Abstract Surface Acoustic Wave (SAW) is a powerful technique for investigating quantum phases appearing in two-dimensional electron systems. The electrons respond to the piezoelectric field of SAW through screening, attenuating its amplitude and shifting its velocity, which is described by the relaxation model. In this work, we systematically study this interaction using orders of magnitude lower SAW amplitude than that in previous studies. At high magnetic fields when electrons form highly correlated states such as the quantum Hall effect, we observe an anomalously large attenuation of SAW while the acoustic speed remains considerably high, inconsistent with the conventional relaxation model. This anomaly exists only when the SAW power is sufficiently low.