232 O.K. Wead — Intensity of Sound. 



Art. XX YI. — On the Intensity of Sound: A Reply to a 

 Critic ; by Charles K. Wead. 



Several years ago I published in this Journal* some results 

 of experimental work on the sounds from tuning forks. The 

 final results as given then in Table YI, col. 6, showed results 

 agreeing far better than one might expect who knew the diffi- 

 culties, both experimental and theoretical, inherent in the 

 problem. 



The want of agreement, however, was great enough to attract 

 the attention of Professor A. Stefamni, who, without repeat- 

 ing the experiments, has attempted to dragoon the figures into 

 line by mathematical processes. An abstract f of his paper 

 indicates a total misapprehension of the problem, and the orig- 

 inal X (only recently accessible in this country) confirms this 

 opinion of his work. 



The critic first verifies my formula (5) for the potential en- 

 ergy of a bent fork, and then determines its mean kinetic 

 energy during a vibration ; by a laborious process he finds this 

 to be half of the potential energy at the extreme of vibration 

 — a conclusion that is one of the common-places of the theory 

 of simple harmonic motion. But having obtained this form- 

 ula he inserts the numbers given in my Table VI, cols. 2 or 3, 

 then divides by the surface of the hemisphere, whose radius is 

 200 ft. ; as the quotients for the different forks agree more 

 closely than my results for S in col. 6, he thinks he is justified 

 in considering that his method of discussing the observations is 

 the better one. 



Other attempts lead to similar conclusions and are based on 

 the same utterly untenable premises. The critic considers the 

 energy in the fork at any instant, and assumes tacitly that the 

 sound given out is closely proportional to the energy : any one 

 who has ever touched the stem of a vibrating fork to a sound- 

 ing board, or held the fork before a suitable resonator, should 

 appreciate readily the fact that it\§ not the amount of energy in 

 the fork that is to be thought of in considering the intensity 

 of the sound, hut the rate at tohich energy is given ujy to the 

 air. On this point text books are misleading when they say 

 the loudness of sound is proportional to the square of the 

 amplitude of vibration of the sounding body. 



]So matter how much energy the body may have, it is only 

 the small fraction being given off at any instant that can cause 

 the sensation of sound — and indeed only a part of this is effec- 



*This Journal. III. xxvi, p. 17 7, 1883. 



\ Beibl. Ann. Phvs. Chem.. xiii, 636, 1889. 



\ Atti della R. Ace. di Lucca, xxv, 239-262. 1888. 



