Special cases of the Doppler effect

The Doppler effect is a fascinating phenomenon that is observed in the propagation of waves. It deals with the apparent distortion that happens in the propagation of waves when the source or the observer of the wave are in relative motion. 

According to the Doppler effect, the frequency of the wave has an apparent change when it is received by an observer when the source and the observer are in motion relative to each other.

What is the Doppler effect?

The basic mechanics of the Doppler effect implies that as the distance between the observer and the source changes, the pitch or the frequency of the wave changes. When the distance that separates the observer and the source increases, the pitch or the frequency decreases. However, when the distance that separates the observer and the source decreases, the pitch or the frequency increases.

The Doppler effect is primarily observed in two types of waves: sound waves and light waves. In the case of sound waves, it involves the change in the pitch with which the sound is heard. But in the case of light, the frequency changes and therefore the wavelength of the light changes. This means that the light undergoes a change in colour.

Special cases

• Source is moving towards the observer but the observer is stationary

When this happens, the relative velocity is such that the separation of the observer from the source is constantly decreasing. This means that the frequency of the soundwave is apparently greater than its original frequency. The formula for the apparent frequency in this case is given as: 

f=fo1-vs / v

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

• Source is moving away from the observer but the observer is stationary

When this happens, the relative velocity is such that the separation of the observer from the source is constantly increasing. This means that the frequency of the soundwave is apparently lesser than the original frequency of the wave from the source. The formula for the apparent frequency in this case is given as:

f=fo1+vs / v

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

• Observer is moving towards the source but the source is stationary

Since the observer is moving towards the source, again the distance between the two points is decreasing, but this time the increase in frequency is caused due to the observer moving closer to the source. The formula for the apparent frequency in this case is given as:

f=fo(1+vov)

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

• Observer is moving away from the source but the source is stationary

Since the observer is moving away from the source, the distance between the two points is increasing, but this time the increase in frequency is caused due to the observer going farther from the source. The formula for the apparent frequency in this case is given as:

f=fo(1-vov)

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

• The source and the observer are moving towards each other

Now the distance between the source and the observer is decreasing but at a speed faster than when either of them move towards each other with one being stationary. The formula for the apparent frequency in this case is given as:

f=fo(v + vov – vs)

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

v is the velocity of the wave in the medium

• The source and the observer are moving away from each other

The distance between the source and the observer is increasing but at a speed faster than when either of them move away from each other with one being stationary. The formula for the apparent frequency in this case is given as:

f=fo(v – vov  + vs)

Here;

f is the frequency apparent to the observer

fo is the frequency of the wave at the source

v is the velocity of propagation of the wave

vo is the observer’s velocity

v is the velocity of the wave in the medium

• Redshift and blueshift

In the case of light waves, the change in frequency gets translated as a change in the wavelength of the light. This change in wavelength results in the colour of the light also changing. When the colour of the light changes to a colour that is closer to the red end of the spectrum, it is called a redshift. When the colour of the light changes to a colour that is closer to the blue end of the spectrum, it is called a blueshift.

Conclusion

The basic mechanics of the Doppler effect implies that as the distance between the observer and the source changes, the pitch or the frequency of the wave changes. When the distance that separates the observer and the source increases, the pitch or the frequency decreases. Whereas when the distance that separates the observer and the source decreases, the pitch or the frequency increases.

The Doppler effect is primarily observed in two types of waves: sound waves and light waves. In the case of sound waves, it involves the change in the pitch with which the sound is heard. But in the case of light, the frequency changes and therefore the wavelength of the light changes. This means that the light undergoes a change in colour.