Waves and ripples in water, air, and æther

by Sir J. A. Fleming

If the pipe is closed at the top, then over-blowing the pipe makes it yield the odd harmonics, or the tones which are related in frequency to the primary tone in the ratio of 1, 3, 5, etc. Hence, if a stopped pipe gives a note, C, its first overtone is the fifth above the octave, or G¹.

It is usual, in adjusting the air-pressure of an organ-bellows, to allow such a pressure as that some of the overtones, or harmonics, shall exist. The presence of these harmonics in a note gives brilliancy to it, whereas an absolutely pure or simple musical tone, though not disagreeable to the ear, is not fully satisfying. Any one with a good ear can detect these harmonics or overtones in a single note sounded on a piano or organ due to the subdivision of the vibrating string or air-column into sections separated by nodes.

It will be seen that the acoustic action of the organ-pipe depends essentially upon some operation tending at the commencement to make an expansion of the air in the pipe at one end, and subsequently to cause an increase of air-pressure in it.

Fig. 61.

This can be effected not only by blowing into the pipe, but in another way, by introducing a hot body into a pipe open at both ends. We can show here as an illustration of this an interesting experiment due to Lord Rayleigh. A long cast-iron water-pipe about 4 inches in diameter and 8 feet long is suspended from the ceiling. About 1 foot up the tube from the lower end a piece of iron-wire gauze is fixed ([see Fig. 61]). By means of a gas-burner introduced into the tube, we heat the gauze red hot, and on withdrawing the lamp the tube suddenly emits a deep organ-like note for a few moments. The heated metal creates an up-draught in the tube at the lower end, and, as in the case of the open organ-pipe, causes also an in-suction of air at the upper end. The column of air is thus set vibrating with a point of alternate condensation and rarefaction in the centre, and in-draughts and out-rushes of air at the ends. Indeed, this rush of air into and out of the pipe at the lower end during the time it is sounding its note is so violent that if the hands are placed just below the bottom end of the tube they will feel chilled, as if placed near an electric fan, by the blast of air. Closing the bottom end of the pipe with a sheet of metal at once stops the air-movement, and with it the musical note.

Fig. 62.—Singing flame.

In another form the experiment has long been known under the name of a singing flame. A small jet of burning hydrogen gas is introduced into a glass tube about 3 feet in length. The jet must consist of a long narrow brass tube, and the proper position for the jet must be found by trial ([see Fig. 62]). When this is done, however, the tube emits a clear musical note, due to the tube acting as an open organ-pipe. If the flame is examined in a revolving mirror when the tube is singing, it will be found to be in vibration in sympathy with the movement of air in the tube. The tube often refuses to start singing, but may be made to do it by giving it a little tap. The actions taking place in the tube are something as follows: When the flame is introduced, it heats and rarefies the air around it. This causes an in-rush of air both at the top and bottom of the tube. A state of steady oscillation is then established, in which the air at the centre undergoes periodical expansions and compressions, and the pressure of the air round the flame changes in the same manner. The flame is therefore alternately expanded and contracted. When it expands, it heats the air more. When it is compressed, it heats it less. This variation of the flame causes air to be sucked in or expelled from both open ends of the tube, and establishes the state of steady vibration in accordance with the length of the tube. The flame and the air-column act and react on each other, and establish a state of stationary aerial oscillation in accordance with the natural time-period of the column of air. The tube can be made to give out not only its fundamental note, but a series of harmonics, or overtones, with frequencies 2, 3, 4, 5, etc., times the fundamental note, by varying the position of the flame, which must always be just under the place where a node, or place of alternate condensation and rarefaction, occurs.

We may, in the next place, with advantage briefly examine the principles of construction of one musical instrument, and allude to some recent improvements. One of the most interesting of all the musical appliances devised by human ingenuity is the violin, comprising as it does in its construction an art, a science, and a tradition. In principle the violin is nothing but a wooden box, along the top of which are stretched four strings, which are strained over a piece of wood called a bridge. These strings have their effective length altered in playing by placing the finger of the performer at some place on them, and they are set in vibration by drawing over them a well-rosined bow made of horsehair. The vibrating string communicates its vibrations to the surface of the box or body by means of the bridge, and this again to the air in the interior. The body thus serves two purposes. It acts as a resonating-chamber, and also it affords a large surface of contact with the surrounding air, whereby a greater mass of air is set simultaneously in wave-motion. The four strings are normally tuned in fifths, so that the fundamental note of each is an interval of a fifth above the next.