Figure 5 shows several transfer functions of the same comb filter with varying amounts of ripple while competing with different amounts of background noise.
Notice how coherence (red trace) is greatly affected by both ripple as well as background noise. In general, less ripple (less degraded, more robust signal) results in overall improved coherence. Interference between multiple copies of the same signal is minimized when relative level offset comes to the rescue.
Simultaneously, lower background noise levels translate into more SNR, which also improves coherence. So, how does ripple typically evolve over distance indoors?
Critical Distance
Ripple goes hand in hand with the direct-to-reverberant ratio (D/R). For frequencies with wavelengths much smaller than the dimensions of a given room, we can resort to statistics. This criterion needs to be met for all acoustics equations that follow from here on. Under such circumstances, the direct sound drops with 6 dB per doubling pf distance (inverse-square-law), whereas reverberation tends to maintain its level regardless of distance (Figure 6).
In the direct field, the direct sound dominates over the reverberation with positive D/R values. In the reverberant field, it’s the other way around with negative D/R values. The distance where direct and reverberant see eye to eye at the same level, with a D/R value of zero, is called critical distance. It’s where the scale tips.
Ultimately, listeners experience and measure the combined SPL of both direct plus reverberation which implies that in the reverberant field, beyond critical distance, the inverse-square law is typically no longer observed or experienced.
