Doppler Effect

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The Doppler effect is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842 in Prague.

It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.

The Doppler shift is a shift in the wavelength of light or sound that depends on the relative motion of the source and the observer.

A familiar example of a Doppler shift is the apparent change in pitch of an ambulance siren as it passes a stationary observer.

When a vehicle with a siren passes you, a noticeable drop in the pitch of the sound of the siren will be observed as the vehicle passes.

This is an example of the Doppler effect. An approaching source moves closer during period of the sound wave so the effective wavelength is shortened, giving a higher pitch since the velocity of the wave is unchanged. Similarly the pitch of a receding sound source will be lowered.

Formula

In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency f and emitted frequency f₀ is given by:

$$ \displaystyle f=\left({\frac {c\pm v_{\text{r}}}{c\pm v_{\text{s}}}}\right)f_{0} $$

where

f = Observer frequency,

f₀ = Actual frequency,

c = The propagation speed of waves in the medium;

v_x = The speed of the receiver relative to the medium, added to c if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;

v_s = The speed of the source relative to the medium, added to c if the source is moving away from the receiver, subtracted if the source is moving towards the receiver.

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