Abstract

One span of this stone arch bridge crosses the Charles River. At the abutment on one side of the river a hand clap is returned as a series of echoes of decreasing intensity. Perhaps the sound waves are roughly focused by the arch, first on one side of the river and then on the other. At any rate, the echoes seem to be produced by reflection from the arch, not from some other object. When the source is, as usual, on the bank it is to be expected that if an observer in a boat half-way across the river hears any echoes they will succeed each other twice as rapidly as when the observer is near the source. This is not the case. The observer in the boat does hear echoes, but they succeed each other at the same rate as when heard near the source. The explanation of this fact has not yet been found. If both source and observer are near the middle of the river it is to be expected that the echoes will succeed each other considerably more frequently than when both are on the bank. On three different occasions this was found not to be the case. The echoes heard under these circumstances succeeded each other a trifle less frequently than when source and observer were on the bank. The reason seems to involve the fact that the boat is some distance above the center of the arch. The sound reflected from the arch is again reflected from the water before it comes to a focus, and this focus is near the vertex of the arch. From this point it spreads downward, is reflected by the water and again by the arch before the first echo is heard. On one occasion when the water was low the source and observer in the boat were nearer to the center of the arch, and the echoes came with a considerably greater frequency.

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