LONGITUDINAL AND RADIAL VIBRATIONS IN LIQUIDS CONTAINED IN CYLINDRICAL TUBES

Abstract

I. The boundary conditions at the tube wall are considered, taking into account the natural frequency of the wall itself. An expression is derived for the radial displacement of the wall due to the excess pressure acting in the liquid. II. A formula is developed for the resonant frequencies of radial vibration in the cylinder of liquid. For tubes of ordinary size these lie well up in the ultrasonic frequencies. III. The character of a longitudinal sound wave in tubes of liquid is analyzed. Selective absorption of the longitudinal vibration is found to occur at the natural frequency of the radial vibration of the column of liquid. Examination of the expression for particle velocities reveals that the vibration for low frequencies is of a different type from that for high.