In my understanding, the energy of a photon, in wave terms, just translates to the frequency of the wave. If I make a photon with more energy, it will use the extra energy to just oscillate faster.
Where does the amplitude come in here?
In contrast, if I am creating sound waves by beating on a drum, if I consider the oscillation of the drum fabric as simple harmonic, if I beat on it harder, the drum will just produce a louder sound, i.e. its amplitude would increase. Since the motion of the drum fabric is simple harmonic, beating the drum harder doesn't change frequency, so energy only goes into increasing the amplitude. Tapping on a wooden table harder increases both the amplitude(loudness) of the wave and the frequency (pitch) of the wave, since I guess it's not simple harmonic motion.
Coming back to light waves, the only similar concept I can find is wave intensity. If more number of waves come in (constructively interfering at the observation point) then the brightness will increase, while keeping the color (based on frequency) constant. This constructive interference seems to be represented by increasing the amplitude in the wave diagram.
*Is amplitude just a way of representing light intensity in the wave diagram, possessing no physical differences from intensity?
In other words, can a light wave with more amplitude only be created by constructively interfering light from coherent sources?
If so, what is the amplitude of just a single photon? Does it even mean anything?