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<-   The Doppler effect   ->
figures/humason-spectre.png
Copyright : Paris Observatory / ASM / Hale Observatory

When a wave is emitted, the sound heard by the listener differs if the transmitter is stationary or moving with respect to the listener.

If its wavelength is lambda(meters), the wave emitted has peaks of length lambdaand period P (seconds), such that lambda=c* P, where c is the speed of light ( 3*10^8meters per second).

  • If the source is stationary, the listener receives a wave whose peaks are separated by a time P, and which the wavelength is lambda, equal to the emitted wavelength.

  • If the source is moving with a velocity v_r with respect to the observer, the peaks are emitted at intervals P. During the time interval separating the emission of 2 peaks, the source has moved, with a distance d=v_r *P.

  • If the source moves away from the listener, the second peak covers a greater distance to reach the observer, a distance equal to lambda+d. The listener receives a wave of wavelength lambda' = lambda+d=P*c+v_r *P=P*c*(1+v_r/c). The received wavelength is lambda*(1+v_r/c). Therefore, it is greater than lambda. If the emitted wave is a sound, the received sound is deeper than the emitted sound. If the wave is light, the observed light is redder than the emitted light.

  • Conversely, if the source moves closer to the listener, the second peak covers a smaller distance to reach the observer, a distance equal to lambda-d. The observer receives a wave of wavelength lambda^'=lambda-d=P*c-v_r *P=P*c*(1-v_r/c). The received wavelength is lambda*(1-v_r/c). Therefore, it is smaller than lambda. If the emitted light is a sound, the received sound is more high-pitched than the emitted sound. If the wave is light, the observed light is more blue than the emitted light.