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XXXVI. Acoustical Observations. III. By Lord Rayleigh, 

 FM.S., Professor of Experimental Physics in the University 

 of Cambridge* '. 



Intermittent Sounds. 



IN the Philosophical Magazine for May 1875, Prof. A. M. 

 Mayer describes some experiments on this subject, made 

 by rotating a perforated cardboard disk between a resonator 

 and a vibrating fork. " When the disk is stationary with one 

 of its openings opposite the mouth of the resonator, it is evi- 

 dent that the ear will experience a simple sonorous sensation 

 when a tuning-fork is brought near the mouth of the resona- 

 tor. On revolving the perforated disk, two additional or 

 secondary sounds appear — one slightly above, the other 

 slightly below the pitch of the fork. An increasing velocity 

 of rotation causes the two secondary sounds to diverge yet 

 further from the note of the beating fork, until, on reaching 

 a certain velocity, the two secondary sounds become separated 

 from each other by a major sixth, while at the same moment 

 a resultant sound appears, formed by the union of the sound 

 of the fork with the upper and lower of the secondary sounds. 

 This resultant is the lower second octave of the note given by 

 the fork. On further increasing the velocity of rotation of 

 the disk, the two secondary sounds and the resultant disappear, 

 and the ear experiences only the sensation of the simple sound 

 produced by the fork, whose beats at this stage of the experi- 

 ment have blended into a smooth continuous sensation." 



In concluding his paper Prof. Mayer calls attention "to 

 the evident difference existing between the dynamic constitu- 

 tion of the sonorous waves belonging to beating pulses pro- 

 duced by the action of a perforated rotating disk on a con- 

 tinuous stream of sonorous vibrations, and those waves which 

 cause beats, and which are formed by the joint action of sono- 

 rous vibrations differing in pitch. That these two kinds of 

 beats are alike in their effects when following in the same 

 rapidity I have assumed to be the fact in this paper." 



At the time when Prof. Mayer's paper first appeared, I ex- 

 amined this question more closely ; and some of my results 

 were referred to in a discussion before the Musical Associa- 

 tion. The difference between the two kinds of beats is con- 

 siderable. If there are two vibrations of equal amplitude and 

 slightly differing frequencies, represented by cos 27rn 1 t and 

 cos 2irn 2 t, the resultant may be expressed by 



2 cos 7r (% — n 2 )t cos it (n x + n 2 )t, 



* Communicated by the Author. 



