Propagation of Sound.— When a sound is produced in free air at a distance from all ob stacles it spreads in spherical waves, diminish ing as it spreads over greater and greater sur faces, the intensity of the sound diminishing as the wave increases. The area of a sphere be ing proportional to the square of the radius we have the so-called law of the inverse square of the distance. The velocity of propagation of a sound through a medium is independent of the pitch of the sound or of its loudness and depends only on the nature of the medium — its elasticity and its density. In any medium the velocity of the sound is proportional directly to the square root of the elasticity and in versely to the square root of the density of the medium. Since the waves follow each other with so great rapidity that the air does not have time to cool during compression, the elasticity here referred to is that of adiabatic compres sion. A table is here given of the velocity of sound in various media: Carbonic acid gas 06 Air 1.coga Hydrogen Wer at 4.10 4.730Pinewood so,tioo Copper 12.200 Iron 15.7oo In this table the velocities given are in feet per second and at 0° C. A variation in tem perature produces a variation in the velocity, particularly in the case of gases. A rise in temperature results in an increase of velocity, the increase being about .18 per cent for every degree Centigrade for all gases. This amounts to a little less than two feet per second in the case of air.
When the source of sound is coming toward the observer, the observer being sta tionary, the sound as heard is of a higher pitch than if the source were stationary, for the num ber of waves reaching the observer per second is increased in the ratio of the velocity of sound plus the velocity of the source to the velocity of sound. Similarly when the source is receding from the observer the sound re ceived is of lower pitch. The change is strik ingly observed as a bicycle bell or a clanging street car gong passes close by an observer. In this case the fall in pitch is abrupt and marked. Similar phenomena are produced as the ob server approaches or recedes from a stationary source. This is called Doppler's principle.
When the sound instead of being produced in uniform and stationary air is produced in air moving with various velocities the phenomena are much complicated. These phenomena were first studied with care in connection with fog signals by Henry, Tyndall, and Stokes. It was an old observation that fog signals plainly audi ble at a very great distance could often not be heard at a little less distance, still nearer were audible again, still nearer inaudible,— that these regions of silence and audibility varied, not merely on different days, but rapidly in the most mysterious and disconcerting manner, so much so as to receive the name of asound ghosts." The explanation, for a long time
sought in vain, was ultimately given in a sug gestion by Stokes that they were due to a varia bility in the velocity of the wind in different strata of the atmosphere. The result of such an irregularity would be that the spreading sound waves instead of remaining spherical would be distorted very considerably. For ex ample, the waves would be tipped back if the wind were greater at the higher altitude and against the sound. In such case the sound would rise from the water and there would be a region close to the surface over which the fog signal would be inaudible. If, on the other hand, the wind retarded the sound less above than below, or if the wind above favored the sound the wave would be tipped forward and the sound would descend upon the sea and there would be a resulting area of audibility. As the wind at different altitudes varies greatly and changes abruptly we have an entirely ade quate explanation of the phenomena.
If the medium through which the sound is i being propagated is not homogeneous another very interesting series of phenomena will occur. Whether the variation in homogeneity results from the variation in composition or a variation in temperature, the effect is the same. A .change in either temperature or composition re sults in general in a change in the velocity of the sound.. Whenever sound passes from one medium to another or from one region to an otherin which the velocity is different the direction of the sound is changed. It is said to be refracted. The law of refraction is a -very simple one,— that the ratio of the sines of the angles made by the direction of propagation of the sound in the two media with a normal to the surface separating the media is equal to the ratio of the velocities in the two media. The sound is thus always bent toward the nor mal in passing from a medium in which the velocity is greater to a medium in which it is less. According to this principle the so-called acoustical lenses have been made. This may be done by filling a large but thin walled spher ical balloon with some heavy gas. Such a lens properly placed will focus the sound of the tick ing of a watch so that it can be heard at a dis tance considerably greater than that at which it can ordinarily be heard. When the lens is thus made with heavy gas it is a converging lens; when made with light gas it is a diverging lens. A curious but unintentional example of the latter occurred in the House of Parliament when a shaft of warm air, rising through the large ventilator in the middle of the floor, so diverted the sound that a speaker on one side could not be heard clearly by a member imme diately opposite him.