Harmonic Echoes.—If the primary sound has a complex wave form, containing high harmonics of a fundamental tone, the component tones will be scattered or diffusely reflected in un equal proportions. The amplitude of the secondary-waves varies inversely as the square of the wave-length (and intensity as consequently the higher harmonics of the complex wave are scattered back in far greater proportion than the fundamen tal. To an observer near the source, therefore, the returning echo appears to be raised in pitch one or more octaves according to the nature c_ the primary sound.
Reflectors as Sound Screens.—To produce shadows comparable with optical shadows, it is essential that the reflector should be large compared with the wave-length of the sound employed. The high pitched tick of a watch may be effectively screened by a relatively small reflector but the sound of a man's voice or of a motor horn requires a much larger screen. The wave-lengths in the two cases vary from a few inches to several feet, and the linear dimensions of the reflector must consequently vary in the same proportion to produce the same degree of screening. Behind the reflector the sound is generally found to have changed in quality, the high frequency components being more perfectly screened than the lower frequencies—on this account the sound appears to be "purified." Musical Echoes from Palings. Echelon Reflectors. (Gratings).— If a sharp sound is made near one end of a row of palings, or similar "stepped" structure, the echo takes the form of a musical note. The successive palings each reflect the impulse (or, selec tively, its higher harmonics) and the observer receives a succes sion of reflections which, if sufficiently rapid, blend into a musical note. The time intervals hi are equal to 26x/c, where ox is the path difference to the successive reflectors, consequently the frequency N of the note will approximate to C/25x or some higher harmonic. If, for example, near a row of palings bx = 4 inches, and c= iioo ft./sec., N will be a multiple of ¶65o cycles/sec. i.e., a high pitched note. An echelon structure of this kind serves as the equivalent of a "grating" by which complex high frequency sounds might be analysed (see p. 26).
high frequency and reflectors of moderate dimensions.
Whispering Gallery Effects.—The well known whispering gallery of St. Paul's Cathedral, London, owes its peculiar acoustical properties to the reflection of sound by the walls. The gallery takes the form of a circle around the base of the dome. The exact mode of action is still a moot point. Rayleigh (Sound, vol. ii., p. 126) pointed out that the sound tends to creep round the inside of a curved wall, being continuously reflected by the wall, without ever getting far from it. "A whisper seems to creep round the gallery horizontally, not neces sarily along the shorter arc, but rather along that arc towards which the whisperer faces. This is a consequence of the very unequal audibility of a whisper in front of, and behind, the speaker. The abnormal loudness with which a whisper is heard is not confined to the position diametrically opposite to that occupied by the whisperer and therefore, it would appear, does not depend materially on the symmetry of the dome." It should be noted that whispers contain a higher proportion of high pitched sounds than ordinary speech, and whispering is heard more distinctly than ordinary conversation especially if the speaker looks along the gallery towards the listener. C. V. Raman (Ind. Assoc. Sci. Proc., 1922) describes an investigation of 5 whispering galleries in India which confirm a view held by Sabine of the importance of the inward slope of the wall of the gallery for giving the best effects, and the concentration by a spherical dome of a maximum sound at the opposite end of a diameter. Multiple sounds which are observed are shown not to be echoes, but sound-waves travelling circumferentially round the gallery several times before they are appreciably diminished in intensity.
Rayleigh suggests that the propagation of earthquake dis turbances is probably affected by the curvature of the surface of the earth acting like a whispering gallery. It is not im probable also that sounds travelling long distances in the sea are dependent on a similar action, and on repeated reflection at the surface and bottom. Taking the depth of a sea as uniformly 24 fathoms (144 ft.) the maximum possible distance of direct propagation of a sound-wave in it will be 29.3 miles approximately —whereas ranges 2 or 3 times this value have actually been ob served in the North sea. The possibility of a curved path due to temperature gradients must also be considered in seeking an explanation of these long ranges in the sea.