Pitch bends when something moves
The siren that sails past you drops its pitch the instant it passes — that is the Doppler effect, and the sanity rail you must never let go of: approach raises pitch, retreat lowers it. Any answer that disagrees is wrong before the arithmetic starts.
Two machines, depending on who moves. A moving SOURCE squeezes its own wavefronts: — read aloud: f-prime equals f v over v minus v-s. The cast, in words: is the pitch the source actually emits, (said f-prime) is the pitch the listener hears — the one you are solving for — and is the speed of sound in the air, all in the usual hertz and m/s. The subscripts name who is moving: is the source's speed, the observer's — the listener's. A moving LISTENER meets wavefronts more often: . Approach makes both fractions top-heavy — the rail, built into the algebra.
And when two nearly equal tones sound together, they drift in and out of step and the loudness pulses: beats, at with the higher. A violinist tuning to a fork listens for the beats to slow to nothing — silence between two pitches is what "in tune" means.
- = Observed frequency (frequency)
- = Source frequency (frequency)
- = Speed of sound (speed)
- = Source speed (speed)
- = Observed frequency (frequency)
- = Source frequency (frequency)
- = Speed of sound (speed)
- = Observer speed (speed)
- = Beat frequency
- = Higher frequency
- = Lower frequency
each variable a frequency