C.5 · Doppler effect

Supported SL focus. First assessment 2025; full Physics guide acquired (84 PDF pages). Remaining guide, assessment and practical requirements retain their recorded holds.

Prerequisites: read the stated quantities and units, use arithmetic and the model conditions below. Each lesson develops its own method before independent transfer.

These are original or explicitly fictional teaching examples, not actual measurements or completed assessed learner investigations.

What would explain this observation?

• A recognizable spectral line appears at a longer wavelength in a distant source. Its shift can provide evidence of recession along the line of sight.
• Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.

Build the model

• Relative source-observer motion changes observed frequency or wavelength. For light at a relative speed much smaller than c, the magnitude of the fractional wavelength shift is approximately v/c. Recession corresponds to longer wavelength, and approach to shorter wavelength.
• redshift 红移: Shift of an identified line toward longer wavelength; rest wavelength 静止波长: Wavelength of the line measured with no relative source motion.

Choose evidence that can test it

• Compare a identified line with its laboratory rest wavelength. Use z = (observed−rest)/rest, then v approximately cz in the stated low-speed model. Do not apply this approximation without checking the regime or treating a cosmological redshift as a simple exact velocity.
• Use attributed spectra with calibration and line identification. Compare several lines for a consistent shift. State uncertainty and distinguish relative line-of-sight motion from an unmeasured transverse component.

Work from known quantities

• State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
• Known: a 500 nm rest line is observed at 501 nm. z = (501−500)/500 = 0.002. With c=3.0×10⁸ m/s, v approximately 6.0×10⁵ m/s away. The sound-source denominator formula is not the required SL light approximation.

Example:

A 600 nm rest line is observed at 601.2 nm. Find z=(observed−rest)/rest. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.

Check the conclusion and its limits

• The approximate shift relation does not show that light travels faster from an approaching source. A single unidentified line cannot safely establish a redshift.
• Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.

Warn:

An observed redshift means light speed increased. This claim is false: The approximate shift relation does not show that light travels faster from an approaching source. A single unidentified line cannot safely establish a redshift.

Key:

Spectral shifts: a low-speed astronomical estimate: Compare a identified line with its laboratory rest wavelength. Use z = (observed−rest)/rest, then v approximately cz in the stated low-speed model. Do not apply this approximation without checking the regime or treating a cosmological redshift as a simple exact velocity.