Book excerpt: The real world is full of sounds: a babbling brook winding through a tranquil forest, an agitated shopping cart plugging down a flight of stairs, or a falling piggybank breaking on the ground. Unfortunately virtual worlds simulated by current simulation algorithms are still inherently silent. Sounds are added as afterthoughts, often using "canned sounds" which have little to do with the animated geometry and physics. While recent decades have seen dramatic success of 3D computer animation, our brain still expects a full spectrum of sensations. The lack of realistic sound rendering methods will continue to cripple our ability to enable highly interactive and realistic virtual experiences as computers become faster. This dissertation presents a family of algorithms for procedural sound synthesis for computer animation. These algorithms are built on physics-based simulation methods for computer graphics, simulating both the object vibrations for sound sources and sound propagation in virtual environments. These approaches make it feasible to automatically generate realistic sounds synchronized with animated dynamics. Our first contribution is a physically based algorithm for synthesizing sounds synchronized with brittle fracture animations. Extending time-varying rigid-body sound models, this method first resolves near-audio-rate fracture events using a fast quasistatic elastic stress solver, and then estimates fracture patterns and resulting fracture impulses using an energy-based model. To make it practical for a large number of fracture debris, we exploit human perceptual ambiguity when synthesizing sounds from many objects, and propose to use pre-computed sound proxies for reduced cost of sound-model generation. We then introduce a contact sound model for improved sound quality. This method captures very detailed non-rigid sound phenomena by resolving modal vibrations in both collision and frictional contact processing stages, thereby producing contact sounds with much richer audible details such as micro-collisions and chattering. This algorithm is practical, enabled by a novel asynchronous integrator with model-level adaptivity built into a frictional contact solver. Our third contribution focuses on another major type of sound phenomena, fluid sounds. We propose a practical method for automatic synthesis of bubblebased fluid sounds from fluid animations. This method first acoustically augments existing incompressible fluid solvers with particle-based models for bubble creation, vibration, and advection. To model sound propagation in both fluid and air domain, we weight each single-bubble sound by its bubble-to-ear acoustic transfer function value, which is modeled as a discrete Green's function of the Helmholtz equation. A fast dual-domain multipole boundary-integral solver is introduced for hundreds of thousands of Helmholtz solves in a typical babbling fluid simulation. Finally, we switch gear and present a fast self-collision detection method for deforming triangle meshes. This method can accelerate deformable simulations and lead to faster sound synthesis of deformable phenomena. Inspired by a simple idea that a mesh cannot self collide unless it deforms enough, this method supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we operate on bounding-volume-related submeshes, and precompute Energy-based Self- Collision Culling (ESCC) certificates, which indicate the amount of deformation energy required for the submesh to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate preprocess and fast runtime energy evaluation.