Radiation from the Mouth

The mouth opening serves as the final acoustic interface between the vocal tract and the external environment, transforming the volume velocity at the lips into radiated sound pressure. Understanding radiation from the mouth requires considering the impedance load presented by the external air, the directional characteristics of radiation, and the acoustic effects of the head and torso surrounding the mouth opening.

The Mouth as an Acoustic Source

The mouth opening acts as a termination of the vocal tract resonator system, where internal acoustic energy transfers to external radiation.

Source Characteristics

Volume Velocity Source

• Vocal tract produces time-varying airflow at lips
• Flow rate modulated by glottal pulses and tract resonances
• Volume velocity (m³/s) drives radiation
• Mouth opening area affects radiation efficiency
• Lip configuration modulates source properties

Effective Source Size

• Typical mouth opening: 2-4 cm² area
• Equivalent circular radius: approximately 0.8-1.1 cm
• Size varies with vowel, speech gesture, singing style
• Rounded vowels reduce opening area
• Open vowels maximize opening area

Frequency-Dependent Behavior

• Low frequencies (f < 500 Hz): wavelength >> mouth dimensions
• Mid frequencies (500-3000 Hz): wavelength comparable to mouth
• High frequencies (f > 3000 Hz): wavelength << mouth dimensions
• Radiation characteristics change across frequency range

Comparison with Simple Sources

At Low Frequencies

• Mouth approximates monopole source
• Nearly omnidirectional radiation
• Radiation impedance similar to piston in infinite baffle
• Efficient coupling to external air

At High Frequencies

• Directional effects become pronounced
• Forward radiation enhanced
• Beaming occurs at very high frequencies
• Complex interaction with head geometry

Radiation Impedance of the Mouth

The radiation impedance determines how efficiently volume velocity at the lips converts to radiated sound pressure.

Definition and Importance

Radiation impedance Z_rad relates pressure to volume velocity at mouth opening:

Z_rad = p/U = R_rad + jX_rad

Where:

• p: acoustic pressure at mouth opening
• U: volume velocity at mouth opening
• R_rad: radiation resistance (real part)
• X_rad: radiation reactance (imaginary part)
• j: imaginary unit

Physical Significance

• Radiation resistance represents power loss to radiation
• Radiation reactance represents stored reactive energy
• Determines acoustic load on vocal tract
• Affects formant frequencies and bandwidths
• Influences overall spectral shape of radiated sound

Frequency Dependence

Figure 9.3: Radiation resistance and reactance as functions of frequency for a circular mouth opening, showing transition from reactance-dominated low frequencies to resistance-dominated high frequencies.

Low-Frequency Region (ka << 1)

For ka << 1 (where k = wave number, a = mouth radius):

R_rad ≈ ρc(ka)² × (area/4π)
X_rad ≈ ρcka × (area/2π)

Characteristics

• Reactance much larger than resistance
• Inertive (mass-like) reactance dominates
• Poor radiation efficiency
• Most energy stored reactively near mouth

Mid-Frequency Transition

• Resistance increases with frequency
• Reactance increases more slowly
• Gradual shift toward resistance domination
• Occurs around ka ≈ 0.5 to 1.0

High-Frequency Region (ka > 1)

• Radiation resistance approaches constant: R_rad ≈ ρc × area
• Reactance becomes negligible
• Efficient radiation
• Real impedance characteristic

Practical Frequency Values

For typical mouth opening (equivalent radius a ≈ 1 cm):

Low-Frequency Limit (f = 500 Hz)

• ka = 2πf × a / c ≈ 0.09
• Reactance dominates
• Poor radiation efficiency

Transition Region (f = 2000 Hz)

• ka ≈ 0.37
• Resistance and reactance comparable
• Improving radiation efficiency

High-Frequency Region (f = 5000 Hz)

• ka ≈ 0.92
• Resistance dominates
• Good radiation efficiency

Effect on Vocal Tract Transfer Function

Radiation impedance affects the vocal tract in several ways:

Formant Frequency Shifts

• Inertive reactance at mouth lowers formant frequencies
• Magnitude depends on frequency
• Largest effect on F1 (first formant)
• Smaller effects on higher formants
• Can shift F1 by 50-100 Hz downward

Formant Bandwidth Effects

• Radiation resistance increases formant damping
• Broader bandwidths at higher frequencies
• Affects formant amplitude
• Contributes to natural spectral slope

Overall Spectral Shaping

• High-pass filter characteristic
• +6 dB/octave slope (pressure proportional to frequency)
• Emphasizes high-frequency harmonics
• Partially compensates for glottal source spectral decline
• Results in net spectral slope of approximately -12 dB/octave

Directivity of Mouth Radiation

Sound radiation from the mouth is not uniform in all directions, particularly at higher frequencies.

Angular Dependence

Low Frequencies (Long Wavelengths)

• Nearly omnidirectional radiation
• Minimal variation with angle
• Pressure approximately equal in all directions
• Mouth acts as simple monopole source

Mid Frequencies (Moderate Wavelengths)

• Forward direction begins to dominate
• Lateral radiation reduces
• Backward radiation significantly attenuated
• Gradual transition to directional pattern

High Frequencies (Short Wavelengths)

• Strong forward directivity
• Beaming effect prominent
• Side and rear radiation greatly reduced
• Head shadow creates additional attenuation

Measured Directivity Patterns

Research on voice directivity reveals:

Typical Patterns

• At 500 Hz: nearly uniform (±3 dB variation)
• At 2000 Hz: 6-10 dB front-to-back difference
• At 4000 Hz: 15-20 dB front-to-back difference
• At 8000 Hz: 20-30 dB front-to-back difference

Individual Variation

• Head size affects directivity
• Facial features influence patterns
• Mouth opening configuration matters
• Vowel shape creates variations

Practical Implications

For Listeners

• Speech most intelligible directly in front of speaker
• High-frequency consonants critically affected
• Turning away reduces clarity
• Distance and angle interact

For Speakers/Singers

• Must orient toward audience for maximum intelligibility
• Cannot reliably monitor own high-frequency output
• Microphone placement critical for recording
• Stage position relative to audience matters

For Clinical Assessment

• Standardize angular position (typically 0° or 45°)
• Document microphone placement
• Control for head position
• Consider directivity in interpretation

Influence of Head and Torso

The mouth opening is not an isolated source but part of a complex acoustic system including the head and torso.

Head Effects

Diffraction Around Head

• Sound bends around head to reach opposite side
• Diffraction frequency-dependent
• Low frequencies diffract easily
• High frequencies create “head shadow”

Baffle Effect

• Head acts as partial acoustic baffle
• Increases forward radiation efficiency
• Reduces backward radiation
• Similar to mounting speaker in cabinet

Acoustic Scattering

• Head scatters high-frequency energy
• Complex interference patterns
• Direction-dependent effects
• Individual anatomical variation significant

Torso Effects

Reflections from Chest

• Low-frequency sound reflects from chest
• Creates interference patterns
• Can produce comb-filtering effects
• Affects self-perception of voice

Body Resonances

• Chest cavity has resonant frequencies
• Can couple to voice at specific frequencies
• Contributes to perceived “chest resonance”
• More prominent in males due to larger thorax

Postural Effects

• Body position affects acoustic environment
• Sitting versus standing creates differences
• Proximity to reflecting surfaces matters
• Performance posture influences radiation

Lip Radiation Characteristic

The transfer function from volume velocity to radiated pressure exhibits a characteristic frequency response.

First-Order High-Pass Filter

The radiation characteristic can be approximated as:

H_rad(ω) ≈ jωρ/2π for low frequencies

Where:

• H_rad: radiation transfer function
• ω: angular frequency
• ρ: air density
• j: imaginary unit

Implications

• Magnitude increases linearly with frequency (+6 dB/octave)
• Phase shift of 90° at all frequencies
• Acts as first-order differentiator
• Emphasizes rapid changes in volume velocity

Effect on Speech Spectrum

Source-Filter-Radiation Chain

The complete speech spectrum results from:

P_rad(ω) = U_g(ω) × H_tract(ω) × H_rad(ω)

Where:

• P_rad: radiated pressure spectrum
• U_g: glottal flow spectrum
• H_tract: vocal tract transfer function
• H_rad: radiation transfer function

Individual Contributions

• Glottal source: approximately -12 dB/octave slope
• Vocal tract: resonances (formants) with peaks and valleys
• Radiation: +6 dB/octave slope
• Net result: approximately -6 dB/octave overall slope with formant peaks

Volume Velocity versus Pressure

Understanding the distinction is crucial:

Volume Velocity at Lips

• Actual air flow rate
• Determined by glottal source and vocal tract filtering
• Has characteristic spectral shape
• Not directly measurable in speech

Radiated Pressure

• What microphones sense
• What listeners hear
• Result of volume velocity × radiation impedance
• Includes +6 dB/octave radiation boost

Clinical Measurement

• Most measurements capture radiated pressure
• Inverse filtering can recover volume velocity
• Radiation effect must be removed to obtain glottal flow
• Important for source-filter separation

Modifications of Mouth Radiation

Speakers and singers can modify radiation characteristics through articulatory adjustments:

Lip Rounding

Acoustic Effects

• Reduces effective mouth opening area
• Increases radiation reactance
• Lowers formant frequencies
• Changes directivity pattern
• Common in [u] and [o] vowels

Radiation Consequences

• Reduced high-frequency radiation efficiency
• More omnidirectional pattern
• Lower overall intensity (all else equal)
• Spectral energy shifted to lower frequencies

Lip Spreading

Acoustic Effects

• Increases effective mouth opening area
• Decreases radiation reactance
• Raises formant frequencies
• More directional at high frequencies
• Common in [i] and [e] vowels

Radiation Consequences

• Enhanced high-frequency radiation
• More directional pattern
• Higher overall intensity (all else equal)
• Brighter spectral quality

Mouth Opening Size

Wide Opening (Open Vowels)

• Maximum radiation efficiency
• Lowest radiation reactance
• Most effective high-frequency radiation
• Used in loud singing and projection

Narrow Opening (Closed Vowels)

• Reduced radiation efficiency
• Higher radiation reactance
• Less effective high-frequency radiation
• Requires more internal pressure for same output

Clinical and Pedagogical Applications

Understanding mouth radiation informs assessment and training:

Assessment Considerations

Microphone Placement Standards

• Distance: typically 30 cm to 1 meter
• Angle: 0° (directly in front) or 45° (off-axis)
• Height: level with mouth
• Document all parameters
• Maintain consistency across measurements

Directivity Compensation

• Off-axis measurements show reduced high frequencies
• Can correct mathematically if directivity known
• Or maintain standard geometry
• Important for comparing across studies

Radiation Efficiency Factors

• Vowel differences affect radiated level
• Open vowels radiate more efficiently than closed
• Must consider in vowel-specific measures
• Normalize for comparison

Pedagogical Strategies

Teaching Projection

• Emphasize forward orientation
• Open mouth configuration for maximum radiation
• “Speaking/singing to back of room”
• Awareness of directional effects

Vowel Modification for Loudness

• Opening vowels increases radiation efficiency
• Common strategy in operatic singing
• Must balance with vowel intelligibility
• Systematic training approach

Acoustic Feedback Awareness

• Singers hear different spectrum than audience
• Bone conduction adds low frequencies
• Direct radiation differs from reflected sound
• Training to compensate for perceptual differences

Summary

The mouth opening serves as the critical acoustic interface between the vocal tract and external environment, with radiation characteristics determined by opening size, frequency, and surrounding anatomical structures. Radiation impedance, comprising frequency-dependent resistance and reactance, governs the efficiency of converting volume velocity to radiated pressure, transitioning from reactance-dominated behavior at low frequencies to resistance-dominated behavior at high frequencies. This frequency dependence creates a +6 dB/octave spectral boost that partially compensates for the declining glottal source spectrum.

Directivity of mouth radiation increases with frequency, from nearly omnidirectional patterns at low frequencies to strong forward bias at high frequencies, with typical front-to-back differences of 15-20 dB at 4000 Hz. The head and torso significantly influence radiation through diffraction, baffling, and reflection effects, creating complex angular patterns that vary individually. Articulatory modifications—particularly lip rounding/spreading and mouth opening size—allow speakers and singers to adjust radiation efficiency and directivity for different communicative demands.

Clinical assessment must standardize microphone position and angular orientation to ensure measurement consistency, while pedagogical applications emphasize forward orientation, optimal mouth opening, and awareness of the difference between self-perception and listener perception of voice quality. Understanding mouth radiation mechanics enables more effective voice training, more accurate acoustic assessment, and better interpretation of voice measurements in research and clinical contexts.

Key Takeaways

• ✅ Mouth radiation impedance transitions from inertive reactance dominance at low frequencies to radiation resistance dominance at high frequencies
• ✅ Radiation characteristic provides +6 dB/octave spectral boost, partially compensating for declining glottal source spectrum
• ✅ Directivity increases with frequency: omnidirectional below 500 Hz, strong forward bias above 3000 Hz
• ✅ Head acts as acoustic baffle enhancing forward radiation and creating head shadow reducing backward radiation
• ✅ Typical front-to-back differences reach 15-20 dB at 4000 Hz, critically affecting high-frequency consonant perception
• ✅ Lip configuration (rounding vs. spreading) and mouth opening size significantly affect radiation efficiency
• ✅ Clinical measurement requires standardized microphone distance (30 cm - 1 m) and angle (0° or 45°)
• ✅ Speakers/singers cannot reliably monitor their own high-frequency output due to different acoustic path

Related Topics

• Sound Intensity Level and Sound Pressure Level
• Radiation from Simple Sources
• Vocal Tract Transfer Gain
• Acoustic Impedance of Tubes
• The Glottal Source Function

Further Reading

1. Flanagan, J. L. (1972). Speech Analysis, Synthesis and Perception (2nd ed.). Springer-Verlag.
2. Kinsler, L. E., Frey, A. R., Coppens, A. B., & Sanders, J. V. (2000). Fundamentals of Acoustics (4th ed.). John Wiley & Sons.
3. Dunn, H. K., & Farnsworth, D. W. (1939). Exploration of pressure field around the human head during speech. Journal of the Acoustical Society of America, 10, 184-199.
4. Chu, W. T., & Warnock, A. C. C. (2002). Detailed directivity of sound fields around human talkers. NRC Publications Archive.
5. Marshall, A. H., & Meyer, J. (1985). The directivity and auditory impressions of singers. Acustica, 58, 130-140.