Mapping the submillimeter spiral wave in NGC 6946

12 pages, 9 figuresWe have analysed SCUBA 850\\mum images of the (near) face-on spiral galaxy NGC 6946, and found a tight correlation between dust thermal emission and molecular gas. The map of visual optical depth relates well to the distribution of neutral gas (HI+H2) and implies a global gas-to-dust ratio of 90. There is no significant radial variation of this ratio: this can be understood, since the gas content is dominated by far by the molecular gas. The latter is estimated through the CO emission tracer, which is itself dependent on metallicity, similarly to dust emission. By comparing the radial profile of our visual optical depth map with that of the SCUBA image, we infer an emissivity (dust absorption coefficient) at 850\\mum that is 3 times lower than the value measured by COBE in the Milky Way, and 9 times lower than in NGC 891. A decomposition of the spiral structure half way out along the disk of NGC 6946 suggests an interarm optical depth of between 1 and 2. These surprisingly high values represent 40-80% of the visual opacity that we measure for the arm region (abridged)