Energy of a light wave

I know that the energy of a photon can just be found from the equation E = hv. However, if we measure light as a wave, can the energy be found from the amplitude rather than the frequency, like you would with classical waves? If not, why do we say that light can be described as both a wave and a particle if the equations for waves don't work?

• How do you find the energy in a classical wave using only amplitude and not frequency or wavelength? – Cort Ammon Jul 9 at 18:44
• Honestly, i don't completely understand what are you asking. But remember, while light's frequency shows energy of every single photon in detector, number of received photon at every second determines the amplitude of light. Check photoelectric effect, maybe it helps you out. – Paradoxy Jul 9 at 19:24

I do not understand the expression "measure light as a wave" , it is not possible to measure something as a wave, we can only describe something as a wave. And of course there is an equation for an energy in the electromagnetic wave theory, it is $$Energy = \int_V \left(\frac{E^2(x,y,z) + H^2(x,y,z)}{8\pi} \right)dxdydz$$ which is proportional to the square of the amplitude.
The energy of a collection of photons is given by $$n \hbar \omega$$, where $$n$$ is the number of photons. So the energy of the quantum "wave" depends on two variables: the frequency and the number of particles. $$n$$ depends on the wave amplitude. Higher amplitudes are equivalent to a higher number of particles in the "wave".