[ajax0604]

My answer doesn't agree with the solutions so if someone could verify whether I am correct or not, it would be much appreciated.
I think the C-H bond has a higher wavenumber since the radius of hydrogen is smaller compared to that of oxygen, which means that the bond length will be shorter between C and H and therefore the bond strength will be higher.
The solutions say that C-O has a lower wavenumber due to oxygen having a greater atomic mass than hydrogen, which doesn't make sense to me.
Thank you. 

[mjc123]

Bond length doesn't come into it, it isn't directly related to bond strength, and you're ignoring the important factor of the mass.
Have you done the oscillating mass on a spring in physics? If so, you will remember that the heavier the mass, the lower the frequency. Basically this is due to inertia; acceleration = force/mass, so for a given force in the spring, the bigger the mass the slower you can make it move.
For a molecular vibration, the frequency is proportional to sqrt(k/μ), where k is the force constant of the bond and μ is the reduced mass (e.g. for a diatomic molecule, μ = m₁m₂/(m₁+m₂).)
Although the force constants for a C-H and C-O bond are not likely to be exactly the same, the difference is much less than the difference in mass between H and O. The main reason for the high frequencies of vibrations involving H is the low mass of H.
The effect of mass is best seen in isotopic substitution, where the electronic structure (and hence the bond strength) is unchanged, but the atomic mass is different, leading to a change in the frequency. This is most obvious with the substitution H D, e.g. HCl 2880 cm^-1, DCl 2090 cm^-1; but you also see small diferences between e.g. H³⁵Cl and H³⁷Cl.

[ajax0604]

Thank you. I understand what you are saying about the mass of the atoms affecting the frequency of the vibrations. You said that the bond length doesn't come into it but doesn't it also have an effect, even though it may not be as great as the effect of mass? Hooke's Law shows that the stronger bonds and lighter atoms lead to higher frequencies. C-H has a shorter bond length, thus higher bond energy which is a measure of the strength of the bond?

[mjc123]

C-H has a shorter bond length, thus higher bond energy

Not necessarily correlated. There is a relation for bonds of similar type, e.g. C-C, C=C, C≡C the bond gets shorter and stronger. But for chemically quite different bonds, there is no direct correlation. In particular, bonds to H are short because H is small, but that doesn't mean that these bonds are necessarily stronger than longer ones, e.g. C-F is stronger than C-H, although C-O is weaker. The important point is that the frequency does not depend directly on the bond length (unlike, say, a pendulum, where the length comes into the equation).
Secondly, bond energy (strength) is not the key quantity, what matters is bond stiffness (force constant). Bond energy is a measure of the depth of the potential energy well (difference in energy between bonded and separated atoms), while stiffness is a measure of its steepness (how fast the energy changes with change in bond length - strictly, the second derivative of the energy). Again, these are often correlated, but not always, e.g. F₂ has a higher force constant than Cl₂ but a lower bond energy.

[Irlanur]

The solution is at least not complete. the frequency is proportional to sqrt(k/mu). So the reduced mass difference will have quite an influence. A priori, you can't say much about the differences in k, neither from bond length nor from the dissociation energy (altough there might be some trends). But of course the k will have an influence.