The Distribution of Energy About a Point Source

Details The Distribution of Energy About a Point Source The Distribution of Energy About a Point Source

Jun 1920

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1920phrv...15..487h&link_type=abstract

Physical Review, vol. 15, Issue 6, pp. 487-491

Computer Science

Sound

Scientific paper

Distribution in two dimensions; case of a vibrating circular membrane.-In the case of stationary waves the outline is that of a Bessel's Function, and the energy at the maxima of the successive loops is slightly less than required by the law of the inverse first power of the radius. This departure is perceptible only within a few wave-lengths of the origin. The deficiency at the first loop amounts to 2.5 per cent., at the sixth to only 0.05 per cent. At the center points of the loops a similar law prevails. Distribution in three dimensions; case of sound in air.-With stationary waves the outline is given by the function rr whose maxima follow a law similar to that of the Bessel's Function, with a slight departure from the law of the inverse square. The departure from the result calculated from this law is about 5 per cent. in the first loop, but only 0.5 per cent. in the fourth loop. At the central points of the loops the law of the inverse square is accurately followed. With running waves, the same displacement of maxima exists, but the time integral of the energy of any loop at a given point is proportional to 1r2 as the conservation of energy demands. Suggestions.-Departures of this nature from simple and well-rounded laws are sometimes required by fact, as in astronomical theory, but have heretofore not been furnished by classical physical theory. This suggests further possibilities of critical study of the older mechanics.

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