Revise Doppler effect for IB Physics (C.5)

The Doppler effect is the change in the frequency and wavelength that an observer measures whenever there is relative motion between the observer and the source of a wave. The crucial word is observer: the source keeps emitting exactly the same frequency the whole time. What changes is what reaches the observer. To see why, picture the wavefronts — the crests — spreading out from the source.

If the source is stationary, the wavefronts are evenly spaced circles and every observer measures the emitted frequency. Now let the source move. In the time between emitting one crest and the next, the source has itself moved forward. So each new crest is emitted a little closer to the crest ahead of it: the wavefronts bunch up in front of the source and spread out behind it. An observer standing in front receives crests that are closer together — a shorter wavelength — and, because the wave speed $v$ in the medium is unchanged, $v = f\lambda$ means a shorter wavelength is a higher frequency. An observer behind receives stretched-out crests: a longer wavelength and a lower frequency.

Take a source emitting frequency $f$ and moving at speed $v_s$ through still air, with a stationary observer listening. The speed of sound is $v$. Because the source moves between emissions, it is the wavelength itself that is altered, and the source speed appears in the denominator of the observed-frequency formula.

$f' = f\dfrac{v}{v \pm v_s}$

Now keep the source fixed and let the observer move at speed $v_o$. The wavefronts in the air are evenly spaced — the source is not moving, so the wavelength is unchanged. What changes is how quickly the observer sweeps through those crests. Move towards the source and you meet crests more often (higher frequency); move away and you meet them less often (lower frequency). Because it is the rate of arrival that changes, the observer speed appears in the numerator.

$f' = f\dfrac{v \pm v_o}{v}$

Light shows a Doppler effect too, but the reasoning is different because light needs no medium and travels at the same speed $c$ for every inertial observer — so only the relative motion of source and observer matters, not their motion through any 'air'. When a light source moves away, the observed wavelength is stretched towards the red end of the spectrum: a red shift. When it moves towards us, the wavelength is squeezed towards the blue end: a blue shift. For relative speeds far below the speed of light ($v \ll c$) the size of the shift is given by a simple approximation.

$\dfrac{\Delta f}{f} \approx \dfrac{\Delta \lambda}{\lambda} \approx \dfrac{v}{c}$

In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down. Study how each mark below is earned by a specific line, especially the choice of sign, which examiners award as its own method mark.

The Doppler effect ties the wave behaviour of this option back to motion and to astrophysics. The same wavefront picture explains police speed guns and weather radar, where a reflected wave is Doppler-shifted twice. The light version underpins the evidence for an expanding universe and, at HL, connects to the quantitative treatment of red shift and cosmology. Master the habit here — name the case, write the formula, justify the sign, show every line — and the reasoning transfers directly to those later topics.