We investigated the acoustic vibrations of gold nanobipyramids and bimetallic gold?silver core?shell bipyramids, synthesized by wet chemistry techniques, using a high-sensitivity pump?probe femtosecond setup. Three modes were observed and characterized in the gold core particles for lengths varying from 49 to 170 nm and diameters varying from 20 to 40 nm. The two strongest modes have been associated with the fundamental extensional and its first harmonic, and a weak mode has been associated with the fundamental radial mode, in very good agreement with numerical simulations. We then derived linear laws linking the periods to the dimensions both experimentally and numerically. To go further, we investigated the evolution of these modes under silver deposition on gold core bipyramids. We studied the evolution of the periods of the extensional modes, which were found to be in good qualitative agreement with numerical simulations. Moreover, we observed a strong enhancement of the radial mode amplitude when silver is deposited: we are typically sensitive to the deposition of 40 attograms of silver per gold core particle. This opens up possible applications in the field of mass sensing, where metallic nanobalances have an important role to play, taking advantage of their robustness and versatility.