materials.absorbers.resistive_sheets

Thin resistive facings, and the resistance of one square metre of them.

A porous absorber is usually covered, and what covers it is a wire mesh, a glass cloth or a sheet of sintered metal. The cover is thin enough that it stores no sound and absorbs almost none by itself, and thin enough that what it does to the layer behind it is settled by one number: the pressure drop across it divided by the face velocity through it, which the chapter these rows come from writes R_s = dp/v and calls the specific, or unit-area, flow resistance.

PUBLISHED_POROUS holds a flow resistivity, sigma, in Pa s/m2: a property of a bulk material, per metre of it, which has to be multiplied by a thickness before it means anything. This catalogue holds a flow resistance, R_s, in Pa s/m: a property of a facing as supplied, already integrated through whatever thickness it has, and there is no thickness to multiply by. The two are one letter apart in most books and a factor of the thickness apart in every calculation, so they are held under two field names that cannot be confused: flow_resistivity_pa_s_m2 there and specific_flow_resistance_pa_s_m here. A mesh of 24.6 Pa s/m is not a material of 24.6 Pa s/m2.

The unit has three spellings in the literature and they are all the same thing: N s/m3, Pa s/m, and the mks rayl of an older tradition. The pages here use the first and the third: TABLE 8.5 and TABLE 8.7 head their resistance column N · s/m3, and TABLE 8.6 heads its own “Flow Resistance, mks rayls (N · s/m3)”. Pa s/m is this library’s spelling of that same unit, and it is the one in the field name.

TABLE 8.5 prints every one of its quantities twice, but only three of the four pairs are one quantity in two systems of units: the wire count in wires per centimetre and wires per inch, the wire diameter in micrometres and mils, the mass in kg/m2 and lb/ft2. The fourth pair prints the flow resistance in N s/m3 and again as a multiple of rho_0 c_0, which is no unit at all. TABLE 8.7 prints its thickness and its mass in the two systems of units, and its flow resistance the two ways TABLE 8.5 does. This catalogue keeps the SI printing of each pair of units, so the numbers here are the page’s own digits rather than arithmetic on them, and that leaves the customary printing free to check the SI one. It is how the first of the two defects these pages carry was found: the finest wire mesh of TABLE 8.5 is printed as 0.31 kg/m2 beside 0.63 lb/ft2, when 0.31 kg/m2 is 0.063 lb/ft2 and the decimal point of the pound cell is one place too far right, and the entry in docs/ERRATA.md argues it. The row keeps the kilogramme cell, which the column above it and the weave of the mesh both support, and its note records the pound cell. The note and not a hedge, because the defective cell is the restatement: this catalogue holds no customary column, so there is no cell here to refuse.

TABLE 8.6 is the one that does not print everything twice. It prints its surface density twice, and its weave and its flow resistance once each and in one unit. The two surface densities disagree by about eleven per cent on all thirteen rows, one wrong factor rather than thirteen slips, and the page does not say which of the two columns carries it: the row holds the gramme per square metre the page prints, in surface_density_g_m2, and its note gives the ounce per square yard beside it, with the entry in docs/ERRATA.md that argues the pair. Thirteen of the twenty-nine flow resistances published here therefore have no second printing to check them at all, and nothing but the second reader stands behind them.

In absorbers/data/, one file per printed table: ver-beranek-2006-table-8-5.json, ver-beranek-2006-table-8-6.json and ver-beranek-2006-table-8-7.json, read at import through the package-data reader in phonometry._internal, the same as every other catalogue here. One file per published table is what makes a key mean something: a row of the glass cloth table is keyed "ver-beranek-2006-table-8-6/glass_cloth_120", and its source names that table, that PDF page and that printed folio and nothing else.

It is not a specification. These are commercial products, the cloths and the sintered sheets named by their manufacturers’ own codes and the wire meshes by nothing but their mesh count, and the pages give no measurement method, no laboratory and no standard for any of the three tables. What they do give is two conditions, and each reaches the rows it belongs to: TABLE 8.7 prints its flow resistance for “Air, 70°F”, which is in the note of all eleven sintered sheets and matters because the resistance of a facing follows the viscosity of the air; and footnote a of TABLE 8.6 says its surface densities are “Averaged over a large sample.”, which is in the note of all thirteen cloths. The running text adds the warning that matters most, about the two cloth tables: the values “represent the linear part of the flow resistance, which is appropriate for design use only if the particle velocity is low”, and above 140 dB the resistance has to be measured as a function of face velocity instead. The eleven sintered sheets are the exception the same page makes for them, and a conditional one: backed by a honeycomb-partitioned air space they “remain linear up to high sound pressure levels and for high-Mach-number grazing flow”, and their table prints a nonlinearity factor where the two cloth tables print none.

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

Constant (mapping).

resistive_sheet_named(name: str) -> tuple[ResistiveSheet, ...]

Every facing a page labels name, matched whole and without case.

Whole and not in part, unlike the other catalogues of this library, and the reason is what these pages use for names: a mesh count, a four-digit cloth number, a manufacturer’s product code. A search that matched part of a name would answer "12" with the twelve-wire mesh, the cloth numbered 120, the cloth numbered 126 and the four sintered sheets FM 122, FM 125, FM 126 and FM 127, none of which has anything to do with any other.

Parameters

Returns: The matching rows, in catalogue order. Empty when none match.

ResistiveSheet(
    *,
    name: str,
    source: str,
    table: str = '',
    variant: str = '',
    basis: Mapping[str, str] = ...,
    approximate: frozenset[str] = frozenset(),
    derived: Mapping[str, str] = ...,
    converted: Mapping[str, tuple[str, str]] = ...,
    carried: Mapping[str, str] = ...,
    ranges: Mapping[str, tuple[float | None, float | None]] = ...,
    bounded_above: frozenset[str] = frozenset(),
    bounded_below: frozenset[str] = frozenset(),
    reported: Mapping[str, tuple[float | tuple[float, float], ...]] = ...,
    unquantified: Mapping[str, str] = ...,
    uncertainty: Mapping[str, float] = ...,
    not_derivable: Mapping[str, str] = ...,
    misprinted: Mapping[str, str] = ...,
    attributed_to: Mapping[str, str] = ...,
    group: str = '',
    note: str = '',
    specific_flow_resistance_pa_s_m: float | None = None,
    normalized_flow_resistance: float | None = None,
    wires_per_cm: float | None = None,
    wire_diameter_um: float | None = None,
    weave_construction: str = '',
    thickness_mm: float | None = None,
    mass_per_area_kg_m2: float | None = None,
    surface_density_g_m2: float | None = None,
    nonlinearity_factor: float | None = None,
)

One thin resistive facing, as its published table prints it.

The name, the citation and the hedges a cell can carry instead of a number are the ones every catalogue row has. What varies here is which columns a row has at all: a wire mesh is described by how many wires it has to the centimetre and how thick they are, a glass cloth by its weave, and a sintered sheet by its thickness and how far from linear it goes, so no two of the three tables print the same columns and every quantity below is optional.

Attributes

ResistiveSheet.basis_of(field_name: str) -> str

What the source says this field is, one of CATALOGUE_BASES.

The five are measured, declared, calculated, estimated and extended.

Parameters

Returns: The field’s own entry in basis, else the row’s, else the empty string, which means the source does not say.

classmethod

ResistiveSheet.from_printed(**cells: Any) -> Self

A row built from the cells its page prints, completed and marked.

The one path that works anything out. The cells are what the page prints, under the field names of the class and with the hedges each cell carries, as a data file writes them. A figure written under a unit the class takes as an alias of its own (an AbsorptionAreaSpectrum takes absorption_area_125_ft2 for absorption_area_125_m2) is converted on its digits with an exact factor and rounded once, and converted records the figure and its unit. The row is then built and held to the contract the class docstring lists, so every cell is checked before any arithmetic reads it. Last, the class fills what follows from those cells (a modulus from a plate speed, a density and a Poisson ratio), never over a cell that holds a value or one the row says something else about, and derived says how each filled value was reached and, when the cells it rests on do not share one basis, the basis of each. Cells the arithmetic cannot take are refused rather than turned into a value that would be wrong: a modulus of 1 GPa and a shear modulus of 0.1 GPa give a Poisson ratio of 4, which no isotropic solid has, and a row whose cells are not meant to give a value says so in not_derivable, which keeps the arithmetic from running.

Cls(...) stays literal: it holds what it is given and works nothing out. To change a cell of a row and have what follows from it follow again, change it in printed_fields and build again here; dataclasses.replace would copy the derived values as they were:

cells = row.printed_fields()
cells["density_kg_m3"] = 2400.0
row = type(row).from_printed(**cells)

Parameters

Returns: The row, with what follows from its cells filled in.

Raises

ResistiveSheet.is_approximate(field_name: str) -> bool

Whether the page prints this field with a ~.

Parameters

Returns: True when the page rounded the cell on purpose.

ResistiveSheet.is_derived(field_name: str) -> bool

Whether this library computed this field instead of reading it.

Parameters

Returns: True when the page did not print it and the value follows from cells that it did. derived says how. A value the page prints in another unit, or gives by reference to another of its rows, answers False: the number is the page’s, and converted or carried says so.

ResistiveSheet.printed(
    field_name: str,
    *,
    wanted_by: str = 'the caller',
) -> float

One quantity this page prints, or a refusal that says what it had.

Every quantity of a row is optional, because the pages print different columns, so a caller passing one into a function that requires a float has to narrow it. Doing it here beats an assertion at each call site: the refusal names the field, who wanted it and what the page had in that cell, which is the difference between a cell the book left empty and a cell holding the word “model”.

Parameters

Returns: The value, as a float.

Raises

ResistiveSheet.printed_fields() -> dict[str, Any]

The cells the page prints, as from_printed takes them.

Every field, the name, the citation, the table and every hedge included, except the values this library derived, derived itself, and a field left at a default that holds nothing (a quantity the page leaves out, an empty text or hedge). A text field whose default says something is kept even when it holds no text: the per of an area per unit is a person unless the row says otherwise, and a row that leaves it empty has said otherwise. A value converted from the page’s unit and one the page gives by reference to another of its rows are the page’s, so they stay, with converted and carried beside them.

For every row from_printed builds, and so for every packaged one, type(row).from_printed(**row.printed_fields()) is the row again, and changing a cell before building it again is how a row is edited without carrying a derived value that no longer follows from it. A derived passed to the literal constructor is the caller’s own; it is left out here with its value, like every derived one, so building again gives back only what the class works out.

Returns: A new dictionary of constructor keywords. The values are the ones the row holds, frozen as the row holds them.

ResistiveSheet.reference_impedance_pa_s_m() -> float

The impedance this row’s own two resistance columns were divided by.

Two of the three tables print the flow resistance twice, once in N s/m3 and once as a multiple of rho_0 c_0, and neither says what they took rho_0 c_0 to be. Dividing one column by the other gives it back, and it is worth asking for: the five wire mesh rows give 407 to 421 Pa s/m, and the sintered metal rows give 400 except for the one block whose columns are 350 and 0.88, which gives 397.7. The two normalized columns are not on the same scale, and a caller comparing them without noticing would be out by two to five per cent, depending on which wire mesh row it is.

It is not a property of the facing. It is a property of the page.

Returns: The characteristic impedance implied by the row, in Pa s/m.

Raises

ResistiveSheet.why_missing(field_name: str) -> str

Why this field is None, in the page’s own terms.

A catalogue that answers None and stops is asking the caller to guess whether the material has no such property, whether the book measured it and printed a dash, or whether the cell holds something that is not a number. Each of those is a different answer.

Parameters

Returns: What the page had in that cell, or the empty string when the field is not missing at all. A field the page has no column for and this library cannot derive, because the cells it would need are themselves a range, answers that it does not follow.

Raises