Plane-Waves of Sound Passing a Straight Edge.—Employing the Huyghens-Fresnel principle the distribution of sound beyond the edge of a totally reflecting wall may be determined. Outside the geometrical shadow there is a fluctuation of intensity which settles down, after a few oscillations, to the normal value in the absence of the wall. Inside the geometrical shadow the in tensity steadily falls off from one quarter its normal value at the edge to zero at some distance inside the geometrical shadow. The relatively feeble diffracted sound behind the wall is easily observed by the ear if the incident sound-wave is of audible frequency and of moderate intensity. With high pitched sounds (e.g., from a Galton's whistle or a high frequency diaphragm excited electro-magnetically) and a sensitive receiver the varia tions of intensity at a diffracting edge can be observed experi mentally. A sensitive flame may be used as the indicator of sound intensity or alternatively, if the sound is in the audible range, a stethoscope tube with a small funnel opening may be used to listen directly. The gradual fading away of sound within the geometrical shadow is a common observation at all frequencies.
Circular Obstacle. Scattering of Sound-Waves.—Constructing Fresnel zones outside the edge of a circular obstacle, it will be found that the total effect at a point on the axis is equal to half the effect of the first zone, i.e., the same as if no obstacle at all were interposed This is true whatever the size of the disc rela tive to the wave-length of the sound. Immediately surrounding the central spot there is a ring of almost complete silence and beyond that a further increase of intensity, and so on. These effects can be demonstrated in the manner suggested above for a straight edge. This case is analogous to that of the bright spot at the central point of the optical shadow of a circular disc— one of the "classical proofs" of the wave theory of light. It finds an important application in the directional reception of sound (see p. 28).
Scattering by Small Obstacles.—Rayleigh has shown that the intensity of the sound scattered in all directions by an obstacle is directly proportional to the volume of the obstacle and inversely proportional to the fourth power of the wave-length of the sound. This law also applies to the scattering of light and is used to explain the blue colour of the sky. We have already referred to an illustration in sound, viz., harmonic echoes, in which the higher constituents of a complex sound are scattered more readily than the fundamental, with the result that the scattered or diffusely reflected sound appears raised in pitch by one or more octaves.
Circular A perture.—The transmission of sound through a cir cular opening in an extended wall has already been considered in the analogous case of sound radiation from a piston (such as a Langevin quartz oscillator), the sound distribution beyond the opening consisting of a primary beam and a number of secondaries separated by silent regions. An experiment showing the antag onism between the parts of a wave corresponding to the first and second Fresnel zones is described by Rayleigh (Sound, Vol.
II., p. 141). Sound-waves from a high pitched source fall on a screen with a circular opening of variable diameter. A sensitive flame is situated on the axis on the opposite side of the screen. The flame is unaffected by the sound which gets through a large opening, comprising two opposed Fresnel zones but flares violently when the area is reduced to one zone.
Zone Plates.—Let circles be drawn, on a plane reflector, with radii, ri etc. , given by nXd where n =1, 2, 3, etc., and d is . the distance of the centre 0 from a point P on the axis normal to the reflector. The circles divide the surface of the reflector into Fresnel half-wave zones with respect to the point P. It will be seen that these annular zones are of equal area. If alter nate zones are cut away, a plane sound-wave falling on the plate and passing through the annular openings will arrive in phase at P, resulting in a considerable increase of intensity at that point. A zone plate of this kind therefore acts like a convex lens of focal length OP = f being the radius of the nth zone and X the wave-length of the sound. The focusing properties of such zone plates were demonstrated by Rayleigh by means of high pitched sounds and sensitive flames.
Diffraction Gratings. Reflection from Stepped or Corrugated Surfaces.—The diffraction grating, so familiar in optics, has its counterpart in sound. When sound-waves are reflected from a regular periodic structure, such as a row of palings or a cor rugated surface, the reflected-waves may assist or neutralize each other in certain directions depending on the wave-length X of the sound and the spacing d of the reflectors. The diffracted waves have maxima in directions 0 given by sin e = ± nX/d where n= I, 2, 3, etc. When d is smaller than X there are no dif fracted waves and the incident beam is reflected in the ordinary way. Thus a row of palings or a rough wall reflects sounds of moderate pitch like a perfectly smooth surface, little or no sound being returned towards the source, except in the case of normal incidence. When the sound is high pitched, however, X being less than d, it is thrown back in all directions reinforcing along certain lines and neutralizing in others. A regular row of palings may serve as a "reflection" or a "transmission" grating. W. Altberg (Ann. d. Physik, 23, 1907) demonstrated a diffraction grating of this nature by means of glass rods 1 cm. apart, using a concave reflector to produce plane-waves of sound incident on the grating. The sound was produced by means of a high frequency electric spark emitting waves only a few millimetres in length. A second concave mirror received the diffracted sound and brought it to a focus at a sensitive detector. The sound spectrum was obtained by rotation of the grating with respect to the source and receiver. Wave-lengths of the order 0.2 mm., corresponding to a frequency 1•5 million per second, were measured in this way.