Radio pulsar PSR B1946+35 is a classical example of a core/cone triple pulsar where the observers line-of-sight cuts the emission beam centrally. In this paper we perform a detailed single-pulse polarimetric analysis of B1946+35 using sensitive Arecibo archival and new observations at 1.4 and 4.6 GHz to re-establish the pulsars classification wherein a pair of inner conal outriders surround a central core component. The new 1.4 GHz observation consisted of a long single pulse sequence of 6678 pulses, and its fluctuation spectral analysis revealed that the pulsar shows a time-varying amplitude modulation, where for a thousand periods or so the spectra have a broad low frequency red excess and then at intervals they suddenly exhibit highly periodic longitude-stationary modulation of both the core and conal components for several hundred periods. The fluctuations of the leading conal and the core components are in phase, while those in the trailing conal component in counterphase. These fluctuation properties are consistant with shorter pulse sequence analyses reported in an earlier study by Weltevrede et al. (2006, 2007) as well as in our shorter pulse sequence data sets. We argue that this dual modulation of core and conal emission cannot be understood by a model where subpulse modulation is associated with the plasma {bf E}$times${bf B} drift phenomenon. Rather the effect appears to represent a kind of periodic emission-pattern change over timescales of $sim$18 s (or 25 pulsar periods), which has not been reported previously for any other pulsar.