For mechanical waves, such as sound waves or ocean waves, increasing the intensity of the wave increases both the amplitude (height) of the wave and the energy it carries. In that situation, a low-frequency but high-intensity wave should have the same effect as a high-frequency but low-intensity wave. How does light behave differently from this model?

The energy in the given model depends on the frequency, but not on the intensity.

The given problem is based on the mechanical wave and electromagnetic waves. The mechanical waves depend on a material medium for their propagation, whereas electromagnetic waves are maintained by the oscillation of their electrical magneto scope fields.

In the case of light (electromagnetic wave) the energy is given by the relation,  

E = h f

Here,

h is Planck's constant.

And f is the frequency.

Then the intensity is given by the number of waves (photons) that are in the ray.  So, it is evident the effect is given by the energy that depends on the frequency, but not on the intensity.

Thus, we can conclude that the energy in the given model depends on the frequency, but not on the intensity.

Learn more about the intensity of wave here:

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the effect is given by the energy that depends on the frequency, but not on the intensity

Explanation:

There are similarities and differences between mechanical waves and electromagnetic waves. The main difference is that mechanical waves depend on a material medium for their propagation, whereas electromagnetic waves are maintained by the oscillation of their electrical magnetoscope fields.

In the case of light (electromagnetic wave) the energy is given by the relation

          E = h f

where h is Planck's constant and f is the frequency.

Then the intensity is given by the number of waves or quasiparticles (photons) that are in the ray.

Consequently the effect is given by the energy that depends on the frequency, but not on the intensity

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