Chapter 6 In Front of the Camera and Microphone: Proximity Effect, Signal-to-Noise Ratio and Reverberation

The same voice at different distances

Anyone who records courses, live streams or podcasts soon discovers that with the mouth a little closer to the microphone the voice sounds fuller, with more bass, more like “speaking in your ear”; a little farther away, it thins out, and the room’s echo and background noise become obvious. This chapter explains these effects with the basic equations of acoustics.

The proximity effect

Most dynamic microphones used for voice, and many condenser microphones, are cardioid: most sensitive to sound from the front, least to sound from behind. A cardioid can be understood as half omnidirectional (sensing sound pressure) plus half “figure-of-eight” (sensing the pressure gradient).

When the source is far away the sound wave is close to a plane wave, and the pressure gradient is proportional to the pressure. When the source is close the wave is spherical, and the pressure gradient carries an extra “near-field” term that depends on distance and frequency and is especially large at low frequencies. The result is that a cardioid microphone boosts low frequencies at close range: the proximity effect (Olson 1957; Eargle 2004).

Calculation

In a first-order spherical-wave model, the on-axis response of an ideal cardioid is $|H| = \sqrt{1 + 1/(2kr)^2}$ , where $k = 2\pi f/c$ is the wavenumber and $r$ the distance. Compute the bass boost relative to a distant source at different distances and frequencies.

# The proximity effect of a cardioid microphone, from first-order spherical-wave acoustics.
# A cardioid is half pressure (omnidirectional) and half pressure-gradient (figure-of-eight). For a
# point source at distance r, the pressure gradient carries an extra near-field term: relative to a
# plane wave it is (1 + 1/(j k r)), with k = 2 pi f / c. On axis the cardioid's response is therefore
#     H = 0.5 + 0.5 (1 + 1/(j k r)) = 1 + 1/(2 j k r),   |H| = sqrt(1 + 1/(2 k r)^2)
# i.e. a bass boost that grows as the source comes closer (an ideal capsule; real microphones differ).
import math
C = 343.0

def boost_db(f, r):
    k = 2 * math.pi * f / C
    return 10 * math.log10(1 + 1 / (2 * k * r) ** 2)

freqs = (60, 100, 150, 250, 500, 1000)
print("distance |" + "".join(f"{f:>8d} Hz" for f in freqs) + "   (bass boost relative to a distant source, dB)")
for r in (0.02, 0.05, 0.15, 0.50):
    print(f"{r * 100:6.0f} cm |" + "".join(f"{boost_db(f, r):11.1f}" for f in freqs))
# The frequency below which the boost exceeds 3 dB (where 2 k r = 1):
for r in (0.05, 0.50):
    print(f"at {r * 100:.0f} cm the boost exceeds 3 dB below {C / (4 * math.pi * r):.0f} Hz")
# distance |      60 Hz     100 Hz     150 Hz     250 Hz     500 Hz    1000 Hz   (bass boost relative to a distant source, dB)
#      2 cm |       27.1       22.7       19.2       14.9        9.3        4.6
#      5 cm |       19.2       14.9       11.5        7.6        3.4        1.1
#     15 cm |       10.1        6.3        3.9        1.8        0.5        0.1
#     50 cm |        2.6        1.1        0.5        0.2        0.1        0.0
# at 5 cm the boost exceeds 3 dB below 546 Hz
# at 50 cm the boost exceeds 3 dB below 55 Hz

The proximity effect of an ideal cardioid: the closer the source, the larger the bass boost and the higher the frequency at which it begins.

In the ideal model, at 5 cm the bass boost at 100 Hz is about 15 dB, and everything below 500 Hz is boosted by more than 3 dB; at 50 cm the boost exceeds 3 dB only below 55 Hz, with almost no effect on the voice. Adult men speak with a fundamental around 100 Hz and women around 200 Hz, so at close range the “chest” of a male voice is markedly strengthened.

Note

Real microphones are not the ideal model. The ideal model gives a boost of over 27 dB at 2 cm and 60 Hz; because of diaphragm size, internal design and deliberately built-in bass roll-off, real microphones usually boost much less, and models differ widely, so consult the manufacturer’s close-range frequency response. Very short distances also bring plosives (the air blast of p and b) and harsh sibilance, which usually call for a pop filter and a suitable angle.

Signal-to-noise ratio and reverberation

Distance changes a recording in two other ways.

Calculation

In a free field the level of direct sound follows the inverse-square law: moving from 50 cm to 5 cm raises direct sound by $20\log_{10}(50/5) = 20$ dB. Background noise and reverberant sound in a room are roughly the same everywhere, so the signal-to-noise ratio and the direct-to-reverberant ratio also rise by about 20 dB. The distance at which direct and reverberant energy are equal is the critical distance, about $0.057\sqrt{QV/T_{60}}$ metres (Kuttruff 2009).

# Distance, level and room. Moving the mouth from 50 cm to 5 cm from the microphone:
#  (1) direct sound rises by 20 log10(50/5) = 20 dB (inverse-square law, free field);
#  (2) room noise at the microphone does not change, so the signal-to-noise ratio rises by the same;
#  (3) reverberant sound is roughly constant across the room, so the direct-to-reverberant ratio
#      (DRR) also rises by 20 dB. The critical distance, where direct and reverberant energy are
#      equal, is about r_c = 0.057 sqrt(Q V / T60) m (V room volume m^3, T60 reverberation time s,
#      Q source directivity; Q = 2 is assumed for a talker facing the microphone).
import math

def critical_distance(V, T60, Q=2.0):
    return 0.057 * math.sqrt(Q * V / T60)

speech_at_1m = 60.0        # dB SPL, ordinary conversational speech level at 1 m (approximate)
for label, noise in (("quiet studio", 25.0), ("home office", 35.0), ("cafe", 55.0)):
    row = []
    for r in (0.05, 0.15, 0.50):
        s = speech_at_1m + 20 * math.log10(1 / r)
        row.append(f"{r * 100:3.0f} cm: {s - noise:5.1f} dB")
    print(f"{label:13s} (noise {noise:.0f} dB SPL) SNR at  " + "   ".join(row))
for label, V, T60 in (("small treated room", 30, 0.3), ("untreated living room", 50, 0.7), ("meeting room", 120, 0.9)):
    rc = critical_distance(V, T60)
    print(f"{label:22s}: critical distance {rc * 100:4.0f} cm; DRR at 5 cm {20 * math.log10(rc / 0.05):+5.1f} dB,"
          f" at 50 cm {20 * math.log10(rc / 0.50):+5.1f} dB")
# quiet studio  (noise 25 dB SPL) SNR at    5 cm:  61.0 dB    15 cm:  51.5 dB    50 cm:  41.0 dB
# home office   (noise 35 dB SPL) SNR at    5 cm:  51.0 dB    15 cm:  41.5 dB    50 cm:  31.0 dB
# cafe          (noise 55 dB SPL) SNR at    5 cm:  31.0 dB    15 cm:  21.5 dB    50 cm:  11.0 dB
# small treated room    : critical distance   81 cm; DRR at 5 cm +24.1 dB, at 50 cm  +4.1 dB
# untreated living room : critical distance   68 cm; DRR at 5 cm +22.7 dB, at 50 cm  +2.7 dB
# meeting room          : critical distance   93 cm; DRR at 5 cm +25.4 dB, at 50 cm  +5.4 dB

In a home office with 35 dB of noise, the signal-to-noise ratio is about 51 dB at 5 cm and about 31 dB at 50 cm; in a café with 55 dB of noise, only about 11 dB remains at 50 cm and the voice is nearly drowned. In an untreated living room the critical distance is about 68 cm: at 50 cm direct sound is only about 3 dB above reverberation and clearly “echoey”; at 5 cm it is about 23 dB above, clean and close.

What “speaking in your ear” is

A close-miked voice sounds like “speaking in your ear” for at least three physical reasons: the proximity effect strengthens the bass; direct sound far exceeds reverberation, so the room disappears; and at close range speakers naturally lower their volume, preserving breath and detail in the voice. In daily life only people very close to us speak to us from so near, which may be why such a voice feels intimate.

Hypothesis · not established

The close-range intimacy hypothesis (not yet established). The same explanation, recorded at close range (about 5–10 cm) with sensible control of bass and plosives, leads listeners to rate the presenter as warmer and more trustworthy than a recording at a distance (about 50 cm) in the same room, without lowering ratings of the presenter’s competence. A testable implication: with the two recordings assigned at random under blind listening, ratings of warmth should be higher for the close version. If the two recordings are rated the same, or the close version lowers ratings of competence, the hypothesis is weakened or needs revision.

Note

Recording technique is no substitute for content. Close-range recording makes a voice clearer and more intimate, but intimacy can itself be used to sell what is untrue. This book discusses these techniques to make true content easier to hear, not to manufacture trust that is not deserved.

Summary

A cardioid microphone boosts bass at close range because of the near-field term of the pressure gradient in a spherical wave; the ideal model gives larger boosts than real microphones. Cutting the distance tenfold raises direct sound, signal-to-noise ratio and direct-to-reverberant ratio by about 20 dB each; in an ordinary room, 50 cm is already near the critical distance. The intimacy of close-range recording may come from the bass, the dry sound and the preserved detail, and from our everyday experience of being spoken to from close by, but its effect on trust still needs experimental testing. The next chapter returns to classical texts.

References

Eargle, John. 2004. The Microphone Book. 2nd ed. Focal Press.

Kuttruff, Heinrich. 2009. Room Acoustics. 5th ed. Spon Press.

Olson, Harry F. 1957. Acoustical Engineering. Van Nostrand.

Fan, Y. (2026). Acoustic Persuasion, Prosodic Information Theory and Interpersonal Physiological Synchrony: Pitch Contours, Pause Entropy and Listener Autonomic Coupling in Public Speaking and Leadership [声音说服力、韵律信息论与人际生理同步] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23753267 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).