  We investigate the origin of a resonant period drop of a torsional oscillator
(TO) containing solid ${}^{4}$He by inspecting its relation to a change in
elastic modulus. To understand this relationship directly, we measure both
phenomena simultaneously using a TO with a pair of concentric piezoelectric
transducers inserted in its annulus. Although the temperature, ${}^{3}$He
concentration, and frequency dependence are essentially the same, a marked
discrepancy in the drive amplitude dependence is observed. We find that this
discrepancy originates from the anisotropic response of polycrystalline solid
${}^{4}$He connected with low-angle grain boundaries by studying the shear
modulus parallel to and perpendicular to the driving direction.
