We have seen in class that the general solution to the wave equation in an infinite volume (boundary conditions of vanishing velocity potential and gradients at infinity), with initial conditions specified, is given by 1 de at PUPONSERVATION = 0,0) = D. where por, 0,0), and por, 0,0) are the acoustic pressure and velocity potential at t = 0, and c is the speed of sound in the medium. NOTE: the integral is written in SPHERICAL COORDINATES. It yields the value of the velocity potential for any time at the ORIGIN of the coordinate system (OBSERVATION = 0). Use the above formula to solve the following problem. A solid sphere of radius a is immersed in water and irradiated by a short laser pulse at time t = 0. The sphere absorbs the light uniformly throughout its volume. The energy deposition due to light absorption results in a temperature rise and increased pressure. The pressure increase is localized to the volume of the solid sphere only. The pressure outside the sphere does not change. The pressure increase at inside the sphere is denoted by oThe center of the sphere is placed a distance from a point acoustic detector. By choosing the coordinate system such that the detector is at the origin and the sphere is centered along the z-axis, the initial conditions are: Por,0,0) = 0 Po at 1p-L21