{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"doppler-effect"},"result":{"entity_type":"calculator","id":"doppler-effect","calculator_id":"doppler-effect","canonical_url":"https://tttkmbb.com/physics/doppler-effect","name":"Doppler Effect Calculator","title":"Doppler Effect Calculator – Observed Frequency for a Moving Source and Observer (Sound)","category":"physics","category_name":"Physics","tool_name":"calculate_doppler_effect","featured_mcp_tool":false,"description":"Computes the frequency received by an observer when the source and/or the observer move through a medium at rest, from the acoustic Doppler formula f′ = f·(v ± v_observer) / (v ∓ v_source), plus the shift in hertz and in semitones.","use_when":"You need the pitch change of a siren, horn, engine or ultrasound echo when the source or the listener moves at a known speed relative to the air or another medium.","do_not_use_when":"The wave is light or radio (use the relativistic Doppler formula), the source moves at or above the wave speed (a shock wave forms, no steady tone), or you need the wavelength of a wave without motion (use wavelength-frequency).","inputs":[{"name":"source_frequency_hz","label":"Source frequency","type":"number","unit":"Hz","required":true,"max":1000000000000,"exclusive_min":0,"description":"Frequency emitted by the source in hertz.","example":500},{"name":"wave_speed_m_s","label":"Wave speed in the medium","type":"number","unit":"m/s","required":false,"default":343,"max":100000,"exclusive_min":0,"description":"Propagation speed of the wave in the medium. Default 343 m/s (sound in air at 20 °C); about 331 at 0 °C, 1480 in water, 5960 in steel.","example":343},{"name":"source_speed_m_s","label":"Source speed","type":"number","unit":"m/s","required":false,"default":0,"min":0,"description":"Speed of the source relative to the medium (0 = stationary), along the line joining source and observer.","example":30},{"name":"source_direction","label":"Source direction","type":"enum","required":false,"default":"approaching","values":[{"value":"approaching","label":"Approaching the observer","aliases":["towards","toward","closing"]},{"value":"receding","label":"Receding from the observer","aliases":["away","moving away"]}],"description":"Whether the source moves towards or away from the observer.","example":"approaching"},{"name":"observer_speed_m_s","label":"Observer speed","type":"number","unit":"m/s","required":false,"default":0,"min":0,"description":"Speed of the observer relative to the medium (0 = stationary), along the line joining source and observer.","example":0},{"name":"observer_direction","label":"Observer direction","type":"enum","required":false,"default":"approaching","values":[{"value":"approaching","label":"Approaching the source","aliases":["towards","toward","closing"]},{"value":"receding","label":"Receding from the source","aliases":["away","moving away"]}],"description":"Whether the observer moves towards or away from the source.","example":"approaching"}],"outputs":[{"name":"observed_frequency_hz","label":"Observed frequency","type":"number","unit":"Hz","decimals":2,"description":"f′ = f × (v ± v_observer) / (v ∓ v_source)."},{"name":"frequency_shift_hz","label":"Frequency shift","type":"number","unit":"Hz","decimals":2,"description":"f′ − f; positive when the pitch rises."},{"name":"frequency_ratio","label":"Frequency ratio","type":"number","decimals":4,"description":"f′ / f."},{"name":"shift_semitones","label":"Shift in semitones","type":"number","unit":"semitones","decimals":2,"description":"12 × log₂(f′ / f): the musical interval of the pitch change (12 = one octave)."},{"name":"wavelength_source_m","label":"Emitted wavelength","type":"number","unit":"m","decimals":4,"description":"v / f: wavelength the source would produce in the medium at rest."},{"name":"wavelength_observed_m","label":"Observed wavelength","type":"number","unit":"m","decimals":4,"description":"v / f′: wavelength corresponding to the observed frequency (the compressed or stretched wavelength in the medium when only the source moves)."},{"name":"note","label":"Note","type":"string","decimals":4,"description":"Direction and size of the pitch change and the assumptions of the formula."}],"input_schema":{"type":"object","properties":{"source_frequency_hz":{"description":"Frequency emitted by the source in hertz. Unit: Hz.","type":"number","maximum":1000000000000,"exclusiveMinimum":0,"examples":[500],"x-unit":"Hz"},"wave_speed_m_s":{"description":"Propagation speed of the wave in the medium. Default 343 m/s (sound in air at 20 °C); about 331 at 0 °C, 1480 in water, 5960 in steel. Unit: m/s.","type":"number","maximum":100000,"exclusiveMinimum":0,"default":343,"examples":[343],"x-unit":"m/s"},"source_speed_m_s":{"description":"Speed of the source relative to the medium (0 = stationary), along the line joining source and observer. Unit: m/s.","type":"number","minimum":0,"default":0,"examples":[30],"x-unit":"m/s"},"source_direction":{"description":"Whether the source moves towards or away from the observer.","type":"string","enum":["approaching","receding"],"default":"approaching","examples":["approaching"]},"observer_speed_m_s":{"description":"Speed of the observer relative to the medium (0 = stationary), along the line joining source and observer. Unit: m/s.","type":"number","minimum":0,"default":0,"examples":[0],"x-unit":"m/s"},"observer_direction":{"description":"Whether the observer moves towards or away from the source.","type":"string","enum":["approaching","receding"],"default":"approaching","examples":["approaching"]}},"additionalProperties":false,"required":["source_frequency_hz"]},"output_schema":{"type":"object","properties":{"observed_frequency_hz":{"description":"f′ = f × (v ± v_observer) / (v ∓ v_source). Unit: Hz.","type":"number","x-unit":"Hz"},"frequency_shift_hz":{"description":"f′ − f; positive when the pitch rises. Unit: Hz.","type":"number","x-unit":"Hz"},"frequency_ratio":{"description":"f′ / f.","type":"number"},"shift_semitones":{"description":"12 × log₂(f′ / f): the musical interval of the pitch change (12 = one octave). Unit: semitones.","type":"number","x-unit":"semitones"},"wavelength_source_m":{"description":"v / f: wavelength the source would produce in the medium at rest. Unit: m.","type":"number","x-unit":"m"},"wavelength_observed_m":{"description":"v / f′: wavelength corresponding to the observed frequency (the compressed or stretched wavelength in the medium when only the source moves). Unit: m.","type":"number","x-unit":"m"},"note":{"description":"Direction and size of the pitch change and the assumptions of the formula.","type":"string"}}},"formula":"observed_frequency_hz = source_frequency_hz × (wave_speed_m_s ± observer_speed_m_s) / (wave_speed_m_s ∓ source_speed_m_s), upper signs for approaching (observer +, source −), lower signs for receding; frequency_shift_hz = f′ − f; frequency_ratio = f′ / f; shift_semitones = 12 × log2(f′ / f); wavelength_source_m = v / f; wavelength_observed_m = v / f′","method":"Classical (non-relativistic) Doppler effect for waves in a medium at rest, with source and observer moving along the line joining them; motion of the source and of the observer are not symmetric because the medium defines the reference frame.","sources":[{"name":"Wikipedia – Doppler effect","url":"https://en.wikipedia.org/wiki/Doppler_effect","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Doppler effect","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/dopp.html","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"500 Hz siren approaching at 30 m/s, listener at rest","inputs":{"source_frequency_hz":500,"source_speed_m_s":30,"source_direction":"approaching"},"expected":{"observed_frequency_hz":547.92,"frequency_shift_hz":47.92,"frequency_ratio":1.0958,"shift_semitones":1.58,"wavelength_source_m":0.686,"wavelength_observed_m":0.626},"url":"https://tttkmbb.com/api/v1/calculate/doppler-effect?source_frequency_hz=500&source_speed_m_s=30&source_direction=approaching"},{"name":"Listener approaching a stationary 1000 Hz source at 20 m/s","inputs":{"source_frequency_hz":1000,"observer_speed_m_s":20,"observer_direction":"approaching"},"expected":{"observed_frequency_hz":1058.31,"frequency_shift_hz":58.31,"frequency_ratio":1.0583,"shift_semitones":0.98},"url":"https://tttkmbb.com/api/v1/calculate/doppler-effect?source_frequency_hz=1000&observer_speed_m_s=20&observer_direction=approaching"}],"faq":[{"q":"What happens when the source moves away?","a":"The pitch drops: the same 500 Hz siren receding at 30 m/s is heard at 500 × 343 / 373 = 459.79 Hz, a smaller shift than the 47.92 Hz rise when approaching."},{"q":"Why do a moving source and a moving observer give different results at the same speed?","a":"Sound travels at a fixed speed in the air. A moving source compresses the wavelength itself, while a moving observer only meets the unchanged wavefronts at a different rate, so the two cases differ (547.92 vs 543.73 Hz for 30 m/s at 500 Hz)."},{"q":"Does this work for light or radar?","a":"Not exactly: light has no medium and needs the relativistic formula f′ = f·√((1 + β)/(1 − β)). For speeds far below c the classical result is a close approximation."}],"tags":["doppler effect","doppler shift","observed frequency","siren pitch","moving source","sound frequency"],"related":[{"calculator_id":"wavelength-frequency","reason":"Wavelength of the emitted or observed frequency at the wave speed."},{"calculator_id":"speed-distance-time","reason":"Convert vehicle speeds from km/h or mph to m/s."},{"calculator_id":"frequency","reason":"Convert frequencies between Hz, kHz and MHz."}],"links":{"html":"https://tttkmbb.com/physics/doppler-effect","markdown":"https://tttkmbb.com/physics/doppler-effect.md","json":"https://tttkmbb.com/physics/doppler-effect.json","api":"https://tttkmbb.com/api/v1/calculate/doppler-effect","schema":"https://tttkmbb.com/api/v1/calculators/doppler-effect","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:01Z","next_actions":[{"tool":"run_calculator","calculator_id":"doppler-effect","reason":"Run Doppler Effect Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/doppler-effect.md"}}