Why Does Wave Energy Depend on Frequency and Not Wavelength?

[VVS]

Hey,
I have a question about waves.
Why is it that the energy of a wave depends only on the frequency but not on the wavelength?
Shouldn't two waves that have the same frequency but different wavelengths also have a different energy?
If not there should be some other quantitiy with which one can distinguish the two waves other than the wavelength itself. This should particularly be the case if space and time are deemed as equivalent.

Hope for an interesting discussion.

 

[Nugatory]

Why is it that the energy of a wave depends only on the frequency but not on the wavelength?
Shouldn't two waves that have the same frequency but different wavelengths also have a different energy?

The frequency and the wavelength are connected by the equation $v=\lambda\omega$ where $\lambda$ is the wavelength, $\omega$ is the frequency, and $v$ is the speed. Thus, as long as a wave of given frequency always travels at the same speed, the frequency sets the wavelength and the case you're asking about (same frequency, different wavelength) cannot arise.