Waves and ripples in water, air, and æther

by Sir J. A. Fleming

The action of the phonograph leads us to inquire how a disc of metal or other elastic material responds to aerial vibrations which fall upon it, and I shall conclude this lecture by showing you one experiment of a kind to illustrate this point, which, though not very easy to perform, is certainly one of the most attractive that can be shown.

There is on the table a brass tube, of a shape somewhat like a square-shouldered funnel, and over the smaller end is loosely slipped a wide indiarubber tube with a mouthpiece. It is essential that the indiarubber tube shall not fit tightly, but shall be supported so that an air space exists all round between it and the brass funnel tube. The latter may be carried on a wooden stand. The wider end of the funnel must have a diameter of about 2¹⁄₂ inches, and the lip must be quite smooth. The interior of the funnel should be blackened. A soap solution has then to be prepared as for blowing soap-bubbles. A good formula for making this solution is given by Professor Vernon Boys, in his book, “Soap Bubbles and the Forces which mould them,” and is as follows: Fill a clean stoppered bottle three-quarters full of soft water. Add one-fortieth part of its weight of oleate of soda, which will probably float on the water. Leave it until it is dissolved. Then nearly fill up the bottle with Price’s glycerine, and shake well. Leave the bottle stoppered for a week in a dark place. Then syphon off the clear liquid from the scum at the top. Add one or two drops of strong ammonia to every pint of the liquid. Do not warm or filter the liquid, and keep it carefully from exposure to the air. Do not expose the liquid to the air more than necessary; but in blowing a bubble pour out a little of the liquid into a saucer.

In default of this good solution a substitute may be found by dissolving bits of clear yellow soap in soft water; but this soapy water does not yield films which last so long as those made with the Plateau solution above described.

By dipping the wide end of the funnel tube into some of the soap solution placed in a saucer, it is easy to cover the end with a flat soap film which will last a considerable time. This tube has then to be fixed in front of an electric arc or lime-light lantern, so that a powerful parallel beam of light can be directed on to the film by a small flat mirror or looking-glass. A lens is also placed so as to focus an image of the film on to a screen. In finding the right position for the lens, it is a great help to place a piece of white card with some bold black letters upon it over the brass funnel in the place which will be occupied with the soapy film, and to focus this so as to obtain a sharp image of the letters on the screen. When the soap film is then substituted for the card, we should have on the screen a reflection of the film surface, which at first will appear as a patch of white light upon the screen. If we allow the film to stand for a few seconds, it begins to get thinner at the upper part than at the bottom, and the image on the screen will exhibit gorgeous bands of red and green, called interference colours, which are due, like the colours on a soap-bubble, to the interference of the rays of light reflected from the inner and outer surfaces of the film. If the experiment is skilfully performed, the appearance on the screen will then be very beautiful. We shall have a patch of light which exhibits bands of colours, becoming more intense the longer the film stands, and towards the end having somewhat the appearance of an unusually lovely sunset.

Just before this condition of the film is reached, if we sing gently into the mouthpiece of the indiarubber tube, the soap film will be thrown into vibration. The image on the screen will exhibit a set of regularly arranged concentric stationary ripples, which will alter in appearance with every change in the note sung. The experiment requires some care and practice to perform it properly, and should not be attempted in public without many rehearsals; but when well shown it is a most effective and interesting experiment. We see, therefore, that so delicate an object as a stretched soap-film can take up the vibrations of the air and be itself thrown into vibration. The reason is that the soap-film, as already explained in the first lecture, resists stretching, and behaves like a sheet of elastic indiarubber. Hence, as each air wave falls upon it, the film is alternately pushed out and pulled in, but being held at the edges, it can only accommodate itself by stretching. We have, therefore, set up in the film a set of stationary waves similar to those set up on a rope fixed at one end when the loose end is regularly jerked up and down by the hand. The experiment shows us clearly the way in which an elastic disc is set in vibration when compressional waves fall upon it, and in the next lecture we shall proceed to discuss the vibrations of this kind which give rise to musical effects.

CHAPTER IV.

SOUND AND MUSIC.

OUR discussion of waves and ripples in the air would be very incomplete if we left it without any further reference to the difference between those motions in the air which constitute noise or sound, and those to which we owe the pleasure-producing effects of musical tones. I propose, therefore, to devote our time to-day to a brief exposition of the properties and modes of production of those air-vibrations which give rise to the class of sensations we call music. Sufficient has already been said to make it clear to you that one essential difference between sound or noise and music, as far as regards the events taking place outside of our own organism, is that, in the first case, we have a more or less irregular motion in the air, and, in the second, a rhythmical movement, constituting a train of air waves. The greater pleasure we experience from the latter is, no doubt, partly due to their rhythmic character. We derive satisfaction from all regularly repeated muscular movements, such as those involved in dancing, skating, and rowing, and the agreeable sensation we enjoy in their performance is partly due to their periodic or cyclical character.

In the same way, our ears are satisfied by the uniformly repeated and sustained vibrations proceeding from an organ-pipe or tuning-fork in action, but we are irritated and annoyed by the sensations set up when irregular vibrations of the air due to the bray of a donkey or the screech of a parrot fall upon them. Before, however, we can advance further in an analysis of the nature of musical sounds, two things must be clearly explained. The first of these is the meaning of the term natural period of vibration, and the second is the nature of the effect called resonance. You see before you three small brass balls suspended by strings. One string is 1 foot long, the second 4 feet, and the third 9 feet. These suspended balls are called simple pendulums. Taking in my hands the balls attached to the 1-foot and the 4-foot strings, I withdraw them a little way from their positions of rest and let them go. They vibrate like pendulums, but, as you see, the 1-foot pendulum makes two swings in the time that the 4-foot makes one swing. Repeating the experiment with the 1-foot and the 9-foot pendulum, we find that the short one now makes three swings in the time the long one makes one swing. The inference immediately follows that these pendulums, whose respective lengths are 1, 4, and 9 feet, make their swings from side to side in times which are respectively in the ratio of 1, 2, and 3.

Again, if we withdraw any of the pendulums from its position of rest and let it swing, we shall find that in any stated period of time, say 1 minute, it executes a certain definite number of oscillations which is peculiar to itself. You might imagine that, by withdrawing it more or less from its position of rest, and making it swing over a larger or smaller distance, you could make these swings per minute more or less as you please. But you would find, on trying the experiment, that this is not the case, and that, provided the arc of vibration is not too great, the time of one complete swing to and fro is the same whether the swing be large or small.