In this paper we describe the effect of the vicinity of a liquid 3He-vacuum interface on the behavior of a vibrating wire viscometer. It was found that in the fluid near the liquid interface the quality factor is lower than in the bulk liquid. We further report on the observation of a doubling of the resonance peak of the wire in a saturated 3He-4He mixture. The frequencies and amplitudes of the two peaks strongly depend on the distance between the phase boundary and the vibrating wire; the temperature and the velocity of the phase boundary have no significant influence on the peak frequencies. The observed peak doubling is attributed to the coupling of the vibrating wire with a standing second-sound wave in the dilute phase where the volume of the dilute phase can be regarded as a resonating cavity for second sound.