The amplitudes and frequencies of the components of the acoustical spectrum of an acoustical wave, generated in a non-viscous liquid filling a cavity, are calculated by solving a boundary value problem. Apart from forced oscillations, the frequencies of the acoustical spectrum are equal to the frequency of the fundamsntal oscillation of the liquid in the cavity and its higher harmonics. If the frequency of the driving acoustical wave coincides with one of these (proper) frequencies, thefractional harmonic components appear. The amplitudes of the component oscillations decrease monotonically as the absolute value of the difference between the frequency of the driving acoustical wave and the frequency of the respective oscillation is increased. The derived relations are compared with the results of some published measurements.

Fractional-harmonic components in an acoustical wave in a liquid

Korpel and Adler showed that above a certain energy‐density threshold in an intense ultrasonic standing wave that subharmonics of the driving frequency were present [Appl. Phys. Letters, 7, 106 (1965)]. To study this effect, an acoustic Fabry‐Perot interferometer was constructed using two air‐backed x‐cut quartz transducers submerged in water, driving one around its 3‐MHz resonance, and examining the frequency spectrum across the other with a spectrum analyzer. An investigation of thresholds and frequencies of the subharmonic waves was conducted for various configurations of reflectors, driving frequencies, and distances between reflectors. All subharmonics observed had frequencies that are integer harmonics of the fundamental cavity resonance. The frequencies of the subharmonic “modes” occur in hands around 12, 13, and 14 of the driving frequency, but it should be noted that this does not necessarily imply that subharmonics occur at 1/n of the driving frequency. [Sponsored by the Office of Naval Research.]

Jack A. Bamberg

Papers

Subharmonic Generation in an Acoustic Interferometer