Why does the existence of a cutoff frequency in the photoelectric effect favor a particle theory of light rather than a wave theory?

According to the wave theory, light of any frequency can cause electrons to be ejected as

long as the light is intense enough. A higher intensity corresponds to a greater electric

field magnitude and more energy. Therefore, there should be no frequency below which

the photoelectric effect does not occur. According to the particle theory, however, each

photon carries an amount of energy that depends upon its frequency. Increasing the

intensity of the light increases the number of photons but does not increase the energy of

the individual photons. The cutoff frequency is that frequency at which the energy of the

photon equals the work function. If the frequency of the incoming light is below the

cutoff, the electrons will not be ejected because no individual photon has enough energy

to impart to an electron.