Doppler effect: separate source motion from wave speed
Введено| English | Значение |
|---|---|
| Doppler shift/ˈdɒplə ʃɪft/ | доплеровское смещение |
| wavefront/ˈweɪvfrʌnt/ | волновой фронт |
What would explain this observation?
- An approaching sound source is heard at a higher pitch even when the source produces a constant frequency.
Build the model
- Doppler shift 多普勒频移 arises from relative source-observer motion.
- A moving source compresses wavefront 波面 spacing ahead and increases it behind.
- For sound in a stationary medium, the wave speed relative to that medium need not change.
- Doppler shift: Change of observed frequency due to relative motion.
- wavefront: A surface joining points with the same wave phase.
Why is pitch higher in front of an approaching sound source?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
An approaching source emits each wavefront closer to the previous one in the direction of travel, so the spacing - the wavelength - shrinks in front, and at fixed wave speed a shorter wavelength means a higher pitch.
Match each technical term to its precise meaning.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- For a source approaching a stationary observer along the line of sight, f observed = f source × v/(v−v source).
- Recession uses v+v source in the denominator.
- These are sound-wave models; light requires its appropriate relation.
In the lab: Use a simulation or recorded data with stated source and observer directions. Draw wavefronts before choosing signs. Avoid demonstrations near moving traffic or unsafe high-volume sources.
Which two habits make the investigation or model in this case more defensible?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- Known: source frequency 500 Hz, sound speed 340 m/s, source approaches at 20 m/s.
- Observed frequency = 500 × 340/(340−20) = 531.25 Hz.
- The increase is 31.25 Hz; it is not the source frequency changing.
Your turn: A 600 Hz source approaches a stationary observer at 20 m/s. Use v = 340 m/s. Find observed frequency.
A 600 Hz source approaches a stationary observer at 20 m/s. Use v = 340 m/s. Find observed frequency.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The result is 637.5 Hz. Known: source 600 Hz approaching a stationary observer at 20 m/s; v = 340 m/s. Use observed frequency = source frequency x v/(v - source speed). f = 600 x 340/(340 - 20) = 637.5 Hz. The source frequency itself never changed.
Check the conclusion and its limits
- A stationary source and moving observer require the observer-motion relation.
- Do not use the same denominator formula for every arrangement or import a sound formula into relativity.
Not true: The Doppler effect always means the wave speed in the medium changed. The wave speed in the medium is fixed by the medium. The Doppler shift comes from relative motion changing the spacing of wavefronts (moving source) or the rate they meet the observer (moving observer) - not from a change in wave speed.
- Doppler shift arises from relative source-observer motion.
- For a source approaching a stationary observer along the line of sight, f observed = f source × v/(v−v source).
- Watch for: A stationary source and moving observer require the observer-motion relation.
Write from an observed frequency of 510 Hz
- A 450 Hz source approaches a stationary observer at 40 m/s. The wave speed is 340 m/s.
- Find the observed frequency. The wave speed in the medium does not change.
The Doppler effect always means the wave speed in the medium changed.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
The wave speed in the medium is fixed by the medium. The Doppler shift comes from relative motion changing the spacing of wavefronts (moving source) or the rate they meet the observer (moving observer) - not from a change in wave speed.
Change of observed frequency due to relative motion: write the technical term.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Doppler shift means Change of observed frequency due to relative motion.
A 450 Hz source approaches a stationary observer at 40 metres per second, and the wave speed is 340 metres per second. What frequency is observed, and why has the wave speed in the medium not changed?
For a source moving toward a stationary observer, divide the wave speed by the wave speed minus the source speed, then multiply by the source frequency.
What frequency does the observer hear?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
340 minus 40 is 300, and 450 times 340 divided by 300 is 510 Hz. Other options — 637.5 Hz (the lesson example's result for a 600 Hz source at 20 metres per second); 450 Hz (the source frequency).