The Doppler effect represents a change in the signal frequency occurring due to movement of the signal source relative to the receiver. The effect is named after the Austrian physicist Christian Doppler.

The Doppler effect is easy to be observed in practice, when a car passes by with an alarm turned on. Let’s suppose an alarm produces a certain tone and it does not change. When the car is not moving relative to the observer, then the observer hears exactly the tone the alarm emits. But if a car approaches the observer, then the frequency of sound waves will be increased and the observer will hear a higher tone than the alarm actually emits. At the moment in which a car passes the observer, he\she will hear the same tone that the alarm actually emits. When the car passes farther away and is already moving away instead of coming closer, then the observer will hear a lower tone due to the lower frequency of sound waves.

If a source of waves moves relative to the medium, then the distance between wave extremes (wavelength λ) depends on the speed and direction of movement. If the source moves towards the receiver, that is, it catches up with the wave emitted, then the wavelength decreases; if it moves away - then the wavelength increases:

ω0 is the angular frequency with which the source emits waves, c is the speed of wave propagation in the medium, v is the speed of the wave source relative to the medium (it is positive if the source is approaching the receiver and negative if it is moving away).

The frequency recorded by a stationary receiver

Similarly, if the receiver moves towards the waves, then it registers their extremes more often and vice versa. Stationary source and moving (mobile) receiver

where u is the receiver's velocity with respect to the medium (positive if the receiver moves towards the source).

By substituting ω0 in the formula (2) for the frequency ω taken from formula (1), we obtain the formula applied for the general case:

Observation of the Doppler effect will be provided using the example of telegraph code reception from satellites. Prepare equipment for operation and set up the necessary software as described in Lesson 09.

Wait for a “proper and suitable” satellite to pass at least 30° above the horizon.

Activate headphones and listen to the changing tone of the moving satellite.

Turn on all elements in the “Zoom FFT” section.

A user can check perfectly how the frequency of the passing satellite is changed in the “Auto spectrum” chart.