Radiation Factor

[Lars H]

Where does the Radiation Factor / Radiation Impedance come from and why does it boost higher frequencies?
[regarding “Elements of Acoustic Phonetics”, Chapter 7]

[Simon]

Radiation is what happens at the lips as sound waves within the vocal tract are propagated out into the free air.

A detailed understanding of the physics is a little beyond our needs, but here’s a simple way to understand what is happening at the lips:

The sound pressure variations inside the vocal tract are due to waves propagating up and down the tube and being reflected back at both the ends. The air within the vocal tract is approximately, on average, stationary (forget about the flow caused by breathing – it’s very slow compared to the speed of sound).

The radiation effect is what happens when this trapped “piston” of air in the vocal tract causes the air in the free field outside the lips to move, creating sound waves that propagate out from the lips.

The effect is to differentiate the signal, which has the same effect as imposing a filter that boosts higher frequencies, as in Figure 7.7 of “Elements of Acoustic Phonetics” by Ladefoged.

Because this is a constant effect (independent of the settings of the articulators and of F0), it is common to omit this filter and include the effect in the source spectrum. Or, if the source is a simple pulse train with a flat spectrum, the vocal tract filter will include the lip radiation effect.

[Joseph M]

Following up on Radiance Factor:

Q1: Since vowels are essentially ‘low pass filtered’ by the effects of the resonances in the vocal tract, is it fair to say that the Radiance Factor is more pronounced/noticeable on consonants, especially unvoiced ones?

Q2: Also, is this effect localized, in the sense that it dissipates with distance? If I measure the spectrum of recorded speech from further away from the speaker’s mouth, will the high freq boost go away (as a function of distance), or is it that once the air outside the mouth is perturbed, the spectrum is essentially fixed? The latter would be my intuition, but if radiance factor is caused by some pressure differential between the air in the vocal tract and the air outside the lips, maybe it could change as the pressure normalizes to some steady state as the sound waves propagate further outward. Kind of like how a rock in a pond makes a big splash but then the ripples become normalized as they move away from the splash point.

[Simon]

A1: Think of the vocal tract as a set of bandpass filters (one for each resonant frequency), rather than a low-pass filter. The radiation effect at the lips is essentially a constant and has the same effect on all speech sounds.

A2: It should not matter how far from the speakers’ mouth you place the microphone: in theory the signal should be the same (just with reducing intensity further from the mouth). In practice, microphone placement will have an effect if the microphone is directional (e.g., the proximity effect which is evident in the voiceovers of the videos on this site). A perfect omnidirectional microphone recording speech in a perfect anechoic chamber could in theory be placed at any distance from the mouth.

[Author]

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