Whispering-gallery wave

Whispering-gallery waves, or whispering-gallery modes, are a type of wave that can travel around a concave surface. Originally discovered for sound waves in the whispering gallery of St Paul's Cathedral, they can exist for light and for other waves, with important applications in nondestructive testing, lasing, cooling and sensing, as well as in astronomy. Whispering-gallery waves were first explained for the case of St Paul's Cathedral circa 1878 by Lord Rayleigh, who revised a previous misconception that whispers could be heard across the dome but not at any intermediate position. He explained the phenomenon of travelling whispers with a series of specularly reflected sound rays making up chords of the circular gallery. Clinging to the walls the sound should decay in intensity only as the inverse of the distance — rather than the inverse square as in the case of a point source of sound radiating in all directions. This accounts for the whispers being audible all round the gallery. Rayleigh developed wave theories for St Paul's in 1910 and 1914. Fitting sound waves inside a cavity involves the physics of resonance based on wave interference; the sound can exist only at certain pitches as in the case of organ pipes. The sound forms patterns called modes, as shown in the diagram. Many other monuments have been shown to exhibit whispering-gallery waves, such as the Gol Gumbaz in Bijapur and the Temple of Heaven in Beijing. In the strict definition of whispering-gallery waves, they cannot exist when the guiding surface becomes straight. Mathematically this corresponds to the limit of an infinite radius of curvature. Whispering-gallery waves are guided by the effect of the wall curvature. Whispering-gallery waves for sound exist in a wide variety of systems. Examples include the vibrations of the whole Earth or stars. Such acoustic whispering-gallery waves can be used in nondestructive testing in the form of waves that creep around holes filled with liquid, for example.