A Further Case of Sub-Harmonics

Abstract

THAT notes may be produced by the intermittent contact of a tuning-fork and another body, the frequencies being sub-multiples of that of the fork, has been shown in my earlier communications (NATURE, March 8, 1924; Phil. Mag., January 1925). This letter is to point out that such sub-harmonic notes can also be obtained by rubbing with a wetted finger on or near the rim of an ordinary thin tumbler or of a wine glass. The note most easily obtained corresponds to the fundamental “bell” mode of vibration in four segments, as may be seen by the ripples produced on a little water placed in the glass (one of the four nodal lines ends at or near the moving finger). By pressing harder and moving the finger more slowly, notes of a half, a third, and a quarter of the frequency of the above note can similarly be obtained. All these notes fall in pitch simultaneously when more water is placed in the glass. (Another note may occur, apparently due to the simple torsional vibration of the glass. This note is unaltered in pitch by varying the amount of water.)