Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

## Show that the measured pressure in the far field is approximately p(r, t) = zf(t − c−1r)/r2.

An acoustic dipole can be modeled by two point sources (monopoles) residing close together but vibrating exactly out of phase. Suppose point source 1 is located at (0, 0, −d) and point source 2 is located at (0, 0, d), where d is very small. Further suppose that source 1 is generating the narrow-band signal f(t), leading to a spherical pressure wave given by p(r_{1},t) = f(t − c^{−1}r_{1})/r1 and source 2 is generating the narrow-band signal −f(t), leading to a spherical pressure wave given by p(r_{2},t) = −f(t − c^{−1}r_{2})/r_{2}, where the two radii r_{1} and r_{1} are measured from their respective sources.

(a) Show that the measured pressure in the far field is approximately p(r, t) = zf(t − c^{−1}r)/r2.

(b) Sketch isopressure lines in the x-z plane for the above field pattern.