A piezoelectric-based transducer that generates variable frequency torsion waves into solid or quasifluids (tissue) is presented. First, the torsion waves propagation is governed mainly by shear stiffness, which is most sensitive to pathological changes, and therefore a good indicator for them. Second, this design minimizes spurious waves and motion modes to achieve a cleaner measurement. In addition, it generates low strain waves, which are more sensitive to pathology than high strain. Third, in comparison to other approaches for generating torsional waves, this device efficiently generates a wide range of higher frequencies.