noise_control.silencers

Reactive silencers by the four-pole (transmission-matrix) method.

A reactive silencer controls noise by reflecting it back to the source with impedance discontinuities — sudden area changes and side branches — rather than by dissipating it in absorptive material. The one-dimensional plane-wave theory represents each acoustic element by a 2x2 transfer (four-pole) matrix relating the sound pressure p and volume velocity S u at its two ends, and a compound silencer is the ordered matrix product of its elements (Bies, Hansen & Howard, Engineering Noise Control 5th ed., §8.8-8.9; Munjal, Acoustics of Ducts and Mufflers).

Transfer matrix (Bies Eq. (8.133)), state vector [p, S u] with the characteristic acoustic impedance Z = rho c / S. The plane-wave element for a straight duct of length L and area S is (Bies Eq. (8.143), no flow)

[[ cos(kL),              j (rho c / S) sin(kL) ],
 [ j (S / rho c) sin(kL), cos(kL)              ]],    k = omega / c,

and a side branch of acoustic impedance Z_b is the shunt element (Bies Eq. (8.144))

[[ 1,       0 ],
 [ 1 / Z_b, 1 ]].

Transmission loss from the compound matrix T (Munjal, Acoustics of Ducts and Mufflers 2nd ed., Eq. (3.27), no flow; reduces to Bies Eq. (8.148) for equal inlet/outlet areas):

TL = 10 log10[ (Zn / Z1) (1/4) | T11 + T12 / Zn + Z1 T21 + (Z1 / Zn) T22 |^2 ]

with Z1 = rho c / S_in and Zn = rho c / S_out. A zero-length element between unequal areas then reproduces the classic sudden-expansion result TL = 10 log10[(1 + m)^2 / (4 m)] with m = S_out / S_in, and the TL is the same from either side, as reciprocity of a passive two-port requires. Bies Eq. (8.141) prints this formula with impedance ratios on T11 and T22 (Z_A1/Z_An and Z_An/Z_A1) instead of the overall Zn/Z1 prefactor; as printed it fails the sudden-expansion limit (see docs/ERRATA.md). TL is the intrinsic attenuation for an anechoic termination. The insertion loss for a source of internal impedance Z_s radiating into a termination impedance Z_r is the extra attenuation of inserting the silencer in place of a direct connection,

IL = 20 log10 | (T11 Z_r + T12 + Z_s Z_r T21 + Z_s T22) / (Z_s + Z_r) |,

which is 0 when the silencer reduces to a through connection (T = I) and, for equal inlet/outlet areas, equals the transmission loss for the anechoic reference Z_s = Z_r = rho c / S (with unequal areas the direct connection contains the same area jump, so its mismatch loss cancels from the insertion loss but not from the transmission loss).

Simple expansion chamber. A chamber of area S_exp and length L between pipes of area S_duct has the closed-form transmission loss (Bies Eq. (8.111)) with area ratio m = S_exp / S_duct

TL = 10 log10[ 1 + (1/4) (m - 1/m)^2 sin^2(kL) ],

peaking at 10 log10[1 + (1/4)(m - 1/m)^2] when kL = pi/2, 3pi/2, ... and dropping to 0 at kL = n pi (no dissipation). The four-pole product reproduces this exactly, and the machinery extends to side-branch (Helmholtz, quarter-wave) and extended-tube resonators that the closed form cannot cover.

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

expansion_chamber

expansion_chamber(
    frequencies: ArrayLike,
    length: float,
    chamber_area: float,
    pipe_area: float,
    *,
    speed_of_sound: float = 343.0,
    density: float = 1.206,
    source_impedance: ArrayLike | None = None,
    radiation_impedance: ArrayLike | None = None,
) -> ReactiveSilencerResult

Simple expansion-chamber silencer (Bies Eq. (8.111) / four-pole).

Parameters

Name	Description
frequencies	Frequencies f, Hz (1-D array).
length	Chamber length L, m.
chamber_area	Chamber cross-sectional area S_exp, m2.
pipe_area	Inlet/outlet pipe area S_duct, m2.
speed_of_sound	Speed of sound c, m/s.
density	Air density rho, kg/m3.
source_impedance	Optional source impedance Z_s for the insertion loss, Pa s/m3.
radiation_impedance	Optional radiation impedance Z_r for the insertion loss, Pa s/m3.

Returns: A ReactiveSilencerResult (its transmission_loss equals the closed form 10 log10[1 + (1/4)(m - 1/m)^2 sin^2(kL)]).

extended_tube_chamber

extended_tube_chamber(
    frequencies: ArrayLike,
    length: float,
    chamber_area: float,
    pipe_area: float,
    *,
    inlet_extension: float = 0.0,
    outlet_extension: float = 0.0,
    speed_of_sound: float = 343.0,
    density: float = 1.206,
    source_impedance: ArrayLike | None = None,
    radiation_impedance: ArrayLike | None = None,
) -> ReactiveSilencerResult

Extended-inlet/outlet expansion chamber (Bies §8.9.7).

The inlet and outlet pipes extend a distance into the chamber, forming annular quarter-wave side branches (of area S_exp - S_duct and lengths equal to the extensions, Bies Eq. (8.156)) at the two junctions. Tuning the extensions (classically L/4 and L/2) places quarter-wave peaks that fill the kL = n pi troughs of the plain expansion chamber. With both extensions 0 the result reduces exactly to expansion_chamber.

Parameters

Name	Description
frequencies	Frequencies f, Hz (1-D array).
length	Chamber length L, m.
chamber_area	Chamber cross-sectional area S_exp, m2.
pipe_area	Inlet/outlet pipe area S_duct, m2.
inlet_extension	Inlet pipe extension into the chamber L_a, m.
outlet_extension	Outlet pipe extension into the chamber L_b, m.
speed_of_sound	Speed of sound c, m/s.
density	Air density rho, kg/m3.
source_impedance	Optional source impedance Z_s, Pa s/m3.
radiation_impedance	Optional radiation impedance Z_r, Pa s/m3.

Returns: A ReactiveSilencerResult.

helmholtz_resonator

helmholtz_resonator(
    frequencies: ArrayLike,
    duct_area: float,
    neck_area: float,
    neck_length: float,
    cavity_volume: float,
    *,
    resistance: float = 0.0,
    speed_of_sound: float = 343.0,
    density: float = 1.206,
    source_impedance: ArrayLike | None = None,
    radiation_impedance: ArrayLike | None = None,
) -> ReactiveSilencerResult

Side-branch Helmholtz resonator on a duct (Bies Eqs. (8.144), (8.152)).

Parameters

Name	Description
frequencies	Frequencies f, Hz (1-D array).
duct_area	Main-duct cross-sectional area S_d, m2.
neck_area	Resonator neck area S_neck, m2.
neck_length	Effective neck length l_e, m.
cavity_volume	Cavity volume V, m3.
resistance	Neck acoustic resistance R, Pa s/m3 (default 0).
speed_of_sound	Speed of sound c, m/s.
density	Air density rho, kg/m3.
source_impedance	Optional source impedance Z_s, Pa s/m3.
radiation_impedance	Optional radiation impedance Z_r, Pa s/m3.

Returns: A ReactiveSilencerResult; resonances holds f_0 = (c / 2 pi) sqrt(S_neck / (l_e V)).

quarter_wave_resonator

quarter_wave_resonator(
    frequencies: ArrayLike,
    duct_area: float,
    length: float,
    branch_area: float,
    *,
    speed_of_sound: float = 343.0,
    density: float = 1.206,
    source_impedance: ArrayLike | None = None,
    radiation_impedance: ArrayLike | None = None,
) -> ReactiveSilencerResult

Closed quarter-wave side-branch tube on a duct (Bies Eqs. (8.144), (8.146)).

Parameters

Name	Description
frequencies	Frequencies f, Hz (1-D array).
duct_area	Main-duct cross-sectional area S_d, m2.
length	Effective branch length l_e, m.
branch_area	Branch tube area S, m2.
speed_of_sound	Speed of sound c, m/s.
density	Air density rho, kg/m3.
source_impedance	Optional source impedance Z_s, Pa s/m3.
radiation_impedance	Optional radiation impedance Z_r, Pa s/m3.

Returns: A ReactiveSilencerResult; resonances holds the odd multiples of f = c / (4 l_e) within the frequency range.

ReactiveSilencerResult

ReactiveSilencerResult(
    frequencies: np.ndarray,
    transmission_loss: np.ndarray,
    insertion_loss: np.ndarray | None,
    transfer_matrix: np.ndarray,
    kind: str,
    resonances: np.ndarray | None = None,
)

Transmission and insertion loss of a reactive silencer over frequency.

Attributes

Name	Description
frequencies	Frequencies f, Hz.
transmission_loss	Transmission loss per frequency, dB.
insertion_loss	Insertion loss per frequency, dB, or None when no source/radiation impedance was supplied.
transfer_matrix	The compound (n_freq, 2, 2) four-pole matrix.
kind	A short label of the device (e.g. "expansion chamber").
resonances	Notable resonance frequencies, Hz (e.g. the resonator tuning frequency), or None.

ReactiveSilencerResult.plot()

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

Plot the transmission (and insertion) loss against frequency.

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

ReactiveSilencerResult.report()

ReactiveSilencerResult.report(
    path: str,
    *,
    metadata: ReportMetadata | None = None,
    engine: str = 'reportlab',
    verbose: bool = False,
    language: str = 'en',
) -> str

Render a reactive-silencer transmission-loss fiche to path.

Writes a one-page silencer-performance sheet: the method-basis line naming the plane-wave four-pole (transfer-matrix) method (Munjal, Acoustics of Ducts and Mufflers 2nd ed., Eq. (3.27); Bies, Hansen & Howard, Engineering Noise Control 5th ed., sections 8.8-8.9), an optional metadata header (client, device, test environment, instrumentation, climate, date), a per-band table (nominal frequency, the transmission loss TL and, when computed, the insertion loss IL) beside the TL (and IL) curves, the boxed mean transmission loss over the analysis bands with the peak transmission loss and the device kind, an optional verdict row against a declared minimum, and a method-basis strip stating the four-pole transmission-loss relation.

Parameters

Name	Description
path	Destination path of the PDF file.
metadata	Optional ReportMetadata supplying the header (client, specimen the device, test_room the test environment, instrumentation, temperature, relative_humidity, pressure, test_date), the footer identity (laboratory, operator, report_id, notes) and, via requirement, a declared minimum mean transmission loss (more transmission loss is better).
engine	Rendering back end; only "reportlab" is supported.
verbose	Accepted for signature symmetry with the other fiches; the silencer table already shows the insertion loss when it was computed.
language	Fiche language: "en" (default) or "es".

Returns: The written path as a str.

Raises

Exception	When
ValueError	If engine is not "reportlab" or language is unknown.
ImportError	If reportlab (or, for the figure, matplotlib) is not installed (pip install phonometry[report]).