The correct order of carbonyl stretching frequency for the given compounds is

Concept:

Infrared Spectroscopy:

• Infrared spectroscopy (IR) is an absorption method widely used in both qualitative and quantitative analyses. IR spectroscopy is the measurement of the interaction of infrared radiation with the matter by absorption, emission, or reflection.  IR spectroscopy is used for the identification of organic compounds. 
• An IR spectrum is a graph plotted with the infrared light absorbed on the Y-axis against and frequency or wavelength on the X-axis.
• The value of the IR stretching frequency increases with increases in bond strength and decreases with reduced mass of the system.
• The IR stretching frequency of a bond can be expressed as ;

 \(\vartheta = {1 \over {2\pi }}\sqrt {{k \over \mu }} \), where k is the force constant and µ is reduced mass. 

Explanation:

• The carbonyl stretching frequency of a molecule increases with increases in the %S character in the carbonyl bond.
• In compounds A, B, and C the carbon atom of the carbonyl group (C=O) is sp², sp, and sp² hybridized respectively. The %S character in the carbon atom in compounds A, B, and C are 33%, 50%, and 33% respectively.
• Compound B has the highest carbonyl stretching frequency as the %S character is highest.
• Because of more strain in compound A, there is more %S character present in compound A. Thus compound A has more carbonyl stretching frequency than compound C.
• The correct order of carbonyl stretching frequency for the given compounds is B > A > C.

​Conclusion:

Hence, the correct order of carbonyl stretching frequency for the given compounds is  B > A > C.