+9

CHANGELOG.md

Reviewed

··· 17 17 grid. Its `.plot()` draws the response on a logarithmic frequency axis, the 18 18 combined curve with the two stages as light companions; `language="es"` 19 19 renders the Spanish labels. 20 20 + - `piston_directivity_pattern()` and the `PistonDirectivity` result: the 21 21 + far-field directivity of a rigid baffled circular piston 22 22 + (`D(theta) = 2 J1(ka sin theta)/(ka sin theta)`, Beranek & Mellow Eq. (4.42)) 23 23 + is now a plottable result carrying the polar-angle grid, the linear 24 24 + directivity and its dB form and the `ka` value(s). Its `.plot()` draws the 25 25 + classic polar beam pattern in dB over the front hemisphere; passing several 26 26 + `ka` shows them as one family, so the main lobe narrowing and the emergence 27 27 + of the side lobes read at a glance. `language="es"` renders the Spanish 28 28 + labels. The underlying `piston_directivity()` maths is unchanged. 20 29 - `TrendTestResult.plot()`: a one-line canonical figure for the nonparametric 21 30 trend test (Bendat & Piersol, *Random Data* Sec. 4.5.2), mirroring the 22 31 companion `StationarityTestResult.plot()`. It draws the tested sequence

+2

llms-full.txt

Reviewed

··· 12296 12296 | `radiating_piston` | `function` | **Radiation of a rigid baffled circular piston (Beranek & Mellow §4.19/§13.7).**<br>• `radius` a [m], `frequencies` [Hz]<br>• `speed_of_sound` (Default: 343), `density` (Default: 1.206)<br>• `angles`: directivity polar angles [rad] (Default: None) | `res = radiating_piston(0.1, freqs)`<br><br>• `RadiatingPistonResult` | 12297 12297 | `piston_resistance` / `piston_reactance` | `function` | **Normalized piston radiation impedance R1 = 1−2J1(x)/x, X1 = 2H1(x)/x, x = 2ka (Beranek & Mellow Eqs. 13.117/13.118).** | `piston_resistance(2.0) # 0.4233` | 12298 12298 | `piston_directivity` | `function` | **Far-field piston directivity 2·J1(ka·sinθ)/(ka·sinθ).**<br>• `ka`, `theta` [rad] | `piston_directivity(5.0, 0.3)` | 12299 12299 + | `piston_directivity_pattern` | `function` | **Far-field directivity (beam) pattern of one or more baffled pistons.**<br>• `ka` (scalar or 1-D)<br>• `angles` [rad] (Default: front hemisphere −90°…+90°) | `p = piston_directivity_pattern([3, 8, 16])`<br><br>• `PistonDirectivity` | 12299 12300 | `RadiatingPistonResult` | `dataclass` | **Piston radiation result.**<br>• `ka`, `resistance`/`reactance`, `radiation_resistance`/`radiation_reactance` [N·s/m], `radiation_mass` = 8ρa³/3 [kg], `directivity_index` [dB], `directivity`<br>• `.plot()`: R1/X1 vs ka | `res.radiation_mass` | 12301 12301 + | `PistonDirectivity` | `dataclass` | **Piston directivity-pattern result.**<br>• `angles` [rad], `ka`, `directivity` (linear), `directivity_db`<br>• `.plot()`: polar beam pattern in dB (family over ka) | `p.plot()` | 12300 12302 | `loudspeaker_characteristics` | `function` | **Rated loudspeaker characteristics for an IEC 60268-5 report.**<br>• `frequencies`, `spl_db` (on-axis SPL), `rated_impedance` R [Ω]<br>• `input_voltage` (Default: √R → 1 W), `distance` (Default: 1 m), `sensitivity_band`, `tolerance_db`<br>• `impedance`, `distortion`, `directivity`/`polar` panels | `res = loudspeaker_characteristics(f, spl, 8.0)`<br><br>• `LoudspeakerCharacteristics` | 12301 12303 | `LoudspeakerCharacteristics` | `dataclass` | **Loudspeaker rated-characteristics result (IEC 60268-5).**<br>• `sensitivity_level_db` (1 W/1 m, 20.3/20.4), `effective_range` (21.2), `reference_level_db`, `characteristic_sensitivity_pa`, `minimum_impedance`<br>• `.report()`: IEC 60268-5 fiche (graphs to IEC 60263) | `res.effective_range` | 12302 12304 | `microphone_characteristics` | `function` | **Rated microphone characteristics for an IEC 60268-4 report.**<br>• `frequencies`, `response_db` (free-field, re the reference frequency), `sensitivity_mv_per_pa` M [mV/Pa]<br>• `reference_frequency` (Default: 1 kHz), `tolerance_db` (Default: 2), `rated_impedance`/`minimum_load_impedance` [Ω], `noise_voltage` or `equivalent_noise_level_db`, `max_spl_db`/`max_spl_thd_percent`<br>• `distortion`, `noise_spectrum`, `polar` panels; `powering`, `supply_current_ma` | `res = microphone_characteristics(f, resp, 12.5)`<br><br>• `MicrophoneCharacteristics` |

+2

docs/api-reference.md

Reviewed

··· 377 377 | `radiating_piston` | `function` | **Radiation of a rigid baffled circular piston (Beranek & Mellow §4.19/§13.7).**<br>• `radius` a [m], `frequencies` [Hz]<br>• `speed_of_sound` (Default: 343), `density` (Default: 1.206)<br>• `angles`: directivity polar angles [rad] (Default: None) | `res = radiating_piston(0.1, freqs)`<br><br>• `RadiatingPistonResult` | 378 378 | `piston_resistance` / `piston_reactance` | `function` | **Normalized piston radiation impedance R1 = 1−2J1(x)/x, X1 = 2H1(x)/x, x = 2ka (Beranek & Mellow Eqs. 13.117/13.118).** | `piston_resistance(2.0) # 0.4233` | 379 379 | `piston_directivity` | `function` | **Far-field piston directivity 2·J1(ka·sinθ)/(ka·sinθ).**<br>• `ka`, `theta` [rad] | `piston_directivity(5.0, 0.3)` | 380 380 + | `piston_directivity_pattern` | `function` | **Far-field directivity (beam) pattern of one or more baffled pistons.**<br>• `ka` (scalar or 1-D)<br>• `angles` [rad] (Default: front hemisphere −90°…+90°) | `p = piston_directivity_pattern([3, 8, 16])`<br><br>• `PistonDirectivity` | 380 381 | `RadiatingPistonResult` | `dataclass` | **Piston radiation result.**<br>• `ka`, `resistance`/`reactance`, `radiation_resistance`/`radiation_reactance` [N·s/m], `radiation_mass` = 8ρa³/3 [kg], `directivity_index` [dB], `directivity`<br>• `.plot()`: R1/X1 vs ka | `res.radiation_mass` | 382 382 + | `PistonDirectivity` | `dataclass` | **Piston directivity-pattern result.**<br>• `angles` [rad], `ka`, `directivity` (linear), `directivity_db`<br>• `.plot()`: polar beam pattern in dB (family over ka) | `p.plot()` | 381 383 | `loudspeaker_characteristics` | `function` | **Rated loudspeaker characteristics for an IEC 60268-5 report.**<br>• `frequencies`, `spl_db` (on-axis SPL), `rated_impedance` R [Ω]<br>• `input_voltage` (Default: √R → 1 W), `distance` (Default: 1 m), `sensitivity_band`, `tolerance_db`<br>• `impedance`, `distortion`, `directivity`/`polar` panels | `res = loudspeaker_characteristics(f, spl, 8.0)`<br><br>• `LoudspeakerCharacteristics` | 382 384 | `LoudspeakerCharacteristics` | `dataclass` | **Loudspeaker rated-characteristics result (IEC 60268-5).**<br>• `sensitivity_level_db` (1 W/1 m, 20.3/20.4), `effective_range` (21.2), `reference_level_db`, `characteristic_sensitivity_pa`, `minimum_impedance`<br>• `.report()`: IEC 60268-5 fiche (graphs to IEC 60263) | `res.effective_range` | 383 385 | `microphone_characteristics` | `function` | **Rated microphone characteristics for an IEC 60268-4 report.**<br>• `frequencies`, `response_db` (free-field, re the reference frequency), `sensitivity_mv_per_pa` M [mV/Pa]<br>• `reference_frequency` (Default: 1 kHz), `tolerance_db` (Default: 2), `rated_impedance`/`minimum_load_impedance` [Ω], `noise_voltage` or `equivalent_noise_level_db`, `max_spl_db`/`max_spl_thd_percent`<br>• `distortion`, `noise_spectrum`, `polar` panels; `powering`, `supply_current_ma` | `res = microphone_characteristics(f, resp, 12.5)`<br><br>• `MicrophoneCharacteristics` |

+30

docs/electroacoustics.md

Reviewed

··· 327 327 callable directly. The piston is the companion radiator of the 328 328 [industrial noise-control silencers](noise-control.md). 329 329 330 330 + The far-field **directivity pattern** is a plottable result in its own right: 331 331 + `piston_directivity_pattern(ka)` samples `D(theta)` at one or more `ka` values 332 332 + and returns a `PistonDirectivity` (the polar angle grid, the linear `directivity` 333 333 + and its dB form `directivity_db`, and the `ka` values) whose `.plot()` draws the 334 334 + classic polar beam pattern. Several `ka` are shown as one family, so the main 335 335 + lobe narrowing and the side lobes appearing read at a glance: 336 336 + 337 337 + ```python 338 338 + from phonometry import piston_directivity_pattern 339 339 + 340 340 + pattern = piston_directivity_pattern([3.0, 8.0, 16.0]) 341 341 + print(pattern.directivity_db.shape) # (3, 361): one row per ka 342 342 + pattern.plot() # polar beam pattern in dB (needs matplotlib) 343 343 + ``` 344 344 + 345 345 + <picture><source media="(prefers-color-scheme: dark)" srcset="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/piston_directivity_dark.svg"><img src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/piston_directivity.svg" alt="Polar far-field directivity of a baffled circular piston at ka of 3, 8 and 16 over the front hemisphere, the on-axis level at the top as the 0 dB reference, showing the main lobe narrowing and the side lobes appearing as ka grows" width="72%"></picture> 346 346 + 347 347 + <details> 348 348 + <summary>Show the code for this figure</summary> 349 349 + 350 350 + ```python 351 351 + import matplotlib.pyplot as plt 352 352 + from phonometry import piston_directivity_pattern 353 353 + 354 354 + piston_directivity_pattern([3.0, 8.0, 16.0]).plot() 355 355 + plt.show() 356 356 + ``` 357 357 + 358 358 + </details> 359 359 + 330 360 ## References 331 361 332 362 - Beranek, L. L., & Mellow, T. J. (2012). *Acoustics: Sound fields and

+12

scripts/generate_graphs.py

Reviewed

··· 4062 4062 plt.close() 4063 4063 4064 4064 4065 4065 + def generate_piston_directivity(output_dir: str) -> None: 4066 4066 + """Far-field beam pattern of a baffled circular piston at three ka values.""" 4067 4067 + print("Generating piston_directivity...") 4068 4068 + from phonometry import piston_directivity_pattern 4069 4069 + 4070 4070 + piston_directivity_pattern([3.0, 8.0, 16.0]).plot(language=_LANG) 4071 4071 + save_figure(output_dir, "piston_directivity.svg") 4072 4072 + plt.close() 4073 4073 + 4074 4074 + 4065 4075 def _loudspeaker_datasheet_example() -> Any: 4066 4076 """The IEC 60268-5 loudspeaker result shared by the section-7 .plot() figures.""" 4067 4077 from phonometry import loudspeaker_characteristics, radiating_piston ··· 8873 8883 # Swept-sine harmonic separation: THD(f) by order from one synchronized 8874 8884 # sweep (Farina 2000 / Novak et al. 2015). 8875 8885 generate_swept_sine_thd, 8886 8886 + # Far-field directivity (beam) pattern of a baffled circular piston. 8887 8887 + generate_piston_directivity, 8876 8888 # Single-concept rated-characteristic .plot() figures, sharing their panel 8877 8889 # drawing with the .report() fiches (IEC 60268-5 loudspeaker, IEC 60268-4 8878 8890 # microphone).

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.github/images/piston_directivity.svg

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+850

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Reviewed

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+850

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Reviewed

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+850

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Reviewed

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776 + L 115.954086 382.941273 777 777 + " style="fill: none; stroke: #1f77b4; stroke-width: 1.6; stroke-linecap: square"/> 778 778 + </g> 779 779 + <g id="text_14"> 780 780 + <!-- $ka$ = 3 --> 781 781 + <g style="fill: #ffffff" transform="translate(122.618086 385.856773)"> 782 782 + <text> 783 783 + <tspan x="0" y="-0.671875" style="font-style: oblique; font-size: 8.33px; font-family: sans-serif; fill: #ffffff">k</tspan> 784 784 + <tspan x="4.82283" y="-0.671875" style="font-style: oblique; font-size: 8.33px; font-family: sans-serif; fill: #ffffff">a</tspan> 785 785 + <tspan x="9.926254" y="-0.671875" style="font-size: 8.33px; font-family: sans-serif; fill: #ffffff"> </tspan> 786 786 + <tspan x="12.573532" y="-0.671875" style="font-size: 8.33px; font-family: sans-serif; fill: #ffffff">=</tspan> 787 787 + <tspan x="19.55159" y="-0.671875" style="font-size: 8.33px; font-family: sans-serif; fill: #ffffff"> </tspan> 788 788 + <tspan x="22.198868" y="-0.671875" style="font-size: 8.33px; 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#ffffff">=</tspan> 806 806 + <tspan x="19.55159" y="-0.671875" style="font-size: 8.33px; font-family: sans-serif; fill: #ffffff"> </tspan> 807 807 + <tspan x="22.198868" y="-0.671875" style="font-size: 8.33px; font-family: sans-serif; fill: #ffffff">8</tspan> 808 808 + </text> 809 809 + </g> 810 810 + </g> 811 811 + <g id="line2d_18"> 812 812 + <path d="M 234.406686 382.941273 813 813 + L 242.736686 382.941273 814 814 + L 251.066686 382.941273 815 815 + " style="fill: none; stroke: #2ca02c; stroke-width: 1.6; stroke-linecap: square"/> 816 816 + </g> 817 817 + <g id="text_16"> 818 818 + <!-- $ka$ = 16 --> 819 819 + <g style="fill: #ffffff" transform="translate(257.730686 385.856773)"> 820 820 + <text> 821 821 + <tspan x="0" y="-0.671875" style="font-style: oblique; font-size: 8.33px; font-family: sans-serif; fill: #ffffff">k</tspan> 822 822 + <tspan x="4.82283" y="-0.671875" style="font-style: oblique; font-size: 8.33px; font-family: sans-serif; fill: #ffffff">a</tspan> 823 823 + <tspan 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+4

src/phonometry/__init__.py

Reviewed

··· 404 404 microphone_characteristics, 405 405 ) 406 406 from .electroacoustics.piston import ( 407 407 + PistonDirectivity, 407 408 RadiatingPistonResult, 408 409 piston_directivity, 410 410 + piston_directivity_pattern, 409 411 piston_reactance, 410 412 piston_resistance, 411 413 radiating_piston, ··· 1139 1141 "piston_resistance", 1140 1142 "piston_reactance", 1141 1143 "piston_directivity", 1144 1144 + "piston_directivity_pattern", 1142 1145 "RadiatingPistonResult", 1146 1146 + "PistonDirectivity", 1143 1147 "loudspeaker_characteristics", 1144 1148 "LoudspeakerCharacteristics", 1145 1149 "microphone_characteristics",

+10

tests/electroacoustics/test_electroacoustics_plot_i18n.py

Reviewed

··· 86 86 res.plot(language="xx") 87 87 88 88 89 89 + def test_piston_directivity_es() -> None: 90 90 + res = ph.piston_directivity_pattern([3.0, 8.0, 16.0]) 91 91 + ax = res.plot(language="es") 92 92 + assert ax.name == "polar" 93 93 + assert ax.get_title() == "Directividad de un pistón circular con pantalla" 94 94 + plt.close("all") 95 95 + with pytest.raises(ValueError): 96 96 + res.plot(language="xx") 97 97 + 98 98 + 89 99 def _loudspeaker() -> ph.electroacoustics.LoudspeakerCharacteristics: 90 100 f = np.geomspace(30.0, 24000.0, 200) 91 101 spl = 87.0 - 10 * np.log10(1 + (50.0 / f) ** 6) - 10 * np.log10(1 + (f / 16000.0) ** 7)

+60

tests/electroacoustics/test_piston.py

Reviewed

··· 18 18 from scipy import special 19 19 20 20 from phonometry import ( 21 21 + PistonDirectivity, 21 22 RadiatingPistonResult, 22 23 piston_directivity, 24 24 + piston_directivity_pattern, 23 25 piston_reactance, 24 26 piston_resistance, 25 27 radiating_piston, ··· 116 118 matplotlib.use("Agg") 117 119 ax = res.plot() 118 120 assert ax.get_ylabel() 121 121 + 122 122 + 123 123 + def test_directivity_pattern_result_and_properties() -> None: 124 124 + # Default grid is 361 points over the front hemisphere -90 deg .. +90 deg. 125 125 + res = piston_directivity_pattern([3.0, 8.0]) 126 126 + assert res.angles.size == 361 127 127 + assert isinstance(res, PistonDirectivity) 128 128 + assert res.ka.shape == (2,) 129 129 + assert res.directivity.shape == (2, res.angles.size) 130 130 + assert res.directivity_db.shape == res.directivity.shape 131 131 + # D = 1 (0 dB) on axis (theta = 0) for every ka. 132 132 + i0 = int(np.argmin(np.abs(res.angles))) 133 133 + assert np.allclose(res.directivity[:, i0], 1.0) 134 134 + assert np.allclose(res.directivity_db[:, i0], 0.0) 135 135 + # dB echoes the linear directivity: 20 log10 |D|. 136 136 + assert np.allclose( 137 137 + res.directivity_db, 20.0 * np.log10(np.abs(res.directivity)), atol=1e-9 138 138 + ) 139 139 + 140 140 + 141 141 + def test_directivity_pattern_first_null() -> None: 142 142 + # First null at ka sin(theta) = 3.8317 (the first zero of J1); it exists 143 143 + # only once ka > 3.8317. Sample the exact null angle for ka = 6. 144 144 + ka = 6.0 145 145 + theta_null = math.asin(J1_FIRST_ZERO / ka) 146 146 + res = piston_directivity_pattern([ka], angles=[0.0, theta_null]) 147 147 + assert abs(res.directivity[0, 1]) < 1e-9 148 148 + assert res.directivity_db[0, 1] < -120.0 149 149 + # No null for a scalar ka below the first zero of J1. 150 150 + below = piston_directivity_pattern(3.0) 151 151 + assert np.min(np.abs(below.directivity)) > 0.1 152 152 + 153 153 + 154 154 + def test_directivity_pattern_plot() -> None: 155 155 + import matplotlib 156 156 + 157 157 + matplotlib.use("Agg") 158 158 + res = piston_directivity_pattern([2.0, 5.0, 10.0]) 159 159 + ax = res.plot() 160 160 + # A polar axes carrying one curve per ka value. 161 161 + assert ax.name == "polar" 162 162 + assert len(ax.lines) == 3 163 163 + assert "piston directivity" in ax.get_title() 164 164 + with pytest.raises(ValueError): 165 165 + res.plot(language="xx") 166 166 + 167 167 + 168 168 + def test_directivity_pattern_validation() -> None: 169 169 + # Build the arguments up front so only the throwing call sits in each block. 170 170 + ka_one = [1.0] 171 171 + infinite_angles = [np.inf] 172 172 + empty_ka = np.empty(0) 173 173 + with pytest.raises(ValueError): 174 174 + piston_directivity_pattern(-1.0) 175 175 + with pytest.raises(ValueError): 176 176 + piston_directivity_pattern(ka_one, angles=infinite_angles) 177 177 + with pytest.raises(ValueError): 178 178 + piston_directivity_pattern(empty_ka) 119 179 120 180 121 181 def test_validation() -> None:

+60 -1

src/phonometry/_plot/electroacoustics.py

Reviewed

··· 29 29 from ..electroacoustics.frequency_response import FrequencyResponseResult 30 30 from ..electroacoustics.loudspeaker import LoudspeakerCharacteristics 31 31 from ..electroacoustics.microphone import MicrophoneCharacteristics 32 32 - from ..electroacoustics.piston import RadiatingPistonResult 32 32 + from ..electroacoustics.piston import PistonDirectivity, RadiatingPistonResult 33 33 from ..electroacoustics.swept_sine import SweptSineDistortionResult 34 34 35 35 #: Shared frequency-axis label of the electroacoustics renderers. ··· 45 45 _OHM_TEXT = "Ω" 46 46 #: IEC 60263 clause 3 polar reference-circle span, in dB (radius = 25 dB). 47 47 _POLAR_SPAN_DB = 25.0 48 48 + #: Radial span of the baffled-piston beam pattern, in dB (40 dB keeps the first 49 49 + #: side lobes of a narrow high-``ka`` main lobe on scale below the 0 dB axis). 50 50 + _POLAR_SPAN_PISTON_DB = 40.0 48 51 #: Ordinate span of the loudspeaker on-axis response panel, in dB (a multiple of 49 52 #: 25 keeps the IEC 60263 25 dB-per-decade grid on whole gridlines). 50 53 _RESPONSE_SPAN_LSP = 50.0 ··· 75 78 "$X_1$ (reactance)": "$X_1$ (reactancia)", 76 79 r"Normalized radiation impedance $Z_r / \rho c S$": r"Impedancia de radiación normalizada $Z_r / \rho c S$", 77 80 "Baffled circular piston radiation impedance": "Impedancia de radiación de un pistón circular con pantalla", 81 81 + "Baffled circular piston directivity": "Directividad de un pistón circular con pantalla", 78 82 # --- IEC 60268-4/-5 datasheet panels (shared by .report() and .plot()) --- 79 83 "Sound pressure level [dB]": "Nivel de presión sonora [dB]", 80 84 "On-axis response": "Respuesta en el eje", ··· 338 342 ax.legend(loc="best", fontsize="small") 339 343 localize_axes(ax, language) 340 344 return ax 345 345 + 346 346 + 347 347 + def plot_piston_directivity( 348 348 + result: "PistonDirectivity", ax: Any | None = None, *, 349 349 + language: str = "en", **kwargs: Any 350 350 + ) -> "Axes": 351 351 + """Far-field directivity (beam) pattern of a baffled circular piston. 352 352 + 353 353 + Draws the directivity in dB against the polar angle on a polar axes: one 354 354 + curve per ``ka`` in the result, shown as a single family (the directivity 355 355 + pattern). The on-axis level is the 0 dB reference at the top; the main lobe 356 356 + narrows and the first side lobes appear as ``ka`` grows. 357 357 + 358 358 + :param result: A 359 359 + :class:`~phonometry.electroacoustics.piston.PistonDirectivity`. 360 360 + :param ax: Existing polar axes, or ``None`` to create a polar figure. 361 361 + :param language: Label language, ``"en"`` (default) or ``"es"``. 362 362 + :param kwargs: Forwarded to the per-``ka`` ``Axes.plot`` calls. 363 363 + :return: The (polar) axes. 364 364 + """ 365 365 + from .._i18n import decimal_comma, localize_axes 366 366 + 367 367 + ax = ax if ax is not None else _new_polar_axes() 368 368 + theta = np.asarray(result.angles, dtype=np.float64) 369 369 + ka = np.asarray(result.ka, dtype=np.float64) 370 370 + levels = np.clip( 371 371 + np.asarray(result.directivity_db, dtype=np.float64), 372 372 + -_POLAR_SPAN_PISTON_DB, 0.0, 373 373 + ) 374 374 + colors = (_C_PRIMARY, _C_SECONDARY, _C_TERTIARY, _C_REFERENCE, _C_EDGE) 375 375 + # Axis (theta = 0) points up; positive angles swing clockwise so the front 376 376 + # hemisphere (the baffle blocks the rear) fills the upper half-disk. 377 377 + ax.set_theta_zero_location("N") 378 378 + ax.set_theta_direction(-1) 379 379 + ax.set_thetamin(-90.0) 380 380 + ax.set_thetamax(90.0) 381 381 + for i, ka_value in enumerate(ka): 382 382 + label = f"$ka$ = {decimal_comma(f'{ka_value:.3g}', language)}" 383 383 + line_kwargs: dict[str, Any] = { 384 384 + "color": colors[i % len(colors)], "lw": 1.6, "label": label, 385 385 + } 386 386 + line_kwargs.update(kwargs) 387 387 + ax.plot(theta, levels[i], **line_kwargs) 388 388 + ax.set_ylim(-_POLAR_SPAN_PISTON_DB, 0.0) 389 389 + ax.set_yticks([-40.0, -30.0, -20.0, -10.0, 0.0]) 390 390 + ax.set_yticklabels(["-40", "-30", "-20", "-10", "0 dB"], fontsize="x-small") 391 391 + ax.tick_params(axis="x", labelsize="x-small") 392 392 + ax.grid(True, ls=":", lw=0.4, alpha=0.7) 393 393 + ax.set_title(_t("Baffled circular piston directivity", language)) 394 394 + if ka.size > 1: 395 395 + ax.legend(loc="lower center", bbox_to_anchor=(0.5, -0.12), 396 396 + ncol=min(ka.size, 3), fontsize="small") 397 397 + localize_axes(ax, language) 398 398 + axes: Axes = ax 399 399 + return axes 341 400 342 401 343 402 # ---------------------------------------------------------------------------

+4

src/phonometry/electroacoustics/__init__.py

Reviewed

··· 24 24 from .loudspeaker import LoudspeakerCharacteristics, loudspeaker_characteristics 25 25 from .microphone import MicrophoneCharacteristics, microphone_characteristics 26 26 from .piston import ( 27 27 + PistonDirectivity, 27 28 RadiatingPistonResult, 28 29 piston_directivity, 30 30 + piston_directivity_pattern, 29 31 piston_reactance, 30 32 piston_resistance, 31 33 radiating_piston, ··· 42 44 "LoudspeakerCharacteristics", 43 45 "MicrophoneCharacteristics", 44 46 "ModulationDistortionResult", 47 47 + "PistonDirectivity", 45 48 "RadiatingPistonResult", 46 49 "SweptSineDistortionResult", 47 50 "coherence", ··· 56 59 "microphone_characteristics", 57 60 "modulation_distortion", 58 61 "piston_directivity", 62 62 + "piston_directivity_pattern", 59 63 "piston_reactance", 60 64 "piston_resistance", 61 65 "radiating_piston",

+102

src/phonometry/electroacoustics/piston.py

Reviewed

··· 148 148 return out[()] if out.ndim == 0 else out 149 149 150 150 151 151 + #: Default polar-angle grid of the directivity pattern: 361 points spanning the 152 152 + #: front hemisphere ``-90 deg`` to ``+90 deg`` (the baffle blocks the rear), 153 153 + #: 0.5 deg apart, so the beam pattern is smooth even for a narrow high-``ka`` 154 154 + #: main lobe. 155 155 + _DEFAULT_DIRECTIVITY_ANGLES = np.radians(np.linspace(-90.0, 90.0, 361)) 156 156 + 157 157 + 158 158 + @dataclass(frozen=True) 159 159 + class PistonDirectivity: 160 160 + """Far-field directivity pattern of a baffled circular piston. 161 161 + 162 162 + Bundles the far-field directivity 163 163 + ``D(theta) = 2 J1(ka sin theta) / (ka sin theta)`` (Beranek & Mellow 164 164 + Eq. (4.42)) of one or more baffled circular pistons over a shared 165 165 + polar-angle grid, so the classic beam pattern can be drawn with 166 166 + :meth:`plot`. The maths is :func:`piston_directivity`; this is a thin, 167 167 + plottable bundle around it. 168 168 + 169 169 + :ivar angles: Polar angles ``theta`` from the axis, rad. 170 170 + :ivar ka: Wavenumber-radius products ``ka``, one per pattern (a 1-D array). 171 171 + :ivar directivity: Linear directivity ``D(theta)``, normalized so 172 172 + ``D(0) = 1``, as a ``(len(ka), len(angles))`` array; row ``i`` is the 173 173 + pattern for ``ka[i]``. 174 174 + :ivar directivity_db: Directivity in dB, ``20 log10 |D|``, same shape as 175 175 + :attr:`directivity` (the side-lobe nulls floor at a large negative 176 176 + value rather than ``-inf``). 177 177 + """ 178 178 + 179 179 + angles: np.ndarray 180 180 + ka: np.ndarray 181 181 + directivity: np.ndarray 182 182 + directivity_db: np.ndarray 183 183 + 184 184 + def plot(self, ax: "Axes | None" = None, *, language: str = "en", 185 185 + **kwargs: Any) -> "Axes": 186 186 + """Plot the far-field directivity (beam) pattern on a polar axes. 187 187 + 188 188 + Draws the directivity in dB against the polar angle: one curve per 189 189 + ``ka`` value as a single family (still one concept, the directivity 190 190 + pattern). A polar axes is created when ``ax`` is ``None``. Requires 191 191 + matplotlib (``pip install phonometry[plot]``). 192 192 + 193 193 + :param ax: Existing (polar) axes, or ``None`` to create a figure. 194 194 + :param language: Label language, ``"en"`` (default) or ``"es"``. 195 195 + :param kwargs: Forwarded to the per-``ka`` ``Axes.plot`` calls. 196 196 + :return: The axes. 197 197 + """ 198 198 + from .._i18n import check_language 199 199 + from .._plot.electroacoustics import plot_piston_directivity 200 200 + 201 201 + check_language(language) 202 202 + return plot_piston_directivity(self, ax=ax, language=language, **kwargs) 203 203 + 204 204 + 205 205 + def piston_directivity_pattern( 206 206 + ka: ArrayLike, 207 207 + angles: ArrayLike | None = None, 208 208 + ) -> PistonDirectivity: 209 209 + """Far-field directivity pattern of one or more baffled circular pistons. 210 210 + 211 211 + Samples the directivity ``D(theta) = 2 J1(ka sin theta) / (ka sin theta)`` 212 212 + (Beranek & Mellow Eq. (4.42)) at every ``ka`` over a polar-angle grid and 213 213 + bundles it into a :class:`PistonDirectivity` that exposes ``.plot()``. The 214 214 + main lobe narrows as ``ka`` grows; its first null appears once ``ka`` passes 215 215 + the first zero of ``J1`` (``ka sin theta = 3.8317``). 216 216 + 217 217 + :param ka: Wavenumber-radius product(s) ``ka`` (scalar or 1-D array), each 218 218 + non-negative. 219 219 + :param angles: Polar angles ``theta`` from the axis, rad (1-D). ``None`` 220 220 + (default) uses 361 points spanning the front hemisphere ``-90 deg`` to 221 221 + ``+90 deg``, 0.5 deg apart. 222 222 + :return: A :class:`PistonDirectivity`. 223 223 + """ 224 224 + ka_arr = np.atleast_1d(np.asarray(ka, dtype=np.float64)) 225 225 + if ka_arr.ndim != 1 or ka_arr.size == 0: 226 226 + raise ValueError("'ka' must be a non-empty scalar or 1-D array.") 227 227 + if np.any(ka_arr < 0.0) or not np.all(np.isfinite(ka_arr)): 228 228 + raise ValueError("'ka' must be non-negative and finite.") 229 229 + 230 230 + if angles is None: 231 231 + angle_arr = _DEFAULT_DIRECTIVITY_ANGLES.copy() 232 232 + else: 233 233 + angle_arr = np.atleast_1d(np.asarray(angles, dtype=np.float64)) 234 234 + if angle_arr.ndim != 1 or angle_arr.size == 0: 235 235 + raise ValueError("'angles' must be a non-empty 1-D array.") 236 236 + if not np.all(np.isfinite(angle_arr)): 237 237 + raise ValueError("'angles' must be finite.") 238 238 + 239 239 + directivity = np.asarray( 240 240 + piston_directivity(ka_arr[:, None], angle_arr[None, :]), 241 241 + dtype=np.float64, 242 242 + ).reshape(ka_arr.size, angle_arr.size) 243 243 + tiny = np.finfo(np.float64).tiny 244 244 + directivity_db = 20.0 * np.log10(np.maximum(np.abs(directivity), tiny)) 245 245 + return PistonDirectivity( 246 246 + angles=angle_arr, 247 247 + ka=ka_arr, 248 248 + directivity=directivity, 249 249 + directivity_db=directivity_db, 250 250 + ) 251 251 + 252 252 + 151 253 def _directivity_index(ka: NDArray[np.float64]) -> NDArray[np.float64]: 152 254 """Directivity index ``DI = 10 log10 Q`` per ``ka`` by hemisphere quadrature. 153 255

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··· 393 393 callable directly. The piston is the companion radiator model of the 394 394 [industrial noise-control silencers](/phonometry/guides/noise-control/). 395 395 396 396 + The **directivity pattern** itself is a plottable result of its own: 397 397 + `piston_directivity_pattern(ka)` samples $D(\theta)$ at one or more $ka$ values 398 398 + and returns a `PistonDirectivity` (the polar angle grid, the linear 399 399 + `directivity` and its dB form `directivity_db`, and the `ka` values) whose 400 400 + `.plot()` draws the classic beam pattern. Several $ka$ are shown as one family 401 401 + on the same polar axes, so the narrowing of the main lobe and the emergence of 402 402 + the side lobes read at a glance: 403 403 + 404 404 + ```python 405 405 + from phonometry import piston_directivity_pattern 406 406 + 407 407 + pattern = piston_directivity_pattern([3.0, 8.0, 16.0]) 408 408 + print(pattern.directivity_db.shape) # (3, 361): one row per ka 409 409 + pattern.plot() # polar beam pattern in dB (needs matplotlib) 410 410 + ``` 411 411 + 412 412 + <ThemeImage src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/piston_directivity.svg" alt="Polar far-field directivity of a baffled circular piston at ka of 3, 8 and 16 over the front hemisphere, the on-axis level at the top as the 0 dB reference, showing the main lobe narrowing and the side lobes appearing as ka grows" width="72%" /> 413 413 + 414 414 + <details> 415 415 + <summary>Show the code for this figure</summary> 416 416 + 417 417 + ```python 418 418 + import matplotlib.pyplot as plt 419 419 + from phonometry import piston_directivity_pattern 420 420 + 421 421 + piston_directivity_pattern([3.0, 8.0, 16.0]).plot() 422 422 + plt.show() 423 423 + ``` 424 424 + 425 425 + </details> 426 426 + 396 427 ## 7. Loudspeaker characteristics report (IEC 60268-5) 397 428 398 429 The rated characteristics IEC 60268-5 defines around a measured on-axis

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··· 403 403 invocables directamente. El pistón es el modelo de radiador complementario de los 404 404 [silenciadores de control de ruido industrial](/phonometry/es/guides/noise-control/). 405 405 406 406 + El **patrón de directividad** es, por sí mismo, un resultado representable: 407 407 + `piston_directivity_pattern(ka)` muestrea $D(\theta)$ para uno o varios valores 408 408 + de $ka$ y devuelve un `PistonDirectivity` (la malla de ángulos polares, la 409 409 + `directivity` lineal y su forma en dB `directivity_db`, y los valores de `ka`), 410 410 + cuyo `.plot()` dibuja el diagrama de haz clásico. Varios $ka$ se muestran como 411 411 + una familia sobre los mismos ejes polares, de modo que el estrechamiento del 412 412 + lóbulo principal y la aparición de los lóbulos secundarios se leen de un vistazo: 413 413 + 414 414 + ```python 415 415 + from phonometry import piston_directivity_pattern 416 416 + 417 417 + pattern = piston_directivity_pattern([3.0, 8.0, 16.0]) 418 418 + print(pattern.directivity_db.shape) # (3, 361): una fila por ka 419 419 + pattern.plot() # diagrama de haz polar en dB (necesita matplotlib) 420 420 + ``` 421 421 + 422 422 + <ThemeImage src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/piston_directivity_es.svg" alt="Directividad de campo lejano en polar de un pistón circular con pantalla para ka de 3, 8 y 16 sobre el hemisferio frontal, con el nivel en el eje arriba como referencia de 0 dB, que muestra el estrechamiento del lóbulo principal y la aparición de los lóbulos secundarios al crecer ka" width="72%" /> 423 423 + 424 424 + <details> 425 425 + <summary>Mostrar el código de esta figura</summary> 426 426 + 427 427 + ```python 428 428 + import matplotlib.pyplot as plt 429 429 + from phonometry import piston_directivity_pattern 430 430 + 431 431 + piston_directivity_pattern([3.0, 8.0, 16.0]).plot() 432 432 + plt.show() 433 433 + ``` 434 434 + 435 435 + </details> 436 436 + 406 437 ## 7. Informe de características del altavoz (IEC 60268-5) 407 438 408 439 Las características nominales que IEC 60268-5 define en torno a una respuesta en

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··· 82 82 83 83 **Returns:** `D` (float for scalar inputs, else an array). 84 84 85 85 + ## piston_directivity_pattern 86 86 + 87 87 + ```python 88 88 + piston_directivity_pattern( 89 89 + ka: ArrayLike, 90 90 + angles: ArrayLike | None = None, 91 91 + ) -> PistonDirectivity 92 92 + ``` 93 93 + 94 94 + Far-field directivity pattern of one or more baffled circular pistons. 95 95 + 96 96 + Samples the directivity `D(theta) = 2 J1(ka sin theta) / (ka sin theta)` 97 97 + (Beranek & Mellow Eq. (4.42)) at every `ka` over a polar-angle grid and 98 98 + bundles it into a [`PistonDirectivity`](/phonometry/reference/api/electroacoustics/piston/#pistondirectivity) that exposes `.plot()`. The 99 99 + main lobe narrows as `ka` grows; its first null appears once `ka` passes 100 100 + the first zero of `J1` (`ka sin theta = 3.8317`). 101 101 + 102 102 + **Parameters** 103 103 + 104 104 + | Name | Description | 105 105 + | :--- | :--- | 106 106 + | `ka` | Wavenumber-radius product(s) `ka` (scalar or 1-D array), each non-negative. | 107 107 + | `angles` | Polar angles `theta` from the axis, rad (1-D). `None` (default) uses 361 points spanning the front hemisphere `-90 deg` to `+90 deg`, 0.5 deg apart. | 108 108 + 109 109 + **Returns:** A [`PistonDirectivity`](/phonometry/reference/api/electroacoustics/piston/#pistondirectivity). 110 110 + 85 111 ## piston_reactance 86 112 87 113 ```python ··· 122 148 | `x` | Argument `x = 2ka` (scalar or array), dimensionless. | 123 149 124 150 **Returns:** `R1(x)` (float for scalar input, else an array). 151 151 + 152 152 + ## PistonDirectivity 153 153 + 154 154 + ```python 155 155 + PistonDirectivity( 156 156 + angles: np.ndarray, 157 157 + ka: np.ndarray, 158 158 + directivity: np.ndarray, 159 159 + directivity_db: np.ndarray, 160 160 + ) 161 161 + ``` 162 162 + 163 163 + Far-field directivity pattern of a baffled circular piston. 164 164 + 165 165 + Bundles the far-field directivity 166 166 + `D(theta) = 2 J1(ka sin theta) / (ka sin theta)` (Beranek & Mellow 167 167 + Eq. (4.42)) of one or more baffled circular pistons over a shared 168 168 + polar-angle grid, so the classic beam pattern can be drawn with 169 169 + `plot`. The maths is [`piston_directivity`](/phonometry/reference/api/electroacoustics/piston/#piston_directivity); this is a thin, 170 170 + plottable bundle around it. 171 171 + 172 172 + **Attributes** 173 173 + 174 174 + | Name | Description | 175 175 + | :--- | :--- | 176 176 + | `angles` | Polar angles `theta` from the axis, rad. | 177 177 + | `ka` | Wavenumber-radius products `ka`, one per pattern (a 1-D array). | 178 178 + | `directivity` | Linear directivity `D(theta)`, normalized so `D(0) = 1`, as a `(len(ka), len(angles))` array; row `i` is the pattern for `ka[i]`. | 179 179 + | `directivity_db` | Directivity in dB, `20 log10 \|D\|`, same shape as `directivity` (the side-lobe nulls floor at a large negative value rather than `-inf`). | 180 180 + 181 181 + ### PistonDirectivity.plot() 182 182 + 183 183 + ```python 184 184 + PistonDirectivity.plot( 185 185 + ax: Axes | None = None, 186 186 + *, 187 187 + language: str = 'en', 188 188 + **kwargs: Any, 189 189 + ) -> Axes 190 190 + ``` 191 191 + 192 192 + Plot the far-field directivity (beam) pattern on a polar axes. 193 193 + 194 194 + Draws the directivity in dB against the polar angle: one curve per 195 195 + `ka` value as a single family (still one concept, the directivity 196 196 + pattern). A polar axes is created when `ax` is `None`. Requires 197 197 + matplotlib (`pip install phonometry[plot]`). 198 198 + 199 199 + **Parameters** 200 200 + 201 201 + | Name | Description | 202 202 + | :--- | :--- | 203 203 + | `ax` | Existing (polar) axes, or `None` to create a figure. | 204 204 + | `language` | Label language, `"en"` (default) or `"es"`. | 205 205 + | `kwargs` | Forwarded to the per-`ka` `Axes.plot` calls. | 206 206 + 207 207 + **Returns:** The axes. 125 208 126 209 ## radiating_piston 127 210