# The Doppler effect

The Doppler effect, named after C. Doppler, arises in moving acoustic sources. When a acoustic source moves relative to a listener, a shift in the received frequency and wavelength is observed. Thus, the frequency of the received wave is:

$f_{rec}=f_{src}\frac{c_0+v_r}{c_0+v_s}$

where $$f_{rec}$$ is the received frequency, $$f_{src}$$ is the source frequency, $$c_0$$ is the sound speed $$v_r$$ the velocity of the moving receptor and $$v_s$$ the velocity of the moving source.

## Supersonic sources: doppler effect for $$v_s=[1.02, 1.1, 2]c_0$$

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