Two-Source Interference, Transfer Function & The 3:1 Microphone Rule

When an identical acoustic signal reaches a microphone or listener ear via two pathways separated by a time delay $\Delta t = \Delta d / c$, their sinusoidal pressure waves add coherently in some frequency bands and cancel destructively in others. Plotting this summation on a linear frequency scale reveals uniformly spaced notches resembling the teeth of a hair comb.

The first cancellation null occurs at the frequency whose period equals $2\,\Delta t$ (so the delayed path lags by exactly $180^\circ$, or $\lambda/2$). Successive nulls occur at every odd multiple $(2n-1) \cdot f_{\text{null},1}$. However, comb filtering severity depends heavily on the relative amplitude ratio $a = 10^{\Delta L / 20}$: if the secondary reflection or mic bleed is attenuated by at least $-9.5\text{ dB}$ (the basis of the 3:1 Microphone Distance Rule), peak-to-dip ripple shrinks to less than $\pm 2.5\text{ dB}$.