OCIOBEE 6, 1911] 



SCIENCE 



455 



to be noted that the wave-length is equal to 

 twice the width of the steps (see Fig. 1). The 

 advancing wave of sound xy strikes the first 

 step and part of the wave is reflected. When 

 xy reaches the second step, the sound from 

 the first step has already traveled back a dis- 

 tance equal to the width of the steps. 

 Therefore, the distance between the reflected 

 pulses of sound — the wave-length — is equal to 

 twice the width of the steps. It should be 

 noted also that this phenomenon shows clearly 

 the diffraction of sound. The fact that an ob- 

 server can hear the separate pulses of sound 

 at any point in front of the steps, indicates 

 that the sound must spread out from each 

 step as a center of disturbance. 



The results of the observations follow. The 

 observed pitch as determined by an adjust- 

 able Koenig fork was 226 vibrations a second. 

 The pitch was calculated from the relation 



A second example of a musical echo was 

 observed when a sharp sound was reflected 

 from a set of bleachers on the athletic field at 

 the University of Illinois. The pitch was de- 

 tei-mined, as in the former case, although the 

 conditions were different and not so favorable. 

 The bleachers were constructed of wood and 

 were situated in a long straight row. If a 

 rifle was shot off at some distance in front of 

 the bleachers, an observer heard the reflected 

 musical echo distinctly. The data taken fol- 

 lows. Temperature = 25° C, velocity of 

 sound 34,725, width of steps ^Y3.5 cm., 

 n <= 236 vibrations per second. The pitch as 

 observed by a tone variator was 235, although 

 other observers nearer the bleachers obtained 

 a value 241. The agreement between the cal- 

 culated and observed pitches is as close as 

 could be expected. 



Aside from the novelty of the experiment. 



H 



H 



n^v -^X from the following data. The ob- 

 served temperature was 22° C, hence the ve- 

 locity of sound' was v = 33,200 + 61 X 22 = 

 34:,5i2 cm./sec. The width of the steps was 

 76 cm., hence A = 2 X 76 = 152 cm. Finally 

 n = 34,542 -^ 152 = 227 vibrations per second. 



The agreement between the observed and 

 calculated values is closer than one would ex- 

 pect. The pitch of the fork was not corrected 

 for temperature. Another source of error lies 

 in the fact that the outgoing pulse of sound 

 struck the steps at an angle rather than per- 

 pendicularly, so that the wave-length was 

 somewhat greater than twice the width of the 

 steps. 



•Poynting and Thomson, "Sound," p. 21. 



it is interesting to learn that the pitch of the 

 echo is so definite. The notes given out in 

 both cases cited is about a tone below middle 

 C, hence where an observer expects a musical 

 echo from steps about 30 inches wide, he can 

 anticipate the result very nearly by first hum- 

 ming the expected tone. F. E. Watson 

 TjNryERSiTY OF Illinois, 

 May 17, 1911 



SOCIETIES AND ACADEMIES 



AMERICAN MATHEMATICAL SOCIETY 



The eighteenth summer meeting of the 

 American Mathematical Society was held at 

 Vassar College on Tuesday and Wednesday, 

 September 12-13, extending through two ses- 



