materials.absorbers.standing_wave

Standing-wave-ratio method for normal-incidence absorption and impedance.

BS EN ISO 10534-1:2001, the probe-traverse method of the impedance tube: a loudspeaker drives one pure tone at a time, a probe microphone traverses the tube and reads the maximum and minimum sound pressure levels of the standing wave the specimen sets up, and the position of the first pressure minimum fixes the phase. The reflection magnitude, phase, absorption coefficient and normalised impedance follow from those two readings alone (Clause 5, Eqs. (12)-(26)).

That is the whole method, and it is why it is one module: it consumes a standing-wave ratio and a distance, and needs neither a measured transfer function nor the complex wavenumber and air properties every broadband reduction in the tube goes through. The quantities are the same normal-incidence quantities the two-microphone method reports - $\alpha =1-|r{|}^2$ is Eq. (9) here and Eq. (18) there - measured one frequency at a time; see impedance_tube.

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standing_wave_absorption

standing_wave_absorption(swr: ArrayLike) -> Real

Absorption coefficient from the standing-wave ratio (ISO 10534-1).

Combining $\alpha =1-|r{|}^2$ (Eq. (9)) with $|r|=(s-1)/(s+1)$ (Eq. (14)) gives $\alpha =4s/(s+1{)}^2$.

Parameters

Name	Description
swr	Standing-wave ratio s (>= 1).

Returns: Absorption coefficient alpha in [0, 1].

standing_wave_normalized_impedance

standing_wave_normalized_impedance(
    swr: ArrayLike,
    first_min_distance: ArrayLike,
    wavelength: ArrayLike,
) -> Complex

Normalised impedance from the standing wave (ISO 10534-1, Eqs. (24)-(26)).

$z=Z/Z_0=(1+r)/(1-r)$; the real/imaginary split is Eqs. (25)/(26).

Parameters

Name	Description
swr	Standing-wave ratio s (>= 1).
first_min_distance	Distance x_min1 to the first minimum, in metres.
wavelength	Wavelength lambda0, in metres.

Returns: Normalised surface impedance z (complex).

standing_wave_ratio_from_level

standing_wave_ratio_from_level(level_difference: ArrayLike) -> Real

Standing-wave ratio from a level difference (ISO 10534-1, Eq. (15)).

$s=10^{\Delta L/20}$ with $\Delta L=L_{\max }-L_{\min }$ in decibels.

Parameters

Name	Description
level_difference	Level difference $\Delta L=L_{\max }-L_{\min }$, in dB.

Returns: Standing-wave ratio s (>= 1).

standing_wave_reflection

standing_wave_reflection(
    swr: ArrayLike,
    first_min_distance: ArrayLike,
    wavelength: ArrayLike,
) -> Complex

Complex reflection factor from the standing wave (ISO 10534-1, Eqs. (17)-(23)).

$r=|r|e^{j\varphi }$ with $|r|=(s-1)/(s+1)$ (Eq. (14)) and the phase at the first pressure minimum $\varphi =\pi (4x_{\text{min},1}/{\lambda }_0-1)$ (Eq. (20)).

Parameters

Name	Description
swr	Standing-wave ratio s (>= 1).
first_min_distance	Distance x_min1 from the reference plane to the first pressure minimum (toward the source), in metres.
wavelength	Wavelength lambda0, in metres (Eq. (27)).

Returns: Complex reflection factor r.

standing_wave_reflection_magnitude

standing_wave_reflection_magnitude(swr: ArrayLike) -> Real

Reflection magnitude from the standing-wave ratio (ISO 10534-1, Eq. (14)).

$|r|=(s-1)/(s+1)$.

Parameters

Name	Description
swr	Standing-wave ratio s (>= 1).

Returns: Reflection magnitude |r| in [0, 1].