of the transducer to the impedance of the air. This principle is used in both horn loudspeakers and musical instruments. Because most driver impedances are poorly matched to the impedance of free air at low frequencies, loudspeaker enclosures are designed to both match impedance and minimize destructive phase cancellations between output from the front and rear of a speaker cone. The loudness of sound produced in air from a loudspeaker is directly related to the ratio of the diameter of the speaker to the wavelength of the sound being produced: larger speakers can produce lower frequencies at a higher level than smaller speakers. Elliptical speakers are a complex case, acting like large speakers lengthwise and small speakers crosswise. Acoustic impedance matching (or the lack of it) affects the operation of a megaphone, an echo and soundproofing. Optics A similar effect occurs when light (or any electromagnetic wave) hits the interface between two media with different refractive indices. For non-magnetic materials, the refractive index is inversely proportional to the material's characteristic impedance. An optical or wave impedance (that depends on the propagation direction) can be calculated for each medium, and may be used in the transmission-line reflection equation to calculate reflection and transmission coefficients for the interface. For non-magnetic dielectrics, this equation is equivalent to the Fresnel equations. Unwanted reflections can be reduced by the use of an anti-reflection optical coating. Mechanics If a body of mass m collides elastically with a second body, maximum energy transfer to the second body will occur when the second body has the same mass m. In a head-on collision of equal masses, the energy of the first body will be completely transferred to the second body (as in Newton's cradle for example). In this case, the masses act as "mechanical impedances", which must be matched. If and are the masses of the moving and stationary bodies, and P is the momentum of the system (which remains constant throughout the collision), the energy of the second body after the collision will be E2: which is analogous to the power-transfer equation. These principles are useful in the application of highly energetic materials (explosives). If an explosive charge is placed on a target, the sudden release of energy causes compression waves to propagate through the target radially from the point-charge contact. When the compression waves reach areas of high acoustic impedance mismatch (such as the opposite side