What Is the Doppler Effect?

The Doppler effect is the change in the observed frequency and wavelength of a wave caused by relative motion between the source and the observer. Motion toward each other increases the observed frequency, while motion apart decreases it.

This is part of IB Physics C.5 and applies to both SL and HL. The sound-wave equations are an Additional Higher Level (AHL) extension.

How the Doppler Effect Works

A source emits successive wavefronts at regular intervals. If the source moves toward an observer, each new wavefront is emitted from a position closer to the observer, so the wavefronts become more closely spaced. The observed wavelength decreases and, because $v=f\lambda$, the observed frequency increases.

If the source moves away, the wavefronts spread out. The observed wavelength increases and the observed frequency decreases.

For sound, this explains why an approaching ambulance siren sounds higher in pitch and then drops in pitch after passing. A common misconception is that the Doppler effect changes the wave speed. It does not: the speed of sound remains determined by the medium.

For electromagnetic waves, motion away produces a redshift, meaning spectral lines shift toward longer wavelengths. Motion toward the observer produces a blueshift, meaning spectral lines shift toward shorter wavelengths. At speeds much lower than the speed of light,

$$\frac{\Delta f}{f}=\frac{\Delta \lambda}{\lambda}\approx\frac{v}{c}.$$

For AHL sound calculations with a moving source,

$$f'=f\frac{v}{v\pm u_s},$$

where $v$ is wave speed and $u_s$ is source speed. Choose the sign by checking whether the observed frequency should increase or decrease, rather than memorizing signs mechanically.

Exam Technique

In an IB response, state the relative motion, describe the change in wavefront spacing, and connect it to frequency. For calculations, predict whether (f') should be above or below $f$ before substituting values.