Calculation
f' = f·c/(c−v)
An approaching source compresses wavelength in the direction of travel, so a stationary observer perceives a higher frequency than was emitted.
Doppler-Effekt für bewegte Quelle, ruhender Beobachter: f' = f·c/(c−v); Dubbel Meßtechnik W 2.3.1 nennt das Prinzip (Radar)
Doppler effect for an approaching source
An approaching source compresses wavelength in the direction of travel, so a stationary observer perceives a higher frequency than was emitted.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Perceived frequency f' — Frequency arriving at the stationary observer.
- Emitted frequency f — Frequency emitted by the moving source.
- Speed of sound c — Propagation speed of sound in the medium.
- Source speed v — Speed of the source approaching the observer; must be less than c.
Example
f=1,000 Hz, c=343 m/s and v=30 m/s give f'=1,000·343/313≈1,095.85 Hz.
Assumptions and limits
Stationary observer and source moving directly toward the observer along the line of sight; medium motion (wind), oblique motion directions and the stationary-source/moving-observer case are excluded.
Understand Doppler effect for an approaching source
This calculator determines the frequency arriving at a stationary observer from an approaching sound source, the physical principle behind the familiar pitch rise of an approaching vehicle.
What does this quantity describe?
A source approaching the observer at speed v compresses the emitted waves in the direction of travel. The stationary observer perceives the higher frequency f'=f·c/(c−v).
Formula and variables
f' = f·c/(c−v)
f' = f·c/(c−v)
| Symbol / input | Meaning |
|---|---|
| Perceived frequency f' | Frequency arriving at the stationary observer. |
| Emitted frequency f | Frequency emitted by the moving source. |
| Speed of sound c | Propagation speed of sound in the medium. |
| Source speed v | Speed of the source approaching the observer; must be less than c. |
Choose the inputs correctly
f is the frequency emitted by the source, c the speed of sound in the medium, v the speed of the approaching source.
How to use the calculator
Take f from the known emitted frequency, derive c from air temperature, and v from the source's approach speed.
Worked example
f=1,000 Hz, c=343 m/s and v=30 m/s give f'=1,000·343/313≈1,095.85 Hz.
Understand the result and units
The closer v approaches c, the more strongly perceived frequency rises; at v=c the denominator would reach zero and the formula diverges (the sonic-boom limiting case).
f and f' are frequencies, c and v are speeds.
Typical applications
Explaining and calculating the Doppler effect for sirens and passing vehicles and in teaching; a basis for Doppler radar and ultrasonic measurements.
Assumptions, limits and common mistakes
Stationary observer and a source moving exactly along the line of sight directly toward the observer; oblique motion directions (needing a cosine correction), wind effects on c, and the case of a moving observer with a stationary source are excluded.
Common mistake: Do not enter v≥c; the formula holds only for subsonic source speeds and otherwise gives no physically meaningful result.
Frequently asked questions
What is “Doppler effect for an approaching source” used for?
Explaining and calculating the Doppler effect for sirens and passing vehicles and in teaching; a basis for Doppler radar and ultrasonic measurements.
Where do the input values come from?
f is the frequency emitted by the source, c the speed of sound in the medium, v the speed of the approaching source.
What does the result not cover?
Stationary observer and a source moving exactly along the line of sight directly toward the observer; oblique motion directions (needing a cosine correction), wind effects on c, and the case of a moving observer with a stationary source are excluded.