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We launch surface acousticwaves (SAW) along both the and the directions of aHall bar and measure the anisotropic conductivity in a high purity GaAs two-dimensional electron system in the quantum Hall regime of the stripe and the bubble phases. In the anisotropic stripe phase,SAW propagating along the 'easy' direction sense a compressible behavior (finite resistance)which is seen in standard transportmeasurement only if current flows along the 'hard' direction. In the isotropic bubble phase, the SAW data show compressible behavior in both directions, in marked contrast to the incompressible quantum Hall behavior seen in transport measurements. These results challenge models that assume that both the stripe and the bubble phase consist of incompressible domains and raise important questions about the role of domain boundaries in SAW propagation.