= Solution
\b[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 $1710\,\mathrm{cm^{-1}}$ 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 $2500$–$3300\,\mathrm{cm^{-1}}$, with a conjugated C=O band near $1690$–$1700\,\mathrm{cm^{-1}}$ and C=C absorptions around $1600$–$1650\,\mathrm{cm^{-1}}$.
C is an alkynoic acid: spectrum 1 contains the broad acid O–H absorption, a carbonyl near $1700\,\mathrm{cm^{-1}}$, and a conspicuous C≡C stretch near $2250\,\mathrm{cm^{-1}}$. 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 $1730$–$1740\,\mathrm{cm^{-1}}$, alkene features near $1640\,\mathrm{cm^{-1}}$, 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.
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