optics - Double Slit Experiment Temporal Behaviour

Since Electromagnetic waves used for Young's double slit interference experiment are coherent travelling waves, they have temporal variation as well. At the position of the minima the two wavelets always interfere destructively so the intensity is zero there, but at the position of the maxima, there would be times when both waves are zero when the argument of $sin$ becomes a multiple of $2\pi$ due to temporal variations, then there should be zero contribution from the two waves even when they interfere constructively.

So the question is that why we don't observe temporal variations in the brightness at the positions other than the minima?

Answer

It has been done:

1 Analysis of a Temporal Double-slit Experiment Frank Rioux Department of Chemistry

Abstract:

A temporal double-slit experiment with attosecond windows in the time domain has recently been reported. This note demonstrates that the quantum mechanics behind this remarkable experiment is analogous to that for the spatial double-slit experiment for photons or massive particles.

Note the attosecond windows, an attosecond is 10^-18 seconds, not a simple lab experiment for demonstrations.

The experiment is reported here.

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (``slits'') of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are observed. A situation in which one and the same electron encounters a single and a double slit at the same time is discussed. The investigation of the fringes makes possible interferometry on the attosecond time scale. The number of visible fringes, for example, indicates that the slits are extended over about 500as.

So , the answer is that temporal variations are very hard to record and need specialized experiments where attosecond discrimination can be registered. Not feasible with light, but has been checked quantum mechanically with electrons.