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Effect of undulating bed on "singing"

DEPARTMENT OF MATHEMATICS PRESIDENCY COLLEGE, CALCUTTA, India

Abstract

The effect of a sinuous undulating bed, on the "singing" phenomenon discovered by Burg, has been investigated. It has been shown that if the amplitude of undulations is small and if their wave length is much greater than those of the different harmonics in "singing", the first harmonic appears if the amplitude is less than 0.083 times the water depth. In a case when the wavelength of some of the harmonics is much greater than that of the undulations, waves with slightly different wave lengths appear instead of odd harmonics. It is therefore concluded that, in a very gradual undulating bed, not necessarily sinuous, "singing" phenomenon may take place, while in a highly irregular rough bed, it may be totally absent.