The near field and far field: acoustic zones explained

The near field and far field: acoustic zones explained

Sound does not propagate uniformly in all directions from a source. Close to the source, the acoustic field behaves very differently from far away. These two regions — the near field and the far field — have fundamentally different properties, and understanding the boundary between them is essential for measurement, microphone placement, and the design of any acoustic system.

A brief overview for beginners

Imagine throwing a stone into still water. Close to where the stone lands, the water surface is turbulent and chaotic. Further away, the water settles into circular waves that propagate outward uniformly in all directions. The acoustic field around a loudspeaker or musical instrument behaves similarly.

The near field is the region close to the source where sound pressure and particle velocity are not yet in phase and the relationship between them is complex. In the near field, the sound does not yet "look like" a simple expanding sphere of waves. The sound pressure at a point depends strongly on the exact direction from which it arrives — the field is highly directional and structured.

The far field is the region far from the source where sound has settled into simple, outward-propagating spherical waves. In the far field, sound pressure and particle velocity are in phase, and the relationship between them is the same in all directions. Sound pressure decreases predictably with distance (the inverse square law). The field is simpler to measure and to understand.

The boundary between these regions is called the Rayleigh distance or far-field distance. Beyond this distance, the source can be treated as a point, and acoustic behaviour becomes predictable. Within it, the detailed geometry and directivity of the source dominate.

Where is the boundary?

The far-field distance is approximately:

rf = λ² / (4π a)

where λ is the acoustic wavelength and a is the characteristic dimension of the source (its radius or equivalent).

For a loudspeaker with a 10 cm diameter driver at 1 kHz (wavelength ≈ 0.34 m):

rf ≈ (0.34)² / (4π × 0.05) ≈ 0.18 m ≈ 18 cm

At frequencies below 1 kHz, the wavelength is longer and rf increases. At 100 Hz (wavelength ≈ 3.4 m):

rf ≈ (3.4)² / (4π × 0.05) ≈ 18.4 m

This is a critical result: at low frequencies, the far field is extremely distant. A small loudspeaker in a typical room is operating in the near field at all audible frequencies below a few hundred hertz. Low-frequency acoustic behaviour in rooms is also dominated by room modes and boundary effects rather than free-field loudspeaker radiation.

Physical distinction between near and far field

The difference between near and far field becomes clear when examining how sound pressure p and particle velocity u vary with distance r from the source.

In the far field (r >> rf), sound behaves as a spherical wave. Pressure and velocity are related by:

p = ρ c u

where ρ is air density and c is the speed of sound. This relationship is frequency-independent. Pressure decreases with distance as 1/r:

p(r) = (p₀ / r) × e^(i(ωt - kr))

The pressure and velocity oscillations are in phase (their peaks and troughs coincide). Energy propagates radially outward at a rate given by the acoustic intensity I = p² / (ρc), which decreases as 1/r² — the inverse square law.

In the near field (r << rf), the dominant term is the "reactive" or "evanescent" field. Pressure and velocity are no longer simply related. Instead, the particle velocity contains both an in-phase component (radiating away from the source) and a 90°-out-of-phase component (oscillating back and forth without net energy flow). This out-of-phase component dominates close to the source.

At very short distances, the particle velocity oscillates with a component that varies as 1/r², far faster than pressure, which varies as 1/r. Close to the source, velocity can exceed what would be predicted from pressure alone.

Energy in the near field sloshes back and forth rather than propagating away. This stored energy is reactive — it contributes to the acoustic impedance but not to the radiated power.

Acoustic impedance and the near-field signature

The acoustic impedance Z = p / u is the fundamental quantity that differs between near and far field.

In the far field, the acoustic impedance is the characteristic impedance of air:

Z = ρ c ≈ 415 Pa·s/m (at 20°C, sea level)

This is a real, frequency-independent quantity. Knowing the pressure, you can immediately deduce the particle velocity.

In the near field, the impedance is complex and frequency-dependent:

Z(r) = (ρ c k r) / (1 + i k r)

where k = ω/c is the wavenumber. At very short distances (kr << 1), the imaginary (reactive) part dominates — Z ≈ iρω r², which is purely reactive. The phase angle between pressure and velocity shifts from 0° (far field) to 90° (very near field).

This has practical consequences: a microphone placed very close to a source experiences a reactive field where particle velocity far exceeds what pressure alone would suggest. The microphone's acoustic response depends on both its pressure sensitivity and its velocity sensitivity, and the two can interfere in the near field.

Practical implications

Measurement: Near-field measurements of loudspeaker drivers exploit the short wavelengths at high frequencies. A 15 cm microphone placed 10 cm from a driver is in the far field above approximately 500 Hz (where the far-field distance for a 10 cm source is about 5 cm) but in the near field below 500 Hz. The near-field measurement captures the driver's direct output without including acoustic interference from other drivers or room boundaries — but the measured response does not account for how those drivers will interact at the listener's distance in the far field.

Microphone placement: A (uni-directional) lavalier microphone clipped to a performer's chest is in the near field of their mouth (distance ≈ 15 cm) for all but the highest frequencies. The reactive field boosts low-frequency energy, producing a proximity effect — a bass rise of several dB that depends on the microphone's directional characteristics. To minimise this, professional vocal microphones are designed to have compensating high-pass filtering.

Loudspeaker directivity: A loudspeaker's measured on-axis response in the far field may differ significantly from measurements taken at the same distance in the near field. The near field contains additional complexity from the unreacted field structure. Directivity patterns — which describe how output varies with angle — are only meaningful in the far field where the concept of a well-defined radiation pattern exists.

Room acoustics at low frequencies: In a small room, even at the opposite wall, the acoustic field at 100 Hz is in the near field (rf ≈ 18 m). Room mode behaviour dominates; simple inverse-square spreading does not apply. This is why low-frequency room response is so spatially dependent — you are essentially moving through the complex reactive near field of a speaker coupled to room-mode resonances rather than through a simple propagating wave field emanating from the speaker.

The transition region

The boundary between near and far field is not sharp. The region where rf/2 < r < 2rf is sometimes called the transition region or intermediate field, where neither the near-field reactive model nor the far-field plane-wave model fully applies. Measurements and calculations in the transition region require more care and often benefit from numerical simulation rather than analytical formulas.

Frequency dependence

A crucial insight: the distinction between near and far field is frequency-dependent. A measurement position may be in the far field at 10 kHz but the near field at 100 Hz. When designing a microphone placement or measurement setup, the lowest frequency of interest sets the requirement — if you need accurate bass response below 100 Hz, you must account for near-field effects at those frequencies.