= Solution
\b[B should have a lower <carbonyl> stretching frequency because its <ester> <carbonyl> is conjugated with a C=C bond.] A typical diagnostic comparison is a <conjugated ester> <carbonyl> around $1715$–$1730\,\mathrm{cm^{-1}}$ for B versus a nonconjugated <ester> <carbonyl> around $1740$–$1750\,\mathrm{cm^{-1}}$ for C; the precise positions depend on the measurement conditions. <conjugation> distributes the pi bonding over the acyl fragment and lowers the effective <carbonyl> <bond force constant>.
C also has a <terminal alkene>, giving characteristic out-of-plane C–H bending features near 990 and $910\,\mathrm{cm^{-1}}$. B has an internal, trans-disubstituted <alkene>, for which a band near $965\,\mathrm{cm^{-1}}$ is useful. Both compounds contain <ester> C–O bonds and <alkene> C–H bonds, so merely observing those general features would not distinguish them. The <carbonyl> comparison plus the <alkene> substitution pattern is the stronger identification.
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