Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 50.—The refraction of a wave by a prism.

Let ABC be the prism ([see Fig. 50]) represented in plan, and let ab, ab, ab, be a train of sound waves advancing against the face AC. As soon as the left end b of the wave ab touches the face AC, and enters the carbonic acid gas, its speed will begin to be retarded, and in the time taken by the right end a to move in air from a to c, the left end will have moved in carbonic acid gas, by a less distance, bd, the distances ca and db, being in the ratio of 5 to 4. Hence it is clear that the wave-front ab will be swung round, and when the wave has wholly entered the prism, its direction of motion will have been bent round to the left.

The same thing will happen at emergence. The right end, e, of the wave ef gets out into the air whilst the left end, f, is still in carbonic acid. Accordingly, in the time taken for the end f to move to h, the end e will have moved a greater distance, in the ratio of 5 to 4, to g, and therefore we have again a bending round of the wave-direction. It is evident, therefore, that this unequal retarding of the two sides of the wave will result in a refraction, or bending, of the wave-direction, and that whereas the sound-ray was proceeding, before entering the prism, in the direction of the arrow on the right hand, it is altered, after passing through the prism, so as to be travelling in the direction of the arrow on the left-hand side. The double bending of the sound-ray is therefore caused by, and is evidence of the fact that, the sound wave travels more slowly in carbonic acid gas than it does in air.[24]

Let us, then, bring these statements to the test of experiment. We again start in action the whistle W, and place the sensitive flame in the line of the lens-axis, and notice how violently the flame flares ([see Fig. 51]). The flame is now at a distance of 4 feet from the lens. I move the flame 1 foot to the left hand, and it is now outside the beam of sound, and remains quiescent. The prism P, previously filled with carbonic acid gas, is then inserted between the sound-lens and the flame, and close to the former. When properly placed, the sensitive flame F immediately dips and roars. It will be abundantly evident to you that this can only arise because the prism has bent round the sound-beam, and deflected it on to the flame. But if the beam is bent round, then it follows that if the flame is now moved back to the central position F′, the prism remaining in front of the lens, that the flame will not now roar, and this we find to be the case. If, however, the prism is then removed, the flame at once bursts into a roar.

Fig. 51.—The refraction of a sound-ray.

This experiment proves to demonstration that we can refract waves of sound just as we can refract ripples on water.

Having regard to what we have now seen, I do not think you will have any difficulty in seeing how it is that the biconvex sound-lens, filled with carbonic acid gas, is able to render divergent sound-rays parallel; in other words, can convert a spherical sound wave into a plane sound wave.

Consider what the effect really must be. Let the sound-lens be represented in section by AB ([see Fig. 49]), and let W be the whistle sending out spherical sound waves, represented by the dotted lines.