ACOUSTICS. 



medium transmitting it : but the sound 

 thus diverging is comparatively very faint. 

 Hence, in order that a speaking-trumpet 

 may produce its full effect, it must be di- 

 rected in a right line towards the hearer ; 

 and the sound collected into the focus of 

 a concave mirror is far more powerful 

 than at a little distance from it, which 

 could not happen, if sound, in all cases, 

 tended to spread equally in all directions. 

 It is said that the report of a cannon ap- 

 pears many times louder to a person to- 

 wards whom it is fired, than to one placed 

 in a contrary direction. It must, says Dr. 

 Young, have occurred to every one's ob- 

 servation, that a sound, such as that of a 

 mill or a fall of water, has appeared much 

 louder after turning a corner, when the 

 house or oilier obstacle no longer inter- 

 vened. Indeed the whole theory of the 

 speaking-trumpet would fall to the ground 

 if it were demonstrable that sound spreads 

 equally in all directions. In windy wea- 

 ther, it may be often observed, that the 

 sound of a distant bell varies almost in- 

 stantaneously in its strength, so as to ap- 

 pear twice as remote at one time as an- 

 other. Now, if sound diverged equally in 

 all directions, the variation produced by 

 the wind would not exceed one-tenth of 

 the apparent distance ; but on the suppo- 

 sition ot a motion nearly rectilinear, it may 

 easily happen that a slight change in the 

 direction of the wind shall convey a sound, 

 either directly or after reflection, in very 

 different degrees, to the same spot. 



The decay of sound is the natural con- 

 sequence of its distribution throughout a 

 larger and larger quantity of matter, as it 

 proceeds to diverge every way from its 

 centre. The actual velocity of the parti- 

 cles of the medium transmitting it, appears 

 to diminish, simply in the same proportion 

 as the distance from the centre increases ; 

 consequently, their energy, which is to be 

 considered as the measure of the strength 

 of sound, must vary as the square of the 

 distance ; so that, at the distance of ten 

 feet from the sounding body, the velocity 

 of the particles of the medium becomes 

 one-tenth as great as at the distance of one 

 foot ; and their energy, or the strength of 

 the sound, only one-hundredth as great. 



An echo is a reflection of sound strik- 

 ing against some object, as an image is 

 reflected in a glass : but it has been dis- 

 puted, what are the proper qualities in a 

 body for thus reflecting sounds. It is in 

 general known, that caverns, grottoes, 

 mountains, and ruined buildings, return 

 this reflection of sound. We have heard 

 of a very extraordinary echo, at a ruined 



VOL. I. 



fortress near Louvain, in Flanders. If a 

 person sung, he only heard his own voice 

 without any repetition ; on the contrary, 

 those who stood at some distance heard 

 the echo, but not the voice ; but then they 

 heard it with surprising variations, some- 

 times louder, sometimes softer, now more 

 near, then more distant. There is an ac- 

 count, in the Memoirs of the French Aca- 

 demy, of a similar echo near Rome. It 

 has been already observed, that every 

 point against which the pulses of sound 

 strike becomes the centre of a new series 

 of pulses, and sound describes equal dis- 

 tances in equal times; therefore, when 

 any sound is propagated from a centre, 

 and its pulses strike against a variety of 

 obstacles, if the sum of the right lines 

 drawn from that point to each of the ob- 

 stacles, and from each obstacle to a second 

 point, be equal, then will the latter be a 

 point in which an echo will be heard. 

 Thus, let A, fig 4, be the point from which 

 the sound is propagated in all directions, 

 and let the pulses strike against die ob- 

 stacles C, U, E, F, G, H, I, &c. each of 

 these points becomes a newcencre of pul- 

 ses by the first principles, and therefore 

 from each of them one series of pulses will 

 pass through the point B. Now, if the 

 several sums of tin- right lines A G -f- C B, 

 A iJ-f-DlT, ~ 



A E -f- 



A G -f- G B, 



A H-f li B, A 1 + 1 B, &c. be all equal 



to each other, it is obvious that the pulses 

 propagated from A to these points, and 

 again from these points to B, will all ar- 

 rive at B at the same instant, according to 

 the second principle ; and, therefore, if 

 the hearer be in that point, his ear will at 

 the same instant be struck by all these 

 pulses. Now, it appears, from experiment, 

 that the ear of an exercised musician can 

 alone distinguish such sounds as follow 

 one another at the rate of 9 or 10 in a se- 

 cond, or any slower rate : and therefore, 

 for a distinct perception of the direct and 

 reflected sound, there should intervene 

 the interval of 4- of a second ; but in this 



1142 

 time sound describes or 127 feet 



nearly. And, therefore, unless the sum of 

 the lines drawn from each of the obstacles 

 to the point A and B exceeds the interval 

 AB by 127 feet, no echo will be heard at 

 B. Since the several sums of the lines 

 drawn from the obstacles to the points A 

 and B are of the same magnitude, it ap- 

 pears that the curve passing through all 

 the points, C, D, E, F, G, H, I, &c. will be 

 an ellipse. Hence all the points of the 

 obstacles which produce an echo must 

 C 



