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A rigid cylinder changes an incident acoustic field by imposing zero normal particle velocity at its surface. The total field is the superposition of the incident field and the field scattered by the cylinder.
\[\hat p_t=\hat p_i+\hat p_s,\qquad \hat p_s=\hat p_t-\hat p_i.\]The subtraction applies to complex pressures, including phase; subtracting pressure magnitudes does not give the scattered field. Scattering includes radiation into all directions, rather than just a specular reflection.
Each example compares the incident, total and scattered fields. The first row shows complex-pressure magnitudes. The second shows the oscillating real pressure, using \(p(t)=\operatorname{Re}\{\hat p e^{i\omega t}\}\). A magnitude is an amplitude, not an instantaneous pressure.
Sizes are given as \(R/\lambda\), where \(R\) is the cylinder radius and \(\lambda\) the wavelength. This convention follows the original example headings.
Cylinder at \(R/\lambda=0.35\)
Cylinder at \(R/\lambda=1\)
Cylinder at \(R/\lambda=2\)
