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All lessons Waves18 min

The Doppler Effect

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← Sound WavesStanding Waves & Resonance →
01
Hook
02
Explore
03
Formalize
04
Practice
05
Challenge
Interactive simulation
01

Hook

In the 1840s, an astronomer hired a group of trumpet players to ride on a train and play a sustained note. People standing by the track listened carefully. Nobody expected what happened: the note sounded higher when the train approached and lower when it passed — even though the trumpeters swore they played the same note the whole time. What is the train doing to the sound waves?

02

Explore

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03

Formalize

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04

Practice

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Challenge

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Spoilers

The Doppler Effect — summary and key formula

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The question

In the 1840s, an astronomer hired a group of trumpet players to ride on a train and play a sustained note. People standing by the track listened carefully. Nobody expected what happened: the note sounded higher when the train approached and lower when it passed — even though the trumpeters swore they played the same note the whole time. What is the train doing to the sound waves?

This was one of the first experimental confirmations of the Doppler effect — and it turned out to be one of the most powerful tools in modern science. Today the same principle measures the speed of galaxies, tracks weather systems, catches speeding drivers, and monitors blood flow inside your body. Understanding it starts with something very simple: motion compresses waves.

The key idea

When a wave source moves relative to an observer, the observed frequency differs from the emitted frequency. An approaching source compresses wavefronts (higher frequency); a receding source stretches them (lower frequency). The shift is proportional to the source speed relative to the wave speed.

The key insight: it's relative motion that matters. Whether the source moves toward you or you move toward the source, you hear a higher pitch. Police radar guns fire microwaves at a car and measure the Doppler shift of the reflection to calculate speed. Astronomers measure redshift (wavelength stretched to longer, redder values) in starlight to determine how fast galaxies are receding. The expansion of the universe was discovered this way — every galaxy shows redshift, meaning they're all moving away from us.

The formula

f′=fvv±vsf' = \dfrac{fv}{v \pm v_s}f′=v±vs​fv​
  • ·f' = observed frequency (Hz)
  • ·f = emitted frequency (Hz)
  • ·v = wave speed (m/s)
  • ·vs = source speed (m/s) — use minus when source approaches
  • ·plus when receding