The Velocity of Propagation of Longitudinal Waves in Liquids at Audio-Frequencies

A method for measuring the velocity of propagation of longitudinal waves in liquids is described which is at the same time precise and convenient of application. A column of liquid contained in a cylindrical vertical steel tube was brought into resonance vibration at audio frequency by an electromagnetically excited diaphragm at the bottom. From the solution of the equation of propagation it is shown that when the resonance frequency of the system is the same as that of the diaphragm the reaction of the latter on the system is very small. The height of the column of liquid in the tube was adjusted until its natural frequency nearly corresponded with the predetermined resonance frequency of the diaphragm. The height was then varied slightly and the frequency adjusted until resonance occurred. From several observations of this type the appropriate height corresponding to the resonance frequency of the diaphragm was obtained by interpolation. The velocity of propagation of the longitudinal waves was then calculated from the relation $V=f_0$, where $f_0$ is the natural frequency of the diaphragm when clamped in the holder and $\lambda$ is the wavelength.