A Balloon Lens: Acoustic Scattering from a Penetrable Sphere

A balloon filled with a gas that has a different sound speed than that of air has been used by science teachers in the past as an ”acoustic lens.” One purpose of the lens is to show refraction of sound waves as an analogy to geometric optics [H. Kruglak and C. C. Kruse, Am. J. Phys. 8, 260-261 (1940)]. This paper discusses the physics involved with the balloon lens demonstration. In order to determine the validity of a gas-filled balloon as a classroom demonstration of an acoustic lens and to understand the corresponding phenomena, the problem is considered analytically, numerically, and experimentally. The results show that although a geometric analogy is a valid first order approximation, scattering theory is often required to fully understand the observed phenomena. Thus, this demonstration can be adapted to a wide range of students, from those learning basic principles of refraction to mathematically advanced students studying scattering.