Cose

COSE= and the resultant-amplitude is or 2a, when When the observed sound-distribution due to two or more wave-trains of sound is not found to be equal to the sum of the separate wave-trains, the latter are said to have inter fered with each other and the phenomenon is described as interference. Interference is a direct result of the principle of superposition. The phenomena of interference may be observed in any smooth water surface which is disturbed simultaneously at two different points. J. H. Vincent has obtained very beautiful photographs of such effects on the surface of mercury (see Phil. Mag., 1897, 8 and 9). The crests and troughs of the two sets of ripples in certain places reinforce each other, whilst in others they neutralize; the result is a definite "interference pattern" superposed on the ordinary wave systems. When sounds of the same frequency and amplitude reach the ear by different paths, or originate with different phases, interference effects may readily be observed. Thus the waves sent out from the prongs of an ordinary tuning fork interfere, producing approximate silence in certain directions and increased intensity in others—the rise and fall of intensity, four times per revolution, as a vibrating fork is rotated near the ear is easily demonstrated. Any "double source" of sound, such as a vibrating diaphragm exposed on both sides, shows these effects. If sound is led from its source to a receiver by two tubes of equal diameter and length the two sets of waves will arrive together, i.e., in phase. If the length of one tube is gradually varied relatively to the other the path differ ence will be successively X/2, X, 3X/2, 2X, and so on; the ant effect at the receiver alternating between zero, and maxi mum. These phenomena can be demonstrated by means of a tuning fork and two tubes of adjustable length, with a com mon exit placed to the ear. Stationary-waves to which we have already referred (p. 23) form a good example of the inter ference between a primary and a reflected train of waves. Interference between the waves from two sources of sound of nearly equal frequency appears as an increase and decrease of intensity with time—known as the phenomenon of beats (see p. 6) and exemplified by two tuning forks of nearly equal pitch. In certain cases the zones of silence observed by Tyndall when listening on a ship to the sound of a fog siren on a neighbouring cliff, were ascribed to the interference between the direct sound beam with that reflected from the surface of the sea—if these paths differ by any odd multiple of half a wave-length the two trains of waves neutralize each other and the siren is not heard. Wood and Young (Proc. Roy. Soc., ioo, 1921) observed inter ference zones under water due to a similar cause. Such effects

are of considerable importance in the case of long distance sound transmission in the sea. The sound-wave is reflected with reversal of phase when it reaches the water-air surface. At a consider able distance from the source, the path difference between the direct and surface-reflected wave may become very small com pared with the wave-length, resulting in almost complete neutrali zation. Fortunately, however, the surface of the sea is never smooth and the sea-bed reflects sound very efficiently. The bot tom-reflected-wave may therefore, in certain cases, be solely responsible for the sound heard at long ranges.

Diffraction.

Sound-Shadows.—The bending of sound-waves round the edges of obstacles is one of the most familiar of every day observations. If it were not for this effect, short distance intercommunication by means of sound would be much more difficult. Fast motor traffic on our roads is vitally dependent upon such a possibility at turnings and crossings. This bending of sound "round the corner" may be regarded as evidence of its nature as a form of wave motion; the effect being similar to that of "diffraction" in the case of light-waves. The sound-shadow and the geometrical shadow of an obstacle are therefore not coincident. The study of diffraction effects is greatly assisted by the use of a principle which is due to Huyghens:— The wave-front of a disturbance may at any instant be obtained as the envelope of the secondary-waves proceeding from all points of the wave-front at some preceding instant. A disturbance diverging from a point source with velocity c may at any time be represented by a thin spherical shell. This shell may therefore be regarded as the disturbed region, and the disturbance at a subsequent time t2 determined by drawing spheres of radii round each point of the shell. The outer spherical envelope of these spheres will be the new wave-front at the instant By this construction it will be found that the direction of advance of the wave is normal to the wave-front. Huyghens' principle of secondary waves is directly applicable to diffraction problems provided that due allowance is made for the contribution of each surface element of the wave-front to the amplitude at the point P under consideration. This estimation of amplitude involves the use of a device due to Fresnel—in which the initial wave-surface is divided into "half-wave zones" (see text-books on Optics). These zones are such that their resultant effects at some distant point P are alternately in opposite directions (being X/2 different in path length measured from P). Two successive zones therefore neutralize each other's effects at P.