Frequency dependence of mutual friction in rotating He II

Interaction of a second-sound wave with vortices in rotating He II results in an extra-attenuation of the wave and a small decrease $\Delta u_2$ of the velocity of second sound. We report accurate measurements, at 1.9 K, of both effects as functions of the angular velocity $\Omega$ and the second-sound frequency $\omega$. A resonator, whose fundamental mode was near 50 Hz, was specially designed for this work, with the purpose of extending the frequency range commonly used. As suggested by Mehl, the velocity decrease $\Delta u_2$ has been interpreted in terms of an imaginary part of a complex mutual-friction parameter $B=B_1+i{B}_2$. Thus, our measurements have consisted in determining the frequency dependence (at 1.9 K) of $B_1$ and $B_2$. Just as previously pointed out by Mehl et al., in connection with their own data $B_2$ vs $T$, it is found that the detailed predictions of the theory of Hall and Vinen, in spite of the crude approximations contained in it, fit surprisingly well our experimental data $B_1$ and $B_2$ vs $\omega$. We have recently published a hydrodynamic theory of mutual friction which provides an alternate explanation of our experimental results. The latter theory was originally inspired by the present work, which conversely gives experimental evidence of its validity.