Music Production 15 min read Updated: October 2026

Microphone Polar Patterns: Cardioid, Figure-8 & Omni Acoustic Rejection

In the physical recording of acoustic music, a microphone is an electroacoustic transducer—a delicate precision device tasked with converting airborne mechanical air pressure fluctuations into proportional alternating electrical audio voltages. However, not all microphones "hear" the world identically. An omnidirectional microphone captures acoustic vibrations equally from all three hundred and sixty degrees, while a figure-8 ribbon microphone is completely deaf to sounds arriving from its physical sides.

In professional recording studios and live concert sound reinforcement, choosing the correct microphone polar pattern is not merely a creative preference. It is a fundamental application of wave physics that dictates acoustic bleed isolation, stage feedback suppression, frequency response uniformity, and the physical phenomenon of the proximity effect. Understanding the mechanical differences between pure pressure and pressure-gradient capsules, the mathematics of the first-order polar equation, and the precise angle of acoustic nulls is an essential studio discipline.

1. The Two Fundamental Acoustic Transducer Types

Every microphone polar pattern in existence—from cardioid and supercardioid to hypercardioid and figure-8—is derived from the combination of just two fundamental physical transducer mechanisms:

1. The Pure Pressure Transducer (Omnidirectional)

In a pure pressure microphone capsule, the flexible conductive diaphragm is stretched across the front of an acoustically sealed rear chamber. The air trapped inside the chamber maintains a constant atmospheric reference pressure.

When an acoustic sound wave arrives at the capsule, the diaphragm deflects strictly in response to the instantaneous scalar sound pressure ($p$, in Pascals) exerted on its front surface relative to the sealed internal chamber. Because scalar atmospheric pressure acts equally in all directions, the capsule is completely insensitive to the angle of sound arrival. A sound wave arriving from $0^\circ$ (front), $90^\circ$ (side), or $180^\circ$ (rear) compresses the diaphragm with identical mechanical force.

2. The Pure Pressure-Gradient Transducer (Figure-8 / Bidirectional)

In a pressure-gradient capsule (such as a classic aluminum ribbon microphone or an unbaffled dual-diaphragm condenser), the diaphragm is completely open to the air on both its front and rear sides.

The diaphragm does not respond to static air pressure; it responds strictly to the pressure difference ($\Delta p$) between its front and rear faces—a physical quantity known as the pressure gradient, which is directly proportional to acoustic particle velocity ($u$):

$$\text{Force} \propto \Delta p = p_{\text{front}} - p_{\text{rear}} \approx d \cdot \frac{\partial p}{\partial x}$$

Pressure gradient equation where $d$ represents the acoustic path length between front and rear surfaces

Notice what happens as sound angle changes:

Sound arriving from the Front ($0^\circ$): Strikes the front face first, creating a positive pressure differential that pushes the diaphragm forward (positive electrical polarity).
Sound arriving from the Rear ($180^\circ$): Strikes the rear face first, pushing the diaphragm backward (yielding identical amplitude, but $180^\circ$ phase-inverted polarity!).
Sound arriving from the Side ($90^\circ$ or $270^\circ$): The sound wave arrives at the front and rear faces at the exact same microsecond with identical pressure. The instantaneous pressure differential across the diaphragm is precisely zero ($\Delta p = 0$). The diaphragm does not move at all—creating an absolute, mathematically infinite acoustic null rejection!

2. The First-Order Polar Pattern Summation Equation

In 1931, RCA acoustician Dr. Harry F. Olson revolutionized audio engineering by demonstrating that all directional polar patterns (cardioid, supercardioid, hypercardioid) can be mathematically synthesized by summing a pure scalar pressure (omnidirectional) capsule with a pressure-gradient (figure-8) capsule:

$$R(\theta) = (1 - k) + k \cdot \cos(\theta)$$

The First-Order Polar Equation where $\theta$ is the incidence angle and $k \in [0, 1]$ is the gradient weighting coefficient

By varying the gradient weighting fraction $k$, the polar geometry morphs smoothly across the entire directional spectrum:

Polar Pattern	Gradient Fraction ($k$)	Mathematical Equation ($R(\theta)$)	Rear Lobe Level ($180^\circ$)	Acoustic Null Angle(s)	Random Energy Efficiency (Distance Factor)
Omnidirectional	$k = 0.000$	$R(\theta) = 1.0$	`0.0 dB` (Equal sensitivity)	None (No nulls)	1.00 (Distance Factor = 1.0x)
Subcardioid (Wide)	$k = 0.333$	$R(\theta) = 0.67 + 0.33\cos\theta$	`-9.5 dB`	None	0.67 (Distance Factor = 1.2x)
Cardioid (Heart-Shaped)	$k = 0.500$	$R(\theta) = 0.50 + 0.50\cos\theta$	`-\infty \text{ dB}` (Complete cancellation)	180° (Dead rear)	0.33 (Distance Factor = 1.7x)
Supercardioid	$k = 0.586$	$R(\theta) = 0.414 + 0.586\cos\theta$	`-11.6 dB` (Small rear lobe)	126° & 234°	0.27 (Distance Factor = 1.9x)
Hypercardioid	$k = 0.750$	$R(\theta) = 0.25 + 0.75\cos\theta$	`-6.0 dB` (Prominent rear lobe)	110° & 250°	0.25 (Distance Factor = 2.0x, Maximum side rejection!)
Figure-8 (Bidirectional)	$k = 1.000$	$R(\theta) = \cos\theta$	`0.0 dB` (180° out of phase)	90° & 270° (Dead sides)	0.33 (Distance Factor = 1.7x)

3. Strategic Acoustic Rejection: Isolating Bleed in the Studio & Live

Understanding the exact mathematical null angles of different polar patterns enables engineers to eliminate acoustic bleed with surgical precision:

1. The Cardioid 180° Rear Null (Single Floor Wedge Monitor)

Because standard cardioid microphones have their absolute null angle positioned at dead-center rear ($180^\circ$), they are ideal for live vocalists when a single stage floor wedge monitor is placed directly in front of the singer, pointing straight at the back of the microphone.

2. The Supercardioid 126° Null (Dual Floor Wedge Monitors)

Many professional concert stages place two wedge monitors angled on either side of the singer. If you use a standard cardioid microphone, the monitors point directly into the mic's active pickup zone at $135^\circ$! Switching to a supercardioid microphone places its deep acoustic nulls at $126^\circ$, aiming the dead zones directly at the speaker horns and providing maximum acoustic feedback immunity!

3. The Figure-8 90° Side Null (Singer-Songwriter Acoustic Isolation)

One of the hardest studio challenges is recording a singer playing an acoustic guitar simultaneously. If you use cardioid microphones, the vocal mic captures heavy acoustic guitar bleed, and the guitar mic captures vocal bleed, causing phase comb-filtering when mixed.

💡 The Figure-8 Cross-Null Technique

Place two figure-8 microphones: aim the vocal mic at the singer's mouth, but tilt its $90^\circ$ side null plane directly at the acoustic guitar body. Place the guitar mic pointing at the 12th fret, but tilt its side null plane directly at the singer's mouth. Because figure-8 capsules have true physical cancellation nulls exceeding $-30\text{ dB}$ to $-40\text{ dB}$ at their sides, the acoustic bleed is virtually eliminated—giving you pure, isolated vocal and guitar tracks!

4. The Physics of the Proximity Effect

Why do directional microphones boost bass frequencies when placed close to a sound source, while omnidirectional microphones do not? This physical phenomenon is the Proximity Effect.

In a pressure-gradient capsule, the net force driving the diaphragm depends on the vector phase difference between the front and rear ports. When a sound source is far away, the sound waves arrive as planar wavefronts. When a sound source moves close (within $10\text{ to } 15\text{ cm}$), the wavefronts are sharply curved (spherical waves). Under the Inverse-Square Law, the distance from the source to the front port ($r$) is noticeably shorter than the distance to the rear port ($r + \Delta r$).

At low frequencies, this curvature disparity creates an overwhelming amplitude differential between the front and rear ports, boosting bass frequencies by up to +15 dB to +20 dB below 100 Hz! Omnidirectional capsules—having only a single front port—experience zero phase disparity, exhibiting zero proximity effect regardless of distance.

🎛️ Related Studio LOOS Production Tools

Inspect phase alignment and microphone correlation with our Audio Spectrogram & Lossless Phase Checker, eliminate multi-mic comb filtering using our Phase Cancellation & Comb Filtering Guide, master M/S stereo mic arrays in our Mid/Side Processing Guide, or explore monitor placement with the SBIR Speaker Boundary Interference Guide.

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Polar Pattern	Gradient Fraction (\(k\))	Mathematical Equation (\(R(\theta)\))	Rear Lobe Level (\(180^\circ\))	Acoustic Null Angle(s)	Random Energy Efficiency (Distance Factor)
Omnidirectional	\(k = 0.000\)	\(R(\theta) = 1.0\)	`0.0 dB` (Equal sensitivity)	None (No nulls)	1.00 (Distance Factor = 1.0x)
Subcardioid (Wide)	\(k = 0.333\)	\(R(\theta) = 0.67 + 0.33\cos\theta\)	`-9.5 dB`	None	0.67 (Distance Factor = 1.2x)
Cardioid (Heart-Shaped)	\(k = 0.500\)	\(R(\theta) = 0.50 + 0.50\cos\theta\)	`-\infty \text{ dB}` (Complete cancellation)	180° (Dead rear)	0.33 (Distance Factor = 1.7x)
Supercardioid	\(k = 0.586\)	\(R(\theta) = 0.414 + 0.586\cos\theta\)	`-11.6 dB` (Small rear lobe)	126° & 234°	0.27 (Distance Factor = 1.9x)
Hypercardioid	\(k = 0.750\)	\(R(\theta) = 0.25 + 0.75\cos\theta\)	`-6.0 dB` (Prominent rear lobe)	110° & 250°	0.25 (Distance Factor = 2.0x, Maximum side rejection!)
Figure-8 (Bidirectional)	\(k = 1.000\)	\(R(\theta) = \cos\theta\)	`0.0 dB` (180° out of phase)	90° & 270° (Dead sides)	0.33 (Distance Factor = 1.7x)