In interference, why separation of 2 sources has to be much smaller than distance from the listener's point?

Question

In interference, why separation of 2 sources has to be much smaller than distance from the listener's point?

Answer 1

Otherwise, you'll hear one source, then the other source.

When the sources are far apart, you get no interference. When they are on top of each other, you get the addition of the waves. Then it varies as you move from one to the other. The equations you are using are designed for the situation near a mere addition of the waves.

Answer 2

To allow enough similarity of the two interfering waveforms for there to be able to BE interference. Interference works best if the mutually interfering waveforms are similar, if offset. If the two sources are far apart, the waveforms coming to the listener will be wildly dissimilar, and there will be very little discernible interference.