 Pressure-forced standing acoustic wave in a spherical annulus

ID: pressure-forced-standing-acoustic-wave-in-a-spherical-annulus

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

R < r < 2 R

p^{'} (2 R, t) = ε p_{0} cos ω t

produce a standing radial field. With

k = ω / c_{0}

and

α = k R

ϕ (r, t) = - \frac{2 Rε p _{0}}{ρ _{0} ω r} \frac{c o s k ( r - R ) + ( k R ) ^{- 1} s i n k ( r - R )}{c o s α + α ^{- 1} s i n α} sin ω t .

The pressure and radial velocity are in temporal quadrature, so the period-averaged acoustic intensity vanishes.

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