You should see the following peaks.
##3100-3000 cm^(-1) (w)color(white)(XXXXXXXXXXXXXl) Aromatic C-H stretch##
##2960 and 2870 cm^(-1) (m) color(white)(XXXXXXXXXXXl)Methyl C-H stretch##
##1730-1715 cm^(-1) (s) color(white)(XXXXXXXXXXXXXX)Conjugated ester C=O stretch##
##1600-1585 cm^(-1) (m) and 1500-1400 cm^-1 (m)color(white)(X)Aromatic C-C stretch##
##1380 cm^(-1) (w) and 1260 cm^(-1) (m) color(white)(XXXXXXX)Methyl C-H bend##
##1300-1000 cm^(-1)(s) (three bands)color(white)(XXXXXXX) C-O stretch##
##750-700 cm^(-1) (s) and 710-690 cm^(-1) (m) color(white)(XXXX)Aromatic C-H ‘out-of-plane’ bend##
The structure of methyl benzoate is
It has a monosubstituted benzene ring an ester group and a methyl group.
1. ## C-O## stretching
The strongest peak should be the ester ##C=O## stretch.
This normally appears at ##1750-1735 cm^-1## but conjugation with the ring shifts the peak to ##1730-1715 cm^-1##.
There should also be one medium and two strong bands in the region from ##1300-1000 cm^-1##.
The two strong bands arise from the symmetric and antisymmetric ##C-O## stretches of the ester ##COO## group and the weaker band is the ether ##CO## stretch of the ##OCH_3## group.
2. ##C-C## Stretching
The benzene ring has characteristic medium-strength ##C-C## stretching bands in the ##1600-1585 cm^(-1)## and ##1500-1400 cm^(-1)## regions.
3. ##C-H## bending
The monosubstituted phenyl group has characteristic strong bending vibrations at ##750-700 cm^(-1)## and ##710-690 cm^(-1)##.
The methyl group usually shows a weak band at ##1380 cm^(-1)## and a medium band at ##1260 cm^(-1)##.
4. ##C-H## Stretching
The aromatic ##C-H## stretch is usually weak and occurs at ##3100-3000 cm^-1##.
The aliphatic ##CH_3## group shows stronger symmetric and antisymmetric stretches at ##2960 cm^(-1)## and ##2870 cm^(-1)##.
Here’s the actual IR spectrum of methyl benzoate.
(from chemistrytextbookcrawl.blogspot.com)