Anomalous Attenuation of Transverse Sound in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math>

We present the first measurements of the attenuation of transverse sound in superfluid 3He-B. We use fixed path length interferometry combined with the magnetoacoustic Faraday effect to vary the effective path length by a factor of 2, resulting in absolute values of the attenuation. We find that attenuation is significantly larger than expected from the theoretical dispersion relation, in contrast with the phase velocity of transverse sound. We suggest that the anomalous attenuation can be explained by surface Andreev bound states.