409.
ON THE ENERGY ACQUIRED BY SMALL RESONATORS FROM INCIDENT WAVES OF LIKE PERIOD.
[Philosophical Magazine, Vol. XXXIL pp. 188-190, 1916.]
IN discussions on photo-electricity it is often assumed that a resonator can operate only upon so much of the radiation incident upon it as corresponds to its own cross-section*. As a general proposition this is certainly not true and may indeed differ from the truth very widely. Since 1878 f it has been known that an ideal infinitely small acoustical resonator may disperse energy corresponding to an area of wave-front of the primary waves equal to A,2/77"' an efficiency exceeding to any extent the limit fixed by the above mentioned rule. The questions of how much energy can be absorbed into the resonator itself and how long the absorption may take are a little different, but they can be treated without difficulty by the method explained in a recent paper j'. The equation (49) there found for the free vibration of a small symmetrical resonator was
= 0, .................. (1)
in which p denotes the radial displacement of the spherical surface from its equilibrium value r, M the mass, /u. the coefficient of restitution, a the density of the surrounding gas, and k = 2?r 4- wave-length (X) of vibrations in the gas. The first of the two terms containing cr operates merely as an addition to M. If we write
M'=M+ 47TOT3, .............................. (2)
(1) becomes
e = 0 ...................... (3)
* See for example Millikan's important paper on a direct deter miBation of Planck's constant A"; Physical Review, Vol. vii. March 1916, p. 385. j- Theory of Sound, § 319 ; X = wave-length. J Phil. Mag. Vol. xxis. Feb. 1915, p. 210. [This volume, p. 289.] case there is no difficulty in securing the necessary delicacy*. Another manometer of longer range, but only ordinary sensitiveness, would register the low pressure in B. In this way there should be no difficulty in attaining satisfactory results. If F remains unaffected, notwithstanding large alterations of pressure in B, there are no complications to confuse the interpretation.