In the present paper, the ultrasonic velocity u, density ρ and viscosity η measurements of the drug atropine sulphate in aqueous solutions of Cu(II) and Co(II) metal ions at 298.15 K/1atm at a wide range of concentrations (0.01M-0.1M) are reported. They constitute a valuable source of information viz. inter-relationship of system composition, intermolecular interactions and the physical properties of the solute and solvent investigated. The observed values of u, ρ and η were found in the range of 1500-1550 ms-1, 1000-1040 kgm-3 and 0.8900-1.300 Nsm-2 respectively. The effect of concentration on u, ρ and η in all ternary systems of metal ions were found to be positive. Acoustical parameters such as isentropic compressibility Ks, intermolecular free length Lf, specific acoustic impedance Z, relative association RA, free volume Vf, internal pressure πi, viscous relaxation time τ, Gibb’s free energy ΔG, attenuation coefficient α, Rao’s constant Rm, and Wada’s constant w were calculated from the experimental data. It was found that all the parameters increased with increasing concentration except Vf, Lf and Ks. On the basis of the Jones-Dole equation, viscosity data were analyzed and the values of the Falkenhagen coefficient A and Jones-Dole B coefficient were evaluated. The variations in these parameters are discussed in terms of hydrophilic-hydrophilic/hydrophilic-hydrophobic interactions in these systems along with the structure-making/breaking behaviour of the drug.