What the Doppler effect is

The Doppler effect is a wave phenomenon where an observer detects a different frequency from the one emitted by a source, because the source and observer are moving relative to each other along the line of wave travel.

That last part matters. If a source moves sideways across your view, the Doppler shift depends on the component of its velocity towards or away from you, not on the full velocity. In simple IB diagrams, we usually take the motion to be directly along the line joining the source and observer.

For sound, think of a siren. It sounds higher-pitched as it approaches and lower-pitched as it moves away. The siren has not changed its emitted frequency; the observer is receiving wavefronts at a different rate.

Sound compared with light

A mechanical wave is a wave that transfers energy through a material medium by oscillations of the particles of that medium. Sound is mechanical, so it needs air, water, metal, or some other material to travel through. For sound, it makes sense to ask whether the source or the observer is moving relative to the medium.

An electromagnetic wave is a transverse wave made of oscillating electric and magnetic fields that can transfer energy through a vacuum. Light, microwaves, radio waves and X-rays are electromagnetic waves. They do not need a medium, and in a vacuum they travel at the same speed for all inertial observers.

So Doppler calculations for sound and light are slightly different. With sound, wavefronts are laid down in a medium, so a moving source really changes the spacing of wavefronts in that medium. With light, there is no medium to be “stationary relative to”, so the shift is described using the relative motion between source and observer. At low relative speeds, the light result becomes pleasantly simple; at speeds that are not small compared with the speed of light, a relativistic treatment is needed.

Similarities and differences between light and sound waves

Light and sound both show the familiar wave behaviours from Theme C: reflection, diffraction, interference and Doppler shifts. An echo is reflection of sound; optical reflection is reflection of light. Both can be focused by suitable materials, and both can carry information from a source to an observer.

The physical mechanisms are different. Sound reflection involves changes in pressure and particle motion at a boundary. Light reflection is an electromagnetic interaction with charges in the material. The biggest Doppler difference is this: sound has a wave speed measured relative to a medium, while light in a vacuum has speed c, where c is the speed of electromagnetic radiation in a vacuum (m s⁻¹), for all inertial observers. That invariant speed is why light Doppler shifts sit naturally with special relativity.

Reading a wavefront diagram

A wavefront is a surface joining points on a wave that are at the same phase of oscillation. In two-dimensional textbook diagrams, spherical wavefronts appear as circles. The gap between neighbouring wavefronts represents the wavelength: closer wavefronts mean a shorter wavelength and, if the wave speed is fixed, a higher frequency.

If the source and observer are both stationary relative to the medium, a point source gives evenly spaced circular wavefronts centred on the source. The observer receives wavefronts at the same rate as the source emits them, so the observed frequency equals the emitted frequency.

Moving source, stationary observer

When the source moves towards a stationary observer, each new wavefront is emitted from a point slightly closer to the observer than the one before. The wavefronts bunch up in front of the source. More wavefronts cross the observer each second, so the observed frequency is higher and the observed wavelength is shorter.

Behind the moving source, it goes the other way. Successive wavefronts are emitted from positions farther away, so the wavefronts spread out. An observer behind the source detects a lower frequency and a longer wavelength.

The wave speed in the medium has not changed for the stationary observer. What has changed is the spacing of the wavefronts in the medium.

Stationary source, moving observer

When the source is stationary, the wavefronts remain symmetrical circles centred on the source. If the observer moves towards the source, they meet wavefronts more often than they would when standing still, so the observed frequency increases.

If the observer moves away, the wavefronts take longer to catch up, so the observed frequency decreases. Here, the wavelength in the medium is unchanged; the change is the rate at which the moving observer crosses wavefronts.

The useful qualitative distinction is this: a moving source changes the wavelength pattern in the medium; a moving observer changes the encounter rate with an already-existing pattern.

The low-speed Doppler approximation for light

For light, the syllabus uses this low relative speed approximation:

[ \frac{\Delta f}{f}=\frac{\Delta \lambda}{\lambda}\approx \frac{v}{c} ]

Here, Δf is the magnitude of the change in observed frequency (Hz), f is the emitted or rest frequency (Hz), Δλ is the magnitude of the change in observed wavelength (m), λ is the emitted or rest wavelength (m), v is the relative speed between source and observer along the line of sight (m s⁻¹), and c is the speed of electromagnetic radiation in a vacuum (m s⁻¹).

Use this approximation only when v is much smaller than c. In school physics language, “much smaller” means the ratio v/c is small enough that higher-order relativistic terms do not affect the accuracy required.

The equation gives the size of the fractional shift. The physical situation tells you which way the shift goes:

• approaching source and observer: observed frequency increases, observed wavelength decreases;
• receding source and observer: observed frequency decreases, observed wavelength increases.

A redshift is a spectral shift to longer wavelength, usually drawn towards the red end of the visible spectrum. A blueshift is a spectral shift to shorter wavelength, drawn towards the blue end. These names still apply even when the radiation is not visible light.

What if the relative speed is not small compared with the speed of light?

If the relative speed is not much smaller than c, the simple approximation stops being reliable. The full treatment has to include special relativity, because at these speeds ordinary Newtonian ideas do not transform time intervals and measured wavelengths correctly.

For IB, the expectation here is qualitative: know that the simple fractional relation is a low-speed approximation. When speeds become a significant fraction of c, a relativistic Doppler expression is needed instead of (\Delta f/f \approx v/c) or (\Delta\lambda/\lambda \approx v/c).

Calculating speed from light Doppler shifts

The Doppler effect for light is a useful measuring tool because spectroscopy can measure tiny wavelength changes very accurately. If a laboratory line has a known wavelength and the same line is observed from a moving astronomical object, the relative speed along the line of sight can be estimated using

[ v\approx \frac{\Delta \lambda}{\lambda}c ]

with the same symbols as defined above.

This shows how physics can use indirect measurement. We don’t need to chase a star or galaxy; we compare the observed spectrum with a laboratory reference and infer its line-of-sight speed.

Why spectral lines are useful

A spectral line is a narrow range of wavelength in an emission or absorption spectrum, produced when atoms, ions or molecules make a transition between quantised energy levels. Different elements have different spacings between these energy levels, so their line patterns work like fingerprints.

An emission spectrum is a set of bright spectral lines produced when excited atoms, ions or molecules emit photons at specific wavelengths. An absorption spectrum is a set of dark spectral lines produced when cooler gas absorbs selected wavelengths from a continuous spectrum.

In astronomy, the pattern of spectral lines from a star or galaxy is compared with the same pattern measured in a laboratory. If the whole pattern has shifted, the source is moving relative to us along the line of sight. A shift to longer wavelengths shows recession; a shift to shorter wavelengths shows approach.

Stars, galaxies and astronomical distances

For nearby stars and rotating bodies, Doppler shifts can reveal speeds of approach, recession, or rotation. For distant galaxies, redshift is one of the key observations behind the large-scale expansion of the universe. In the low-speed approximation, a measured fractional wavelength shift gives a recessional speed using (v\approx (\Delta\lambda/\lambda)c).

If a relation between recessional speed and distance has been established, such as Hubble’s law for sufficiently distant galaxies, redshift can also be used to estimate distance. The chain goes like this: measure spectral shift → infer recessional speed → use the speed–distance relation to infer distance. It’s indirect, but very powerful.

Not every redshift is simply a Doppler shift caused by motion through space. Gravitational fields can redshift light, and the expansion of spacetime produces cosmological redshift. For this topic, keep the distinction clear: Doppler redshift is about relative motion; other redshifts have different physical origins.

Rotational speed of extended bodies

An extended body is an object whose different parts can have different velocities relative to an observer. A rotating star is a good example. One limb of the star may be moving towards Earth while the opposite limb moves away.

Light from the approaching limb is blueshifted; light from the receding limb is redshifted. Radiation from a point whose surface velocity is perpendicular to the line of sight has no line-of-sight Doppler shift. This broadens the spectral lines from the disk, or can even split them in careful measurements.

Once the tangential speed at the edge is known, the rotational period can be estimated from

[ T=\frac{2\pi R}{u} ]

where T is the rotational period (s), R is the radius of the rotating body (m), and u is the tangential speed of the surface at the measured point (m s⁻¹).