Which of the following structures would you expect to have the strongest (higest wavenumber) streching frequency for the carbonyl stretch?
The key to this type of problem is realizing that there are two contributing forms to any carbonyl compound resonance hybrind. The one shown above, but also the polar charged form below.
You would expect that any group which could cause elctron donation to the carbonyl carbon would favor the polar form (right) and decrease the strecthing frequency. Similarly, any group that causes electron withdraw would enhance the double bond character (left) which increases the stretching frequency.
In this example you are looking at the effects through the conjugation of a phenyl ring. The stongest electron withdrawing group listed above is the nitro group, followed by chlorine, and the methyl group is slightly donating.
You also need to draw the resonance structures. Illustrating the withdraw of the nitro group on both the para and meta substituted phenol rings brings up a good point. You need to be able to draw a resonance strucure where the positive charge build up is next to the carbonyl. Think about what this would look like if you had the dipolar carbonyl-two adjacent positive charges = not a heavily contributing structure, therefore the double bond character is favored by this charge build up. The para substitution allows this but the meta does not (below). The correct answer for the problem above, methyl 4-nitrobenzoate, has a carbonyl strecthing frequency of 1700 cm-1.