Fixed scalar greybody factors in five and four dimensions

We perform the classical gravity calculations of the fixed scalar absorption cross-sections by D=5 black holes with three charges and by D=4 black holes with four charges. We obtain analytic results for the cases where the energy and the left and right moving temperatures are sufficiently low but have arbitrary ratios. In D=5 the greybody factor is in perfect agreement with the recent calculation performed in the context of the effective string model for black holes. In D=4 the formula for the greybody factor in terms of the energy and the temperatures differs from that in D=5 only by the overall normalization. This suggests that the fixed scalar coupling to the effective string in D=4 is identical to that in D=5.