Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Notice how certain sounds, such as b and p and also t are represented by very high notches or teeth in this line of light. These sounds are called explosive consonants, and if you examine the manner in which they are made by your mouth, you will notice that it consists in closing the mouth by the lips or tongue placed between the teeth, and then suddenly withdrawing the obstruction so as to allow the air from the lungs to rush forcibly out. Hence the air outside, and in this case the diaphragm, receives a sudden blow, which is represented by this tall tooth or notch in the luminous band. The experiment teaches us that whereas musical tones are caused by certain very regular and uniform vibrations of the sounding body, vocal sounds and noises are caused by very irregular movements. Also that loud sounds are created by large motions, and feeble ones by small motions. Again, that the difference between tones in music is a difference in the rate of vibration of the sounding body. We may infer also that the difference between the quality of sounds is connected with the form of the wave-motion made by them.

Having established these facts, we must, in the next place, proceed to notice a little more closely the nature of an air wave. It will be necessary to remind you of certain qualities possessed not only by the air we breathe, but by all gases as well. Here is a cylinder with a closely fitting piston, and a tap at the bottom of the tube. If I close the tap and try to force down the piston, I feel some resistance, which increases as the piston is pushed forward. If the pressure is removed, the piston flies back to its old position, as if there were a spring underneath it. The air in the tube is an elastic substance, and it resists compression. At constant temperature the volume into which the air is squeezed is inversely as the pressure applied.

The air, therefore, possesses elasticity of bulk, as it is called, and it resists being made to occupy a smaller volume. Again, the air possesses inertia, and when it is set in motion it continues to move like any other heavy body, after the moving force is withdrawn. We have, therefore, present in it the two essential qualities for the production of a wave-motion, as explained in the first lecture. The air resists compression in virtue of elasticity, and when it is allowed to expand again back, it persists in motion in virtue of inertia.

Let us consider next the process of production of a very simple sound, such as an explosion. Suppose a small quantity of gun-cotton to be detonated. It causes a sound, and therefore an air wave. The process by which this wave is made is as follows: The explosion of the gun-cotton suddenly creates a large quantity of gas, which administers to the air a very violent outward push or blow. In consequence of the inertia of the air, it cannot respond everywhere instantly to this force. Hence a certain spherical layer of air is compressed into a smaller volume. This layer, however, almost immediately expands again, and in so doing it compresses the next outer layer of air and rarefies itself. Then, again, the second layer in expanding compresses a third, and so on.

Accordingly, a state of compression is handed on from layer to layer, and each state of compression is followed by one of rarefaction. The individual air-particles are caused to move to and fro in the direction of the radii of the sphere of which the source of explosion is the centre. Hence we have what is called a spherical longitudinal wave produced.

Each air-particle swings backwards and forwards in the line of propagation of the wave. The actual motion of each air-particle is exceedingly small.

The speed with which this zone of compression travels outwards, is called the velocity of the sound wave, and the extent to which each air-particle moves backwards and forwards is called the amplitude of the wave.

Suppose, in the next place, that instead of a merely transitory sound like an explosion, we have a continuous musical sound, we have to inquire what then will be the description of air-movement executed. The experiments shown already will have convinced you that, in the case of a musical sound, each air-particle must repeat the same kind of motion again and again.

The precise nature of the displacement can be best illustrated by the use of two models. Before you is placed a frame to which are slung a series of golf-balls suspended by threads ([see Fig. 4], Chapter I.). Between each pair of balls there is a spiral brass spring, which elastically resists both compression and extension. You will see that the row of balls and springs, therefore, has similar properties to the air. In virtue of the springs it resists compression and expansion, and in virtue of the mass or inertia of the balls any ball, if displaced and allowed to move back, overshoots its position of equilibrium because it persists in motion. The row of balls, therefore, resists extension and compression in consequence of the elasticity of the springs, and each ball persists in movement in consequence of the inertia of the ball.

If we then administer a little pat to the first ball, you will see a wave-motion run along the line of balls. Each ball in turn moves to and fro a little way, and its movement is handed on to its neighbours. We have here an example of a longitudinal wave-motion which resembles that of the air when it is traversed by a sound wave.