Abstract
A quantitative theory is presented for the frequency dependence of the ultrasonic attenuation in the nearly one-dimensional antiferromagnet which has small, but not negligible, interchain couplings. At temperatures well above the Neel temperature TN, the ultrasonic attenuation alpha is described by a scaling function, alpha = omega 3G( omega t0), where t0 indicates the characteristic time after which the three-dimensional diffusion takes over. The theory is compared with the frequency dependence of the ultrasonic attenuation in CsNiCl3 (a one-dimensional Heisenberg antiferromagnet) and the effect of the interchain coupling on the one-dimensional spin dynamics is discussed.