medium required for the propagation of light-waves, whether through interplanetary space or terrestrial bodies, is the universal ether, of whose existence we have no evidence except that, by assuming it and applying mathematics, the results of computation are exactly corroborated by observation and experiment. The elastic medium required for sound-waves may be solid, liquid, or gaseous. In any case it must be material.
Assuming, then, an obstacle in the path of a wave of sound or light, a shadow should be produced; but since the edges are sources of secondary waves, according to Huygens's principle, these should encroach upon the shadow. The degree of encroachment can be expressed in a mathematical formula, and is thus shown to be proportional to the wave-length. The average length of a wave of green light is now known to be about 150000of an inch. The encroachment on the geometric shadow is hence so small that refined methods are needed to make it perceptible. In the case of audible sound, on the contrary, when propagated through air, the wave-length is ordinarily so great that the encroachment almost wholly masks the presence of any shadow whatever. For the pitch C, 132 vibrations per second, such as is often used by men in conversation, the wave-length is readily calculated, if we know the velocity of sound in air. Taking this as 1,120 feet per second, there will be 132 waves strung out over this distance in each second. The length of each is hence eight feet and six inches, or more than five million times as great as that of the average wave of light. For such waves it is hopeless to attempt producing any well-defined shadows.
One of the most familiar facts in physics is that the pitch of a note becomes higher, and hence its wave shorter, in proportion to the increase of vibration frequency. If well-defined sound-shadows are possible, we must resort to sounds of very short wavelength. If the sound is continuous instead of explosive, this shortness implies very high pitch. There are mechanical difficulties to contend with which make it hard to give much intensity to very acute sounds. The range of audition, moreover, is limited. For persons of good ear the range may be roughly stated as from 25 to 25,000 vibrations per second for sounds of small intensity; indeed, many fail to perceive any pitch exceeding 15,000. To exhibit sound-shadows, therefore, it becomes necessary either to employ a source that sends forth sounds of such high pitch as to be inaudible to most of those who are expected to perceive the shadow, or to resort to a momentary sound of great intensity and short wave-length.
Every one has noticed the decrease in intensity of the sound of a distant railway-train as it passes into a cutting. The observer is in a shadow which is incomplete but nevertheless noticeable.
