Energy and Apparent Intensity of Sounds of different Pitch. 387 



square of the amplitude, and inversely as the fourth power of 

 the wave-length or periodic time. 



In series of notes of equal apparent intensity, but of different 

 pitch, the amplitudejs vary as the squares of the wave-lengths or 

 periodic times. 



In some works which allude to this subject, a confusion exists 

 between the energy of a vibrating instrument, as a string, and 

 the intensity of the tone produced thereby. It is necessary to 

 remember that the energy of the instrument has nothing to do 

 with the tone heard, as it is only that portion of the energy 

 which is lost to the instrument by being communicated to the 

 air that causes the spread of the tone. Thus the energy of a 

 string set in vibration is gradually exhausted by communication 

 to ll»e air, and the energy of the string does not represent the 

 apparent intensity of the tone at any instant, but the total energy 

 expended during the duration of the tone until it dies away. 

 Again, in an organ-pipe there is reason to believe that the energy 

 actually stored up in the vibrations of an organ-pipe in steady 

 motion is considerable ; in fact it goes on storing until the com- 

 munication of energy to the outer air equals the accession con- 

 stantly received from the source of power. Thus the energy of 

 vibration within the pipe may be much greater than that which, 

 so to speak, flows through it. We have neglected in the fore- 

 going the energy of the pipe itself, and confined our attention 

 to that supplied to it, which in steady motion is necessarily equal 

 to that parted with to the surrounding air. The result is then 

 different from that propounded heretofore ; for the energy of a 

 pipe or string necessarily contains the integral of the motion 

 throughout the vibrating mass, a quantity with which the energy 

 which passes out has nothing to do. As another illustration, the 

 energy of a tuning-fork sharply struck is considerable; that of 

 the vibrations excited in the air around is in comparison eva- 

 nescent. When the impulse in this case is constantly renewed 

 in Helmholtz^s machine by the electromagnetic apparatus there 

 applied, and the tone taken over by a resonator into the sur- 

 rounding air, we have another example of what has been de- 

 scribed m the case of the organ- pipe : the store of energy of the 

 fork is quite independent of the flow of energy from the electro- 

 magnet into the resonator; and in estimating the apparent in- 

 tensity of the tone, the latter alone is to be regarded. 



In answer to the note on the second page of Mr. Moon^s 

 paper, as to the law of the intensity in optics, it is enough to 

 observe that the law of Malus, connecting the intensities of the 

 ordinary and extraordinary rays in doubly refracting crystals, 

 affords an experimental confirmation of the law of the squares of 

 the amplitudes, for waves of the same period. 



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