← Sound, the Doppler effect, and resonance

Why a moving observer receives a shifted frequency

An anchored boat bobs over incoming ripples, one crest after another. A second boat motors straight into the same ripples and meets crests noticeably more often.

The ripples are identical for both boats: same spacing, same speed. What changed is how often each boat runs into them.

The ripples cross the bay with a fixed spacing between crests and a fixed speed.

The anchored boat waits in place. Crests reach it at the wave's own rate.

buzzerstationary listener
A stationary source's fronts are evenly spaced. A still listener meets them at the wave's own rate.

The motoring boat closes the gap to each next crest itself, so it meets crests more often than the anchored boat does.

A boat motoring away from the ripples does the opposite: each next crest has to catch up to it, so it meets crests less often.

Sound works the same way for a moving listener.

Walking toward a stationary speaker, you meet its wavefronts more often: a higher received frequency.

buzzerwalkermoves toward the source
The spacing has not changed. Walking toward the source, the walker meets the evenly spaced fronts more often.

Walking away from it, you meet them less often: a lower received frequency.

buzzerwalkermoves away from the source
The spacing still has not changed. Walking away, the walker meets the evenly spaced fronts less often.
That is the observer's mechanism: the received frequency shifts because an observer moving toward a source meets wavefronts more often than a stationary observer would, while an observer moving away meets them less often.

Notice what never changed: the wavefronts' spacing.

An observer's motion cannot squeeze or stretch the wavefronts; only a moving source can do that.

The observer's motion changes how often the fronts are met, and nothing else.

Pim walks toward a stationary speaker playing a steady tone. Explain why he receives a higher frequency than the speaker emits.

The stationary speaker's wavefronts travel outward with a fixed, even spacing.

Pim's walking closes the gap to each next wavefront.

So Pim meets wavefronts more often than a stationary listener would.

He receives a higher frequency than the speaker emits.

Ottoline rollerblades away from a stationary rink buzzer. Explain why she receives a lower frequency than the buzzer emits.

The buzzer's wavefronts keep their fixed, even spacing.

Each next wavefront has to catch up to Ottoline as she moves away.

So she meets wavefronts less often than a stationary listener would.

She receives a lower frequency than the buzzer emits.

Noll bikes toward a stationary church bell as it rings. Why does he receive a higher frequency than the bell emits?

Maren says: 'When I ride toward a stationary siren, my motion squeezes its wavefronts closer together, and that is why the pitch rises.' Is Maren correct?

Pim says: 'A boat motoring into incoming ripples meets crests more often than an anchored boat does.' Is Pim correct?

Your turn

A zip-liner glides away from the platform where a start horn is sounding. Which option explains why she receives a lower frequency than the horn emits?

A stationary buzzer sends out evenly spaced wavefronts. Noll sprints toward it. What happens to the spacing of the wavefronts?

A cross-country runner sprints away from the stationary starting horn while it sounds. Which statement is correct?