Why can wave theory not explain the change in the kinetic energy of an electron with a change in the frequency of incident light?

(N/A) According to the wave theory of light,the energy of a wave is proportional to the square of its amplitude (intensity) and is independent of its frequency.
$1$. Wave theory suggests that the energy delivered to the metal surface depends on the intensity of the light,not its frequency.
$2$. Therefore,if the intensity is kept constant,the wave theory predicts that the kinetic energy of the emitted electrons should remain constant regardless of the frequency of the incident light.
$3$. However,experimental observations show that the maximum kinetic energy of photoelectrons increases linearly with the frequency of incident light.
$4$. This discrepancy arises because light interacts with matter as discrete packets of energy called photons,where the energy of each photon is given by $E = h\nu$. Since the wave theory treats light as a continuous wave,it fails to account for this frequency-dependent energy transfer.