Doppler Effect in Sound

The Doppler effect is also called the Doppler shift. It is the change in frequency of a wave corresponding to an observer who is moving relative to the wave source. This effect was named after the Austrian physicist Christian Doppler, who described the Doppler principle in 1842.

A common example of the Doppler effect in sound is the altering of pitch heard when a bus sounding a horn approaches and recedes from an observer. When compared with the emitted frequency, the perceived frequency is greater during the approach, identical at the instant of passing by and lower during the recession.

This page will help you understand the reason for the Doppler effect with the help of an application of the Doppler effect. Also, we will derive the Doppler effect equation and some illustrating Doppler shift facts.

Now, let us understand what the Doppler effect is with a short description.

Doppler Effect in Real-Life Application

Below is a Real-Life Doppler Effect Example:

Assumption 1:

Suppose that there is a happy bug in the middle of a circular water puddle. The bug is periodically shaking its legs so as to produce disturbances that travel via the water. If these disturbances emanate at a point, they will travel outside from that very point in various directions. Since each disturbance is travelling in an identical medium, they would all travel in each course at an identical speed. The pattern produced by the bug's movement could be a series of concentric circles, as shown in the diagram below:

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These circles would attain the edges of the water puddle on an identical frequency. An observer at point A (the left edge of the circle) could observe the disturbances to strike the puddle's edge on the same frequency that would be observed through an observer at point B (at the right edge of the puddle). In fact, the frequency at which disturbances reach the edge of the puddle could be similar to the frequency at which the bug produces the disturbances. If the bug generates sound/disturbances at a frequency of 2 per second, then each observer would observe them approaching at a frequency of 2 per second.

Assumption 2:

Now assume that our bug is moving to the right across the puddle of water and generating disturbances at the same frequency of 2 disturbances per second. Since the bug is travelling towards the right, each consecutive disturbance/sound originates from a position towards observer B, and away from observer A. Subsequently, each consecutive disturbance has a shorter distance to travel before reaching observer B and takes less time to reach observer B.

Hence, observer B notices that the frequency of arrival of the disturbances is greater than the frequency at which disturbances are produced. On the other hand, each successive disturbance has the same distance to travel before approaching observer A. 

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For this reason, observer A notices a frequency of arrival that is less than the frequency at which the disturbances are generated. The net effect of the motion of the bug (the source of waves) is that the observer towards whom the bug is travelling observes a frequency that is higher than 2 disturbances/second; the observer far away from whom the bug is travelling observes a frequency that is less than 2 disturbances/second. This impact is called the Doppler effect.

Doppler Effect in Sound

The Doppler effect is seen whenever the source of waves is travelling with respect to an observer. The Doppler effect may be defined as the impact produced by a moving source of waves in which there's an apparent upward shift in frequency for observers towards whom the source is approaching and an evident downward shift in frequency for observers from whom the source is receding. 

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It is vital to notice that the effect does not end because of an actual change in the frequency of the source. Using the instance above, the bug is still generating disturbances at a rate of two disturbances per second; it simply seems to the observer whom the bug is reaching that the disturbances are being generated at a frequency higher than 2 disturbances/second. The effect is best observed when the distance between observer B and the bug is lowering and the space between observer A and the bug is increasing.

Doppler Effect Equation

The Formula for The Doppler Effect is given as:

\[f_{o}={\frac{v+v_{o}}{v+v_{s}}}\times{f_{s}}\]

Here,

\[f_{o}\]    = observer frequency of sound

\[f_{s}\]    =  actual frequency of sound waves

v      = speed of sound waves

\[v_{o}\]    = observer velocity

\[v_{s}\]    = source velocity

Application of The Doppler Effect: Example of Astronomy

The Doppler effect is of extreme interest to astronomers who utilise the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about the stars and galaxies. The perception that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. 

Furthermore, definite information about stars within galaxies can be determined by the application of the Doppler effect. Galaxies are clusters of stars that usually rotate about some centre of the mass point. Electromagnetic radiation released by such stars in a distant galaxy could appear to be shifted downward in frequency (a redshift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there's an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

From our context on the Doppler effect and its principle and applications, we understand that the Doppler effect is altering the frequency and wavelength of a wave. This effect is the consequence of a change in distance between the thing creating the wave (causer/source) and whatever is measuring, observing or hearing the wave (watcher or observer). 

Facts on the Doppler Effect

• You might have heard the changing pitch of the siren of an ambulance that passes with its siren blaring: When an ambulance approaches you, the siren’s pitch sounds higher than when it moves away from you. This change is a common Doppler principle.

• The Doppler effect is applicable for both light and sound. For example, astronomers daily determine how fast stars and galaxies are moving away from us by measuring the distance to which their light is "reached" into the lower frequency, red part of the spectrum. 

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This application holds the well-known Doppler principle in Astronomy.