The transverse branch of the phonon dispersion relations of a single‐Q antiferromagnetic Cr sample have been measured near the zone boundary in the [001] direction (around the H symmetry point). The measurements were made with the phonon wave vector q⇒ both parallel and perpendicular to the spin density wave vector Q⇒ at 200°K and 78°K which are above and below the spin flip temperature. All of the measured dispersion curves displayed anomalies similar to those observed in both the paramagnetic (PM) and multi‐Q antiferromagnetic (AFM) phases. The existence of similar anomalies in the PM and single‐Q AFM phases, which are correlated with prominent features of the Fermi surface, suggests that the Fermi surface for the PM and AFM phases are quite similar. However, in the single‐Q measurements differences were observed in the shape of the anomalies for q⇒ parallel and perpendicular to Q⇒ at both temperatures. These directional differences are assumed to arise from the anisotropy of the Fermi surface introduced by the single‐Q spin density wave.