The velocity of sound in air of the temperature 0° C. is 1,090 feet a second; it augments nearly 2 feet for every degree Centigrade added to its temperature.
Hence, given the velocity of sound in air, the temperature of the air may be readily calculated.
The distance of a fired cannon or of a discharge of lightning may be determined by observing the interval which elapses between the flash and the sound.
From the foregoing, it is easy to see that if a row of soldiers form a circle, and discharge their pieces all at the same time, the sound will be heard as a single discharge by a person occupying the centre of the circle.
But if the men form a straight row, and if the observer stand at one end of the row, the simultaneous discharge of the men’s pieces will be prolonged to a kind of roar.
A discharge of lightning along a lengthy cloud may in this way produce the prolonged roll of thunder. The roll of thunder, however, must in part at least be due to echoes from the clouds.
The pupil will find no difficulty in referring many common occurrences to the fact that sound requires a sensible time to pass through any considerable length of air. For example, the fall of the axe of a distant wood-cutter is not simultaneous with the sound of the stroke. A company of soldiers marching to music along a road cannot march in time, for the notes do not reach those in front and those behind simultaneously.
In the condensed portion of a sonorous wave the air is above, in the rarefied portion of the wave it is below, its average temperature.
This change of temperature, produced by the passage of the sound-wave itself, virtually augments the elasticity of the air, and makes the velocity of sound about one-sixth greater than it would be if there were no change of temperature.
The velocity found by Newton, who did not take this change of temperature into account, was 916 feet a second.
Laplace proved that by multiplying Newton’s velocity by the square root of the ratio of the specific heat of air at constant pressure to its specific heat at constant volume, the actual or observed velocity is obtained.
Conversely, from a comparison of the calculated and observed velocities, the ratio of the two specific heats may be inferred.
The mechanical equivalent of heat may be deduced from this ratio; it is found to be the same as that established by direct experiment.
This coincidence leads to the conclusion that atmospheric air is devoid of any sensible power to radiate heat. Direct experiments on the radiative power of air establish the same result.
The velocity of sound in water is more than four times its velocity in air.
The velocity of sound in iron is seventeen times its velocity in air.
The velocity of sound along the fibre of pine-wood is ten times its velocity in air.
The cause of this great superiority is that the elasticities of the liquid, the metal, and the wood, as compared with their respective densities, are vastly greater than the elasticity of air in relation to its density.
The velocity of sound is dependent to some extent upon molecular structure. In wood, for example, it is conveyed with different degrees of rapidity in different directions.
CHAPTER II
Physical Distinction between Noise and Music—A Musical Tone Produced by Periodic, Noise Produced by Unperiodic, Impulses—Production of Musical Sounds by Taps—Production of Musical Sounds by Puffs—Definition of Pitch in Music—Vibrations of a Tuning-Fork; their Graphic Representation on Smoked Glass—Optical Expression of the Vibrations of a Tuning-Fork—Description of the Siren—Limits of the Ear; Highest and Deepest Tones—Rapidity of Vibration Determined by the Siren—Determination of the Lengths of Sonorous Waves—Wave-Lengths of the Voice in Man and Woman—Transmission of Musical Sounds through Liquids and Solids
IN OUR last chapter we considered the propagation through air of a sound of momentary duration. We have to-day to consider continuous sounds, and to make ourselves in the first place acquainted with the physical distinction between noise and music. As far as sensation goes, everybody knows the difference between these two things. But we have now to inquire into the causes of sensation, and to make ourselves acquainted with the condition of the external air which in one case resolves itself into music and in another into noise.
We have already learned that what is loudness in our sensations is outside of us nothing more than width of swing, or amplitude, of the vibrating air-particles. Every other real sonorous impression of which we are conscious has its correlative without, as a mere form or state of the atmosphere. Were our organs sharp enough to see the motions of the air through which an agreeable voice is passing, we might see stamped upon that air the conditions of motion on which the sweetness of the voice depends. In ordinary conversation, also, the physical precedes and arouses the psychical; the spoken language, which is to give us pleasure or pain, which is to rouse us to anger or soothe us to peace, existing for a time, between us and the speaker, as a purely mechanical condition of the intervening air.
Noise affects us as an irregular succession of shocks. We are conscious while listening to it of a jolting and jarring of the auditory nerve, while a musical sound flows smoothly and without asperity or irregularity. How is this smoothness secured? By rendering the impulses received by the tympanic membrane perfectly periodic. A periodic motion is one that repeats itself. The motion of a common pendulum, for example, is periodic, but its vibrations are far too sluggish to excite sonorous waves. To produce a musical tone we must have a body which vibrates with the unerring regularity of the pendulum, but which can impart much sharper and quicker shocks to the air.
Imagine the first of a series of pulses following each other at regular intervals, impinging upon the tympanic membrane. It is shaken by the shock; and a body once shaken cannot come instantaneously to rest. The human ear, indeed, is so constructed that the sonorous motion vanishes with extreme rapidity, but its disappearance is not instantaneous; and if the motion imparted to the auditory nerve by each individual pulse of our series continues until the arrival of its successor, the sound will not cease at all. The effect of every shock will be renewed before it vanishes, and the recurrent impulses will link themselves together to a continuous musical sound. The pulses, on the contrary, which produce noise, are of irregular strength and recurrence. The action of noise upon the ear has been well compared to that of a flickering light upon the eye, both being painful through the sudden and abrupt changes which they impose upon their respective nerves.
The only condition necessary to the production of a musical sound is that the pulses should succeed each other in the same interval of time. No matter what its origin may be, if this condition be fulfilled the sound becomes musical. If a watch, for example, could be caused to tick with sufficient rapidity—say one hundred times a second—the ticks would lose their individuality and blend to a musical tone. And if the strokes of a pigeon’s wings could be accomplished at the same rate, the progress of the bird through the air would be accompanied by music. In the humming-bird the necessary rapidity is attained; and when we pass on from birds to insects, where the vibrations are more rapid, we have a musical note as the ordinary accompaniment of the insects’ flight.24 The puffs of a locomotive at starting follow each other slowly at first, but they soon increase so rapidly as to be almost incapable of being counted. If this increase could continue up to fifty or sixty puffs a second, the approach of the engine would be heralded by an organ-peal of tremendous power.
§ 2. Musical Sounds produced by Taps
Galileo