relationship changes, i.e. in a spherical wave, in which the phase relationship is not in?



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