We have explored the effectiveness of a longitudinal gradient in Alfvén speed in reducing the energy of propagating Alfvén waves under conditions scaled to match solar coronal holes. The experiments were conducted in the Large Plasma Device at the University of California, Los Angeles. Our results show that the energy of the transmitted Alfvén wave decreases as the inhomogeneity parameter, λ/LA, increases. Here, λ is the wavelength of the Alfvén wave and LA is the scale length of the gradient in Alfvén speed. For gradients similar to those in coronal holes, the waves are observed to lose a factor of ≈5 more energy than they do when propagating through a uniform plasma without a gradient. We have carried out further experiments and analyses to constrain the cause of wave energy reduction in the gradient. The loss of Alfvén wave energy from mode coupling is unlikely, as we have not detected any other modes. Contrary to theoretical expectations, the reduction in the energy of the transmitted wave is not accompanied by a detectable reflected wave. Nonlinear effects are ruled out because the amplitude of the initial wave is too small and the wave frequency well below the ion cyclotron frequency. Since the total energy must be conserved, it is possible that the lost wave energy is being deposited in the plasma. Further studies are needed to explore where the energy is going. [ABSTRACT FROM AUTHOR]