Scientific Papers - Vi

414.
PROPAGATION OF SOUND IN WATER.
[Not hitherto published.]
FKOM the theoretical point of view there is little to distinguish propagation of sound in an unlimited mass of water from the corresponding case of air; of course the velocity is greater (about four times). It is probable that at a great depth the velocity increases, the effect of diminishing compressibility out-weighing increased density.
As regards absorption, it would appear that it is likely to be less in water than in air. The viscosity (measured kmematically) is less in water.
But the practical questions are largely influenced by the presence of a free surface, which must act as a nearly perfect reflector. So far the case is analogous to that of a fixed wall reflecting sound waves in air; but there is an important difference. In order to imitate the wall in air, we must suppose the image of the source of sound to be exactly similar to the original; but the image of the source of sound reflected from the free surface of water must be taken negatively, viz., in the case of a pure tone with phase altered by 180°. In practice the case of interest is when both source and place of observation are somewhat near the reflecting surface. We must expect phenomena of interference varying with the precise depth below the surface. The analogy is with Lloyd's interference bands in Optics. If we suppose the distance to be travelled very great, the paths of the direct and reflected sounds will be nearly equal. Here the distinction of the two problems comes in.
For air and wall the phases of the direct and reflected waves on arrival would be the same, and the effect a maximum. But for the free surface of water the phases would be opposite and the effect approximately zero. This is what happens close to the surface. By going lower down the sound would be recovered. It is impossible to arrive at quantitative results unless all the circumstances are specified—distance, depths, and wave-length. If there are waves upon the surface of the water there is further complication; but in any case the surface acts as a nearly perfect reflector. The analogy is with a rough wall in air.
There is also the bottom to be considered. This, too, must act as a reflector in greater or less degree. With a rocky bottom and nearly grazing incidence, the reflection would be nearly perfect. Presumably a muddy or sandy bottom would reflect less. But I imagine that at grazing incidence—as when the distance between source and place of observation is a large multiple of the depth—the reflection would be good. This makes another complication. Dr Aitken, who has also described a simple experiment in illustration.