Abstract
This chapter focuses on the mathematics underlying the scattering of acoustic waves. Scattering of waves and/or particles is a common phenomenon. The scattering of plane waves from spheres is applied in a wide array of fields, from optics and acoustics to meteorology, elasticity, seismology, medical physics, quantum mechanics, and biochemistry. With respect to the problem of electromagnetic wave scattering from a sphere, Lorenz found the complete mathematical solution in 1890 in terms of an infinite series of so-called partial waves. The solution is known as the Mie or Debye-Mie solution. The chapter first considers scattering by a cylinder and time-averaged energy flux before discussing spherically symmetric geometry, taking into account the scattering amplitude, the optical theorem, and the Sommerfeld radiation condition. It also examines the case of a rigid sphere, acoustic radiation from a rigid pulsating sphere, the sound of mountain streams, and mathematical bubbles.
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