Whenever a sound traveling through one medium comes to another medium in which its velocity is different a certain portion is re flected, the amount reflected depending upon the change in velocity of the sound and upon the angle at which it strikes the surface of separation. This furnishes the explanation of the so-called aerial echoes observed by Tyn dall, and a partial explanation of the rolling of thunder.
When the reflecting surface is a solid wall a very large per cent of the sound is reflected, how much, depends, of course, on the nature of the wall. Under these circumstances there are produced a large number of important phe nomena which are most strikingly interesting in connection with architectural acoustics. Under special but usually accidental conditions very peculiar phenomena arise as is illustrated in the case of whispering galleries. Whispering gal leries are of one or the other of two general types usually illustrated, following the lead of Herschel, by the dome in Saint Paul's Cathe dral, London, and by a much less familiar build ing, the cathedral in Girgenti. In Saint Paul's Cathedral if a person takes a position at one side of the dome and very close to the wall he can whisper with great ease and distinctness to a person at the opposite side of the dome. This is not the case of focusing sound in the ordinary sense. The sound starting from one point is carried by the curved surface along great circles on the interior of the almost spher ical dome. The sounds traveling by all these paths meet again at the opposite end of the diameter. As distinguished from this the whis pering gallery in the cathedral at Girgenti is produced by a single, isolated, but focused re flection. A better and more familiar illustra tion of this was until recently to be found in the Hall of Statues in the Capitol at Washing ton. It is a necessary condition for both ts of whispering galleries that the wall should be smooth and free from great projec tions. The, whispering gallery in the Capitol at Washington has recently been destroyed by replacing the formerly smooth spherical ceiling by a rather deeply coffered ceiling in plaster. The ideal whispering gallery, should one be planned, would be secured by constructing a room a considerable portion of whose wall sur face would be part of an ellipsoid of revolu tion with foci at the points between which the whispering is to occur. Another interesting and somewhat related phenomenon is that of multi ple reflections. An interesting example of this recently occurred in a private athletic court at Rhinebeck-on-the-Hudson. In this case the ceiling was a smooth dome so nearly flat that its centre of curvature was at a distance below the floor equal to the height of the room. Here
the echo was repeated very many times and the sound was reflected three times between each repetition of the echo. Such special forms of walls not infrequently occur in auditoriums, often in a subtly concealed manner, and are the occasion of much annoyance. It might be added that it would not be a safe generaliza tion to say that all curved surfaces are bad or that all disturbing surfaces are curved.
In the absence of specially disturbing sur faces the multiple reflection of the sound re sults in a general reverberation, which is from some points of view advantageous and from some harmful. The reverberation results in an increased loudness particularly of sustained tone. On the other hand by the prolongation of each sound it results in more or less confusion. When the room is to be used for musical' pur poses, the effect of this reverberation, unless it be carried to too great an extent, is to blend the tones and to give to the performer a sense of support from the auditorium. There is ap parently a nice balance which for the best mu sical effects must be accurately attained in or der to fully satisfy expert musical taste. The reverberation in the room as well as the gen eral loudness and even the loudness at the sev eral points can be calculated when the dimen sions of the room and the absorbing power of its various surfaces are known.
Another feature of architectural acoustics is the phenomenon of interference. Taking first the simplest possible case when a sound from a distant source strikes normally on a plane wall, the reflected waves meeting the following on-coming waves produce by their superposi tion a system of stationary waves parallel to the reflecting surface. The result would be great nodal and antinodal surfaces parallel to the re flecting wall. An observer moving about in such a medium would hear the sound as very loud at the nodal surfaces. When the sound is produced in a confined space, such as a room, it is reflected from wall to wall many times and in many directions before it is ultimately absorbed. The result is an exceedingly com plicated system of stationary waves. Under certain conditions the sound may be so intense at certain points of the room as to be unen durable, while at other points but a few feet distant it is so faint as to be scarcely audible. The distribution of such a system of stationary waves depends on the shape of the room the material of the walls and the position of the source of sound. It also depends on the pitch of the sounds.