COMPOSITION OF SOUND WAVES. 293 



produced by the pipe may be changed at will. The more the 

 aperture is opened, the higher the pitch. In this manner, slightly 

 raise the pitch of one of the pipes. If the pipes be sounded in 

 succession, even a trained ear would probably fail to detect any 

 difference. If they be sounded simultaneously, the sound will be 

 of varying loudness, very marked jerks or palpitations being per 

 ceptible. 



453. Practical Effect of Beats. The human 

 car may recognize about 38 ; 000 different sounds. If a 

 string, for example, vibrating 400 times per second were 

 sounded, and one vibrating 401 times per second were 

 subsequently sounded, the ear would probably fail to detect 

 any difference between them. But if they were sounded 

 simultaneously, the presence of one beat each second would 

 clearly indicate the difference. Unaided by the beats, the 

 ear can detect about one per cent, of the 38,000 sounds 

 lying within the range of the human ear. Beats are, 

 therefore, very important to the tuner of musical instru* 

 ments. To bring two slightly different tones into unison, 

 he has only to tune them so that the beats cease. 



454. Vibrations of Strings. The laws of musical tones 

 are most conveniently studied by means of stringed instruments. 

 In the violin, etc., the strings are set in vibration by bowing them. 

 The hairs of the bow, being rubbed with rosin, adhere to the string 

 and draw it aside until slipping takes place. In springing back, 

 the string is quickly caught again by the bow and the same action 

 repeated. In the harp and guitar, the strings are plucked with the 

 finger. In the piano, the wires are struck by little leather-faced 

 hammers worked by the keys. The vibrations of the string, and 

 consequently the pitch, depend upon the string itself. The manner 

 of producing the vibrations has no effect upon the pitch. 



455. Laws of the Vibrations of Strings. 



The following are important laws of musical strings : 



(1.) Other conditions being the same, the number of 

 vibrations per second varies inversely as the length of the 

 string. 



