Is the wave model an approximation to the photon model at higher (or lower) frequencies? Certain models hold better in certain regimes. For example, Newtonian mechanics are more useful in the regime of speeds much slower than c. I was wondering, are there specific frequencies for light where the wave model breaks down and we need to think in terms of photons? For low frequencies, for example, maybe a detector would begin to detect pulses of light and no longer a constant stream of light (even though photons still exist at higher frequencies, they arrive so frequently that for example our eyes do not pick up on the arriving pulses as being distinct). I was wondering if my thinking was correct, and if the two models mathematically approximate each other, like how $\frac{1}{2}m_0v^2+m_0c^2$ approximates the more correct relativistic energy?
 A: Rather than frequency, a better way to parametrize this is in terms of the quantum concentration. If you consider a radio wave of wavelength $\lambda$ and frequency $\nu$, the smallest volume to which such a wave can be localized is on the order of $\lambda^3$. If the energy density of the wave is $\rho$, then the number of photons per cubic wavelength is $n=\rho\lambda^3/h\nu$, which is called the quantum concentration.
When $n\gg 1$, we can do things like sticking an antenna into the wave and sampling its electric field, and quantum-mechanical randomness is not important because the antenna is acted on by a large number of photons. In these situations, the quantum-mechanical description (wave-particle) is good, but the classical approximation (pure wave) is also OK.
It is true that when $\nu$ is large, $n$ will tend to be small, and therefore the classical approximation will tend to be worse, for fixed values of all the other variables. This is a decent rough explanation of why the quantum nature of light is so much easier to see for, e.g., gamma rays.
It is definitely not always true that the classical approximation is valid at low frequencies. For example, the hydrogen atom has absorption lines in the microwave spectrum (due to the Lamb shift), and there is no way you're going to explain those discrete lines using classical physics.
