 Solution

The assignments are A → spectrum 3, B → spectrum 4, C → spectrum 1, and D → spectrum 2. The useful infrared spectroscopy evidence is the combination of functional-group absorptions, rather than every feature of the fingerprint region.

A is a saturated diketone: spectrum 3 has a strong ketone C=O band near $1710\mathrm{c}{\mathrm{m}}^{-1}$ without the very broad acid O–H absorption. Its two symmetry-related carbonyls do not require two well-separated diagnostic bands.

B is a conjugated dienoic acid: spectrum 4 combines a broad carboxylic acid O–H envelope, approximately $2500$–$3300\mathrm{c}{\mathrm{m}}^{-1}$, with a conjugated C=O band near $1690$–$1700\mathrm{c}{\mathrm{m}}^{-1}$ and C=C absorptions around $1600$–$1650\mathrm{c}{\mathrm{m}}^{-1}$.

C is an alkynoic acid: spectrum 1 contains the broad acid O–H absorption, a carbonyl near $1700\mathrm{c}{\mathrm{m}}^{-1}$, and a conspicuous C≡C stretch near $2250\mathrm{c}{\mathrm{m}}^{-1}$. Its alkyne is internal, so no terminal ≡C–H stretch is expected.

D is a conjugated vinyl ester: spectrum 2 has a strong ester C=O absorption around $1730$–$1740\mathrm{c}{\mathrm{m}}^{-1}$, alkene features near $1640\mathrm{c}{\mathrm{m}}^{-1}$, and strong C–O fingerprint absorptions, but no broad acid O–H envelope. These are approximate readings of the original axes, not exact assignments of every vibrational mode.