REFLECTION OF SOUND. 197 



or 1 ; then the numbers necessary to produce the other seven notes of the 

 octave will be as follows : 



Name of note C, D, E, F, G, A, B, C. 



Number of vibrations . 1, f , f , |, f , |, '/, 2. 



However far tlu3 musical scale may be extended, it will stUl be found but 



a repetition of similar octaves. The vibrations of a column of air in a pipe 



may be regarded as obeying the same general laws ; notes are naturally higher 



in proportion to the shortuess of the pipes. 



The same note produced on any musical instrument is due 

 Is the same ^ ., . 



note in any in- to the same number of vibrations per second. Thus, a note 



Btrument pro- produced by a string of a piano vibrating 256 times in a sec- 

 same manner? ond, is also produced in the flute by a column of air vibrat- 

 ing the same number of times in a second, and also in the hu- 

 man voice by two chords contained in the upper part of the wind-pipe, also 

 vibrating the same number of times in a second. 



It has been already stated that the number of vibrations of a cord are in- 

 versely as its length ; the number also increases as the square root of the 

 force which stretches it. Thus an octave is given by the same length of string 

 when stretched four times as strongly. 



SECTION II. 



REFLECTION OF SOUND. 



,^ ,, , 4^S. When waves of sound strike ag-ainst 



What ia meant " 



by the rtflec- anv fixed surface tolerably smooth, they are 



Uon of sound ? •; -,{>■, „ 



reflected, or rebound irom that surface, and 

 the angle of reflection is equal to the angle of incidence. 



This law governing the reflection of sound is the same as that which gov- 

 erns the reflection of all elastic bodies, and also, as will be shown hereafter, 

 the imponderable agents, heat and light. ^ 



What is an ^29. Au EcHO is a repetition of sound caused 



Echo ? -jjy. ^Ijq reflection of the sound waves, or undu- 



lations, from a surface fitted for the purpose, as the side 

 of a house, a wall, hill, etc. ; the sound, after its first pro- 

 duction, returning to the ear at distinct intervals of time. 



Thus if a body placed at a certain distance from'a hearer produces a sound, 

 this sound wou'd be heard first by means of the sonorous undulations which 

 produced it, proceeding directly and uninterruptedly from the sonorous body 

 to the hearer, and afterward by sonorous undulations which, after striking on 

 reflecting surflices, return to the ear. These last constitute an echo. 



In order to produce an echo, it is requisite that the reflecting body should 

 be situated at such a distance from the source of sound, that the interval be- 



