CHAPTER III.

INTENSITY, CONSONANCE, INTERFERENCE.

Intensity of Sound. -The waves of rarefaction and condensation issuing from a sonorous body in a homogeneous medium, like the "rays" of light proceeding from a candle, must not be regarded as moving merely in a linear direction. It is true that both in the case of sound, and in that of light, the communication between the producer and the recipient takes a linear form; but the real constitution of the unconfined sound-wave is spherical. There being nothing to impede the oscillation of the ultimate particles, each impulse spreads in an enlarging and concentric shell, the quantity of matter set in motion augmenting as the square of the distance from the source. The intensity, or loudness, must therefore diminish in the same ratio. This is termed the law of Inverse Squares, and is true also for light. The small space through which each particle vibrates backward and forward is termed the amplitude of its undulation, and the intensity of sound is proportional to the square of this amplitude.

If the sonorous wave be confined in a tube, of course its progressive extinction by transference of motion to rapidly increasing masses of matter does not take place, and it may be conveyed for long distances with only very slight enfeeblement. On this principle are constructed the ordinary speaking-tubes. M. Biot, in the experiments by which he determined the velocity of sound in solid bodies, proved the fact that sound transmitted by the air in the waterpipes of Paris was not sensibly enfeebled at the distance of nearly a kilometre. Two persons speaking in whispers could easily hold a conversation through these pipes. "There is

only one way not to be heard," says M. Biot; "not to speak at all."1

There is, however, an important difference between the propagation of sound in a uniform tube and in an open

space. In the former case, the layers of air corresponding to successive wave-lengths are of equal mass, and their move

Quoted in Guillemin's Forces of Nature. Regnault found the report of a pistol in a pipe of 110m. to be audible at a distance equivalent to 10,000 metres.

ments are precisely alike, except in so far as they are interfered with by friction. Regnault found that in a conduit of 108 of a metre in diameter, the report of a pistol charged with a gramme of powder ceased to be heard at the distance of 1,150 metres. In a conduit of 3m. the distance was 3,810m. In the great St. Michel sewer of 1·10m. the sound was made, by successive reflections, to traverse a distance of 10,000 metres without becoming inaudible. In an open space, each successive layer has to impart its own energy to a larger layer; hence there is continual diminution of amplitude in the vibrations as the distance from the source increases. An undulation involves the onward transference of energy; and the amount of energy which traverses, in unit time, any closed surface described about the source, must be equal to that which the source emits in unit time. The intensity therefore follows the same law as that of radiant heat, and of light, as stated above. The energy of a particle executing simple vibrations in obedience to elasticity, has been said to vary as the square of the amplitude of its vibrations; for the amplitude being redoubled, the distance worked through, and the mean working force are both doubled, so that the work done is quadrupled. At the extreme positions all is potential energy; in the middle all is kinetic energy; at intermediate points it is partly in one form and partly in the other. If we sum up the potential and also the kinetic energies of all the particles constituting a wave, we shall find the results to be equal.1

This assumption is not absolutely true; since vibration implies friction, and friction implies the generation of heat. Sonorous energy therefore diminishes more rapidly than according to the law of inverse squares, and, in becoming extinct, is converted into heat.

Mayer has devised a plan by which the intensities of two sounds of the same pitch may be directly compared. The two sounds are separated by an impervious diaphragm, and in front of each is a resonator accurately tuned to them. Each resonator is attached by caoutchouc tubes of equal length to a U-tube, in the middle of which is a branch leading to a manometric capsule.

If the resonators are at the same distance from the sounding bodies, and one be excited, the attached flame vibrates. If both are produced in the same phase and intensity they interfere completely in the tube, and the flame is stationary.

Everett's Deschanel, p. 799.

If they be not of the same intensity, the interference will be incomplete, and the flame will vibrate. If one be then altered until the flame is again still, the intensities will be directly as the squares of their distances from the resonators. This instrument is therefore the correlative of Rumford's shadow Photometer.

Tabular Statement of Intensity.

1. Intensity inversely as square of distance.

2. Intensity directly as square of amplitude of vibrations.

3. Increases with density of medium.

4. Modified by motion of atmosphere.

5. Strengthened by proximity of sonorous body.

Intensity, force, or loudness, may be looked upon as the first characteristic of musical tone: Pitch, dependent solely on the rapidity of the vibration, is the second, and will be considered in the next chapter. Quality or character has been shown to be connected with the form of the vibration, and will be adverted to farther on.

Consonance.-A remarkable property of vibratory motions is the power they possess of communicating themselves to matter in their immediate neighbourhood. Even in a mechanical view of the subject this property is evident. If two pendulums, attached to different clocks, be fastened to one board and set going, it is well known to clockmakers that one will coerce the other into a spurious synchronism, which ceases directly they are divided. A regiment of soldiers crossing a suspension bridge, if keeping step and marching order, communicates regular impulses to the fabric of the bridge, and may even cause such oscillation as to endanger the structure; the swinging of the bells in a tall tower, such as that of Magdalen College at Oxford, itself produced by a succession of small impulses conveyed to the larger mass of each bell, is farther transmitted to the elastic material of the tower, producing in it very distinct oscillatory movements.1 This property is even more noticeable in the swifter alternations which form a musical note. Whatever be

"Illustrations of the powerful effects of isochronism," says Lord Rayleigh (Theory of Sound, p. 61), must be within the experience of every one. They are often of importance in very different fields from any with which acoustics are concerned. For example, few things are more dangerous to a ship than to lie in the trough of the sea, under the influence of waves whose period is nearly that of her own rolling."

F

the source of sound, its effect is immediately transmitted to the particles in contact, and with an amount of force which at first seems disproportionate to its inherent energy. For although the third law of Newton respecting the equality of action and reaction must obviously be fulfilled, the elasticity of most bodies enables them to take up transmitted vibration in a very high degree. Those which possess this property in the most marked manner are called sonorous, and their responsive vibration is termed consonance. Without consonance the effect of musical sound would be slightly, if at all, appreciable, for it is by this means that its chief propagation and dispersion is effected. In the first rank as consonators stand the producers themselves. A tuning-fork is set into sympathetic vibration by another vibrating in unison with it. A string will perform the same office, and an organ pipe instantly reinforces the sound of a corresponding tuning-fork held near its open extremity. Even a jar or bottle, the cavity of which bears some definite ratio to the wave-lengths of the sounding body, answers a similar

purpose.

The weight and density of the consonant body do not necessarily prevent its acting as a propagator of sound if its modulus of elasticity be high. Lead or clay for instance deaden sound by their inertness, while steel and glass convey

it with the utmost facility. But bodies of lighter character and less dense molecular construction, such as the softer woods, are obviously the fittest for this function. It is to the