You are correct that the energy of a photon is directly proportional to its frequency. In the context of electromagnetic waves, the energy of each photon is determined by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the wave.
Amplitude, on the other hand, refers to the maximum displacement or strength of the wave. It represents the extent of oscillation or the magnitude of the electric and magnetic fields associated with the wave. Amplitude is independent of frequency because it is not directly related to the energy of individual photons. Instead, the amplitude of a wave determines its intensity or brightness, which is related to the total energy of the wave, but not to the energy of each photon.
In other words, changing the amplitude of an electromagnetic wave does not alter the energy of individual photons within the wave. It simply affects the overall strength or power carried by the wave. Increasing the amplitude increases the wave's energy per unit area or intensity, while leaving the energy of each photon unchanged.
So, while the energy of photons depends on their frequency, the amplitude of an electromagnetic wave is independent of frequency and primarily determines the wave's intensity or brightness.