116 ACOUSTICS furnished with one opening, a memorane, &c. (as above), at its middle. As pointed out ( 87), if any of the pipes be made to sound, the reflector being at the same time put in motion, a series of separate images will be seen. On sounding another pipe, whose fundamental is an octave higher, we shall have a second line of images separated from each other by half the interval of those in the former series. This is best observed when the two flames are placed in the same vertical line. If the note of the second pipe is a fifth higher than the first, and consequently its vibra tions to those of the first as 3 to 2, then the same space which contains two images of the lower note will contain three of the higher, and so on, for other combinations. When more complicated ratios are to be tested, it is pre ferable to connect both capsules with the same burner, either with or without the reflector. PAET X. Communication of Vibrations. nnmni- 92. The communication of sonorous vibrations from one ion be- body to another plays so essential a part in acoustics that a few words must here be given to the subject. It appears ds and * ^ e we ^ established that while the vibrations of a solid lid s. are in general most readily communicated to other solids in contact with it, they are not so to liquids, and still less so to air and other aeriform fluids. Thus, a tuning-fork is inaudible at any moderate distance unless applied to a table, by whose extended surface the air can be more intensely affected. So likewise a musical string sounds very poorly unless connected with a resonant cavity or wooden chest, to the wood of which it first imparts its vibratory motion, which then produces stationary waves in the continued air. adt sex- 93. A few years ago M. Kundt made known a method iraents. founded on the communicability of vibration, by which the velocities of sound in different media may be compared together with great facility. Take a glass tube 3 feet or up wards in length, drop into it a small quantity of the fine powder of the club-moss or lycopodium, and turn the tube round so as to spread the powder over the internal surface of the tube. Stop both ends of the tube with corks, clamp it at its centre, and rub one of its halves lengthwise with a moist cloth, so as to cause the glass to sound a note. It will then be found that, the air within the tube taking up the motion, and a stationary wave being formed in it, the powder is driven off from the ventral segments and forms little heaps at the nodes. The dust-heaps are, by the laws of stationary waves, separated therefore from each other by intervals each equal to half the length of an air-wave, or - . If, then, the number of heaps = m, and the length of the tube 21 I : X = . m But, by the laws of longitudinal vibrations of rods, the ^ = 21. Hence m, that is, the number of dust-heaps is equal to the ratio of the lengths of a wave of sound in glass and in air, and consequently to the ratio of the velocities of sound in those media. (For the vibrations being in unison, their number in a given time must be the same for the glass and the V V air, i.e., = ; V, V being the velocities). A A Kundt found 16 to be the number of heaps; prior experiments of a different kind had, as we have before mentioned, given this as the number of times that the velocity of sound in glass exceeds its velocity in air. Instead of producing the air-vibrations by friction of the tube containing the air, it is preferable to make use of a emaller tube or rod, furnished with a cork at one end, which fits like a piston into the tube, and projecting at its outer end through an opening in the cork which closes the air- tube. The rod thus inserted is the one which is nibbed longitudinally and communicates its vibrations to the air in the enclosing tube. By means of an apparatus of this kind, Kundt determined the ratio to the velocity of sound in air of its velocity in various solids, and also (replacing the air in the tube by different gases) of its velocity in these gases. PAKT XI. Interference of Sound. 94. When two or more sonorous waves travel through Meaning . the same medium, each particle of the air being simultane- interfer- ously affected by the disturbances due to the different euce - waves, moves in a different manner than it would if only acted on by each wave singly. The waves are said mutually to interfere. We shall exemplify this subject by consider ing the case of two waves travelling in the same direction through the air. We shall then obviously be led to the following results : 95. If the two waves are of equal length X, and are in TWO wav< the same phase (that is, each producing at any given of equal moment the same state of motion in the air-particles), their lengths. combined effect is equivalent to that of a wave of the same length X, but by which the excursions of the particles are increased, being the f * ---- ^ v sum of those due to the two com ponent waves re spectively. If the two inter fering waves, being still of same length X, be in opposite phases, or so that one is in advance of the other by - , and consequently one 2i produces in the air the opposite state of motion to the other, then the resultant wave is one of the same length X, but by which the excursions of the particles are de creased, being the difference between those due to the component waves. If the amplitudes of vibration which thus mutually interfere are moreover equal, the effect is the total mutual destruction of the vibratory motion. Thus we learn that two musical notes, of the same pitch, conveyed to the ear through the air, will produce the effect of a single note of the same pitch, but of increased loudness, if they are in the same phase, but affect the ear very slightly, if at all, when in opposite phases. If the differ ence of phase be varied gradually from zero to -X, the result- 2 ing sound will gradually decrease from a maximum to a minimum. 96. Among the many experimental confirmations which Experi- may be adduced of these proportions, mental il we will mention the following : Take a circular plate, such as is available for the production of Chladni s figures ( 71), and cut out of a sheet of pasteboard a piece of the shape ABOCD (fig. 30), consisting of two circular quadrants of the same diameter as the plate. Let, now, the plate be lustration Vilirating plate. made in the usual manner to vibrate so as to exhibit two nodal lines coinciding with two rectangular diameters. If the ear be placed right above the centre of the plate, the sound will be scarcely audible. But, if the pasteboard be interposed so as to intercept the vibrating segments AOB,
DOC, the note becomes much more distinct. The reason.
