materials.diffusers.metadiffuser

Metadiffusers: deep-subwavelength Schroeder-like sound diffusers.

A metadiffuser is a rigidly backed slotted panel whose slits are each loaded by an array of Helmholtz resonators (Jimenez, Cox, Romero-Garcia and Groby, Metadiffusers: Deep-subwavelength sound diffusers, Sci. Rep. 7, 5389, 2017). The resonators slow the sound inside each slit, so the slit reaches its quarter-wavelength condition at a fraction of the depth a plain well would need; by giving every slit a different geometry the panel presents a spatially dependent complex reflection coefficient R_n(f) along its face. Tuning that profile to a Schroeder phase grating reproduces the scattering of a quadratic-residue or primitive-root diffuser from a panel 1/46 to 1/20 of the design wavelength thick, and driving single slits to critical coupling adds the perfectly absorbing 0 state that ternary sequences require.

Each slit is modelled with the transfer-matrix chain of slit_helmholtz_absorber (visco-thermal effective parameters, resonator end corrections and slit radiation correction); the panel is locally reacting, so the wells do not couple internally and the far field follows from the Fraunhofer integral of the per-well reflection sequence (predict_diffuser_polar_response) reduced to the ISO 17497-2 directional diffusion coefficient.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

metadiffuser_diffusion_spectrum(
    frequencies: ArrayLike,
    wells: Sequence[MetadiffuserWell | None],
    *,
    depth: float,
    period_m: float,
    angles_deg: ArrayLike = (-90, -85, -80, -75, -70, -65, -60, -55, -50, -45, -40, -35, -30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90),
    source_angle_deg: float = 0.0,
    repetitions: int = 1,
    resonator_geometry: str = 'slit',
    fluid: Fluid = ...,
) -> DiffusionSpectrum

Normalized diffusion-coefficient spectrum d_n(f) of a metadiffuser.

Evaluates the far-field polar response at each frequency with metadiffuser_polar_response, forms the ISO 17497-2 directional diffusion coefficient band by band and normalises it against a flat rigid reference of the same footprint (all wells $R=1$) with normalized_diffusion_coefficient, exactly as the paper reports delta_n.

Parameters

Returns: A DiffusionSpectrum carrying the raw d(f) and the normalised d_n(f).

metadiffuser_polar_response(
    frequency: float,
    wells: Sequence[MetadiffuserWell | None],
    *,
    depth: float,
    period_m: float,
    angles_deg: ArrayLike = (-90, -85, -80, -75, -70, -65, -60, -55, -50, -45, -40, -35, -30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90),
    source_angle_deg: float = 0.0,
    repetitions: int = 1,
    resonator_geometry: str = 'slit',
    fluid: Fluid = ...,
) -> DiffuserPolarResponse

Far-field polar response of a metadiffuser at one frequency.

Computes the per-well complex reflection sequence at frequency with metadiffuser_reflection (the panel is locally reacting, so the slit chains see the incidence angle source_angle_deg) and evaluates the Fraunhofer far field and ISO 17497-2 directional diffusion coefficient with predict_diffuser_polar_response.

Parameters

Returns: A DiffuserPolarResponse.

metadiffuser_reflection(
    frequency: ArrayLike,
    wells: Sequence[MetadiffuserWell | None],
    *,
    depth: float,
    period_m: float,
    angle_rad: float = 0.0,
    resonator_geometry: str = 'slit',
    fluid: Fluid = ...,
) -> MetadiffuserResult

Per-well reflection spectra of a metadiffuser panel (Sci. Rep. Eq. (6)).

Runs the rigidly backed slit transfer-matrix chain of slit_helmholtz_absorber once per well: each MetadiffuserWell becomes a slit of height h_n and depth L loaded by its M resonators on the lattice $a=L/M$, and None wells are flat rigid strips with $R=1$. The panel is locally reacting, so a well’s reflection does not depend on its neighbours and the incidence angle_rad enters only through the front air impedance.

Parameters

Returns: A MetadiffuserResult with one reflection row per well.

MetadiffuserResult(
    frequencies: Real,
    reflection: Complex,
    absorption: Real,
    well_absorption: Real,
    *,
    wells: tuple[MetadiffuserWell | None, ...] | None = None,
    depth: float | None = None,
    period_m: float | None = None,
)

Spectra of a metadiffuser panel, one reflection row per well.

reflection has shape (N, len(frequency)) with the complex pressure reflection factor of each well (flat strips are exactly 1), absorption is the face-averaged energy absorption $\alpha (f)=1-{\mathrm{mean}}_n|R_n{|}^2$ and well_absorption the per-well ${\alpha }_n=1-|R_n{|}^2$. The trailing fields retain the geometry the prediction was run with (wells, depth, period_m) so plot_geometry can draw the panel section; they default to None for hand-built results.

MetadiffuserResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the per-well and face-averaged absorption spectra.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

MetadiffuserResult.plot_geometry(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw the panel cross-section to scale (slits and resonators).

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

Raises

MetadiffuserWell(
    slit_height: float,
    resonators: tuple[HelmholtzResonator, ...],
)

One slit of a metadiffuser panel.

slit_height is the slit opening h_n along the panel face and resonators the Helmholtz resonators loading the slit, ordered from the panel face towards the rigid backing; the resonator lattice step is $a=L/M$ for a panel of depth L and M resonators. All lengths are in metres. A None entry in a well sequence stands for a flat rigid strip of the panel face ($R=1$), the +1 state of ternary-sequence designs.

plot_metadiffuser_panel_geometry(
    wells: Sequence[Any],
    ax: Axes | None = None,
    *,
    depth: float,
    period_m: float,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Draw one period of a metadiffuser panel, to scale.

Side cut of the slotted panel (Sci. Rep. 7:5389 Fig. 1(b)): the face runs along the top with the sound arriving from above, the wells repeat horizontally at the pitch d, and each well is a slit of height h_n descending the panel depth, loaded by its resonators at the lattice step a = L / M shelved sideways into the septum; None wells are flat rigid strips; rigid back wall underneath.

Parameters

Returns: The axes.

Raises