Fig. 1. Sound Wave Reflected from a Plane Surface.
It will be well at the outset to remind the reader of the close analogy between sound and light. A burning candle gives out spherical light waves, just as the snapping sparks give out sound waves. The form of the reflected light wave will be identical with that of a sound wave reflected under similar conditions. As we can not see the light waves themselves, we can only determine their form by calculation, and it is interesting to see that the forms photographed are identical in every case with the calculated ones. The object in view was to secure acoustical illustrations of as many of the phenomena connected with light as possible. We will begin with the very simplest case of all: the reflection of a spherical sound wave from a flat surface, corresponding to the reflection of light from a plane mirror. It can be shown by geometry that the reflected wave or echo will be a portion of a sphere, the center of which lies as far below the reflecting surface as the point at which the sound originates is above it. In the case of light, this point constitutes the image in the mirror. Referring to the photograph, we see the reflected wave in three successive positions, the interval between the sound spark and the illuminating spark having been progressively increased. The brass balls are shown at A, and beneath them the flat plate B, which acts as a reflector. In the first picture the sound wave C appears as a circle of light and shade, and has just intersected the plate. The echo appears at D. In the next two pictures the original wave has passed out of the field, and there remains only the echo.
It may, perhaps, be not out of place to remind the reader of the relation between rays of light and the wave surface. What we term light rays have no real existence, the ray being merely the path traversed by a small portion of consecutive wave surfaces. Since the wave surface always moves in a direction perpendicular to itself, the rays are always normal to it. For instance, in the above case of a spherical wave diverging from a point, the rays radiate in all directions from the point; the same is true in the case of the echo, the rays radiating from the image point below the reflecting surface. In all subsequent cases the reader can, if interested in tracing the analogy between sound and light, draw lines perpendicular to the reflected wave surfaces representing the system of reflected waves.
We will now consider a second case of reflection. We know that if a lamp is placed in the focus of a concave mirror, the rays, instead of diverging in all directions, issue from the mirror in a narrow beam. The headlight of a locomotive and the naval searchlight are examples of the practical use made of this property. If the curvature of the mirror is parabolical, the rays leaving it are parallel; consequently mirrors of this form are employed rather than spherical ones. But what has the mirror done to the wave surface which is obviously spherical when it leaves the lamp, and what is its form after reflection? The wave surface, I have said, is always perpendicular to the rays; consequently in cases where we have parallel rays we should expect the wave to be flat or plane.
Fig. 2. Spherical Sound Wave.
Examine the second photograph, which shows a spherical, sound wave starting at the focus of a parabolic mirror. The echo appears as a straight line, instead of a circle as in the previous case, which shows us that the wave surface is flat.
If now our mirror is a portion of a sphere instead of a paraboloid, our reflected wave is not flat, and the reflected rays are not all parallel, the departure from parallelism increasing as we consider rays reflected from points farther and farther away from the center of the mirror. A photograph illustrating the reflection of sound under these conditions is next shown, the echo wave being shaped like a flat-bottomed saucer. As the saucer moves upward the curved sides converge to a focus at the edge of the flat bottom, disappearing for the moment (as is shown in the fourth picture of the series), and then reappearing on the under side after passing through the focus, the saucer turning inside out.
If, instead of having a hemisphere, as in the last case, we have a complete spherical mirror, shutting the wave up inside a hollow ball, we get exceedingly curious forms; for the wave can not get out, and is bounced back and forth, becoming more and more complicated at each reflection. This is illustrated in our next photograph, the mirror being a broad strip of metal bent into a circle.[D] Intricate as these wave surfaces are, they have all been verified by geometrical constructions, as I shall presently show.
[D] Cylindrical mirrors have been used instead of spherical, for obvious reasons. A sectional view of the reflected wave is the same in this case as when produced by a spherical surface.