IR (Infrared) spectrum is used to determine the functional groups in the molecule, by measuring the vibrations of the atoms.
The structure of chrysanthemic acid is shown in the picture.
The five signals of chrysanthemic acid which are above the [tex] 1500 cm^{-1} [/tex] are:
1. The vinylic [tex] C-H [/tex] bond ([tex] \sim 3100 cm^{-1} [/tex]).
2. The [tex] C=O [/tex] bond ([tex] \sim 1720 cm^{-1} [/tex]).
3. The [tex] O-H [/tex] bond of carboxylic acid ([tex] \sim 2200-3600 cm^{-1} [/tex])
4. The [tex] C=C [/tex] bond ([tex] \sim 1650 cm^{-1} [/tex])
5. All other [tex] C-H [/tex] bonds ([tex] \sim 3000 cm^{-1} [/tex]).