{"uid":"cap_oLxkgL3PUk9srJ_ybCbdo","slug":"baffled-circular-piston-radiation-impedance-directivity-calculator-2c32cd60","name":"Baffled Circular Piston Radiation Impedance & Directivity Calculator","description":"Compute ideal piston radiation loading,power and signed far-field angular amplitude.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/baffled-circular-piston-bessel-struve-radiation-impedance-directivity?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["acousticPiston"],"properties":{"acousticPiston":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["radius","frequency_hz","sound_speed","density","velocity_amplitude","angles_radians"],"properties":{"radius":{"type":"number","maximum":100,"minimum":0.000001},"density":{"type":"number","maximum":10000,"minimum":0.001},"sound_speed":{"type":"number","maximum":10000,"minimum":1},"frequency_hz":{"type":"number","maximum":1000000,"minimum":0.01},"angles_radians":{"type":"array","items":{"type":"number","maximum":1.5707963267948966,"minimum":0},"maxItems":32,"minItems":1},"velocity_amplitude":{"type":"number","maximum":100,"minimum":0}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Y4jP-i0Is_18cJmQ_4uZf","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes ideal baffled circular piston radiation loading, radiated power, and signed far-field angular amplitude using Bessel and Struve functions.","exampleAgentPrompt":"Compute the baffled circular piston radiation impedance, radiated power, and signed far-field directivity for a piston with radius 0.05 m, operating at 5000 Hz in air (sound speed 343 m/s, density 1.21 kg/m³, velocity amplitude 0.01 m/s), evaluated at angles 0, 0.3, 0.6, 0.9, and 1.2 radians.","exampleUseCases":[{"title":"Loudspeaker driver acoustic modeling","prompt":"I'm designing a 3-inch woofer cone (radius 0.038 m) operating at 1000 Hz in air — sound speed 343 m/s, density 1.21 kg/m³, velocity amplitude 0.05 m/s. Can you compute the radiation impedance and far-field directivity at angles 0, 0.25, 0.5, 0.785, and 1.0 radians?"},{"title":"Ultrasonic transducer beam pattern analysis","prompt":"For an ultrasonic transducer with a circular piston of radius 0.01 m operating at 40000 Hz in water (sound speed 1500 m/s, density 1000 kg/m³, velocity amplitude 0.001 m/s), calculate the far-field angular amplitude and radiated power at angles 0, 0.2, 0.4, 0.6, 0.8, and 1.0 radians."},{"title":"Sonar array element characterization","prompt":"Model a baffled circular piston sonar element with radius 0.025 m driven at 20000 Hz in seawater (sound speed 1520 m/s, density 1025 kg/m³, velocity amplitude 0.002 m/s) — I need the radiation loading and signed far-field directivity evaluated at 0, 0.3, 0.6, 0.9, 1.2, and 1.5 radians."}],"resultDescription":"Returns the radiation impedance (resistance and reactance components representing acoustic loading), total radiated acoustic power, and the signed far-field angular amplitude values at each requested observation angle — enabling full characterization of a baffled piston's acoustic performance.","failureModes":["Radius out of range (must be 0.000001–100 m) returns validation error","Frequency outside 0.01–1,000,000 Hz returns schema error","Angles array must contain 1–32 values each in [0, π/2] radians","Sound speed below 1 or above 10,000 m/s rejected","Zero velocity amplitude may produce degenerate zero-power output","Missing required fields (radius, frequency_hz, sound_speed, density, velocity_amplitude, angles_radians) causes 422"],"whenToPreferThis":"Use this endpoint when you need analytically rigorous, Bessel/Struve-function-based computation of baffled circular piston acoustics — including radiation impedance (loading), radiated power, and signed far-field directivity — in a single call. Prefer this over numerical FEM solvers when the geometry is exactly a baffled circular piston and analytical precision at fast turnaround is required. Ideal for transducer design, beam pattern characterization, and acoustic impedance matching workflows.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:36:08.675Z","isFirstParty":false,"canonicalSlug":"baffled-circular-piston-radiation-impedance-directivity-calculator-2c32cd60"}