Doppler Shift

Introduction

The terms Doppler effect and Doppler shift are often used synonymously by most people. While for day-to-day usage, there is no problem in doing that, there are still some differences between them that one must be aware of.

Doppler effect arises in waves of all forms and is not limited to sound waves or light waves. However, it is most tangible in the case of sound waves. The frequency shift observed in light waves is too small to be visible to the naked eye. Instead, spectroscopic measurements are required. Further, the Doppler effect theory is only valid when the speeds of the source and receiver are less than the speed of the wave in question. Beyond that, other phenomena start taking place.

Regardless of these limitations, the theory behind the Doppler effect (and consequently, the Doppler shift) is of massive use for scientists and the common folk alike. Astronomers use it to find exoplanets and calculate the speed of distant celestial objects. At the same time, the Doppler Effect comes in handy for things as mundane as speed radars. In this tutorial, we will elaborate on the Doppler Effect and Doppler shift in detail.

What is the Doppler Effect?

Doppler Effect is a phenomenon wherein, the frequency of waves appears altered if their sources or receivers are not stationary with respect to each other. The most interesting part about the Doppler Effect is that while the science behind it is incredibly sound, the effect itself is an illusion. The frequency only appears altered. In reality, the properties of the wave itself remain unchanged.

Further, the Doppler Effect is observed in all kinds of waves. For instance, the shift in frequency of sound waves is employed in emergency sirens, while the shift in frequency of light waves is used in Doppler speed radars.

Doppler Shift

As previously mentioned, the term “Doppler effect” is used synonymously with “Doppler shift”, which is not too incorrect. However, technically speaking, the Doppler effect is the phenomenon of apparent change in frequency whereas, the Doppler shift refers to the change in the frequency itself. Thus, when we talk about the Doppler shift, we are talking about a magnitude, not a phenomenon.

For instance, the Doppler shift in sound waves of a certain vehicle could be 20 Hz. It is a quantity that can be expressed in terms of numbers or variables and its value depends on the relative speeds of the source and observer, as well as the speed of the wave itself. Thus, sound waves undergo a more drastic and tangible change in frequency than light waves.

Types of Doppler Shift

Broadly speaking, Doppler shift is classified into two types. These are known as redshift and blueshift respectively. The names arise from the lower frequency of red color and the higher frequency of blue color in the visible spectrum.

Redshift

Since the color red lies on the lower frequency side of the visible region, we refer to a decrease in the frequency of waves as redshift. Redshift is encountered when the source is moving away from the observer.

For instance, if a planet is moving away from Earth, the light arriving on earth after being reflected off of it would seem to carry a slightly lower frequency. This is used to calculate the speed of celestial objects.

Blueshift

Blueshift is the opposite of redshift. Blue color lies on the higher frequency side and thus, an increase in frequency due to the Doppler effect is termed a blue shift. It is encountered when the source is moving towards the observer.

Just like the redshift, if a planet is moving towards the Earth, the frequency of light bouncing off of it would appear higher.

Difference between Doppler Effect and Doppler Shift

Doppler Effect	Doppler Shift
Doppler effect is a phenomenon	Doppler shift is a measurement.
It refers to the effect observed wherein, there is an apparent change in the frequency of waves.	It refers to the quantity of change encountered in the frequency due to the Doppler effect.
Doppler effect is observed in waves of all forms.	The subtypes of Doppler shift, namely redshift, and blue shift, are generally said to be valid only for light waves. Note that the Doppler shift itself is valid for all waves.

Formula for Doppler Shift

Doppler shift is encountered when there is relative motion between the source and observer. If we assume that the source is stationary and the observer is moving at velocity $\mathrm{v_{r}}$, then

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

Here, the plus sign corresponds to the receiver moving towards the source.

Similarly, if the receiver is stationary but the source is moving at velocity $\mathrm{v_{r}}$, then:

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

This time, the plus sign corresponds to the source moving away from the receiver. The two formulae above may be combined when the source and the receiver are both in motion to give

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

c is used to represent the velocity of the wave itself.

Further, in case the source and the receiver are moving transverse to each other, then the above formulae do not hold valid. the transverse Doppler effect is less pronounced and thus, its effects are visible only when the velocities of the source/receiver and the wave itself are comparable. In such a case, an approximate formula for the apparent frequency is as follows

$$\mathrm{f=\left ( 1-\frac{v.cos\theta }{c} \right )^{-1}f_{0}}$$

Conclusion

Doppler effect refers to the phenomenon of change in frequency of waves with a nonstationary source or receiver. The magnitude of this change is referred to as the Doppler shift. For instance, the Doppler shift in a certain sound wave could be 20 Hz. The Doppler effect is an illusion, and the frequency is not physically altered. Rather, it only appears different from its actual value. Doppler shift in frequency is broadly classified into redshift and blue shift, though this distinction is defined for light waves.

Redshift refers to a decrease in frequency due to the Doppler effect, while blue shift refers to an increase in frequency due to the Doppler effect. They are called so because red lies on the lower frequency end of the visible region, while blue lies on the higher frequency end. The terms “Doppler shift” and “Doppler effect” are often synonymously used, but the former refers to the actual magnitude of change in the frequency, while the latter is a reference to the phenomenon of change of frequency. That said, using them synonymously is not entirely wrong.

FAQs

Q1. Can Doppler effect and Doppler shift exist independently?

Ans. No. Doppler shift is a measure of the magnitude of change of frequency. The frequency change occurs only because of the Doppler effect and thus, the two must exist simultaneously.

Q2. Why do emergency vehicles have rising and falling sirens?

Ans. Due to the Doppler effect, the sound of the siren would affect a person nearby with a sudden frequency change as the emergency vehicles passed them. Thus, the siren has a constantly varying frequency to prevent this.

Q3. State how the Doppler effect is used in speed radars?

Ans. Doppler radars send a beam of microwave at the target and detect the Doppler shift in its frequency as it reflects. This Doppler shift is used to calculate the speed of the target.

Q4. When is the Doppler effect observed?

Ans. Doppler effect is observed only when there is relative motion between the source and the receiver. Thus, if they are moving with the same velocities in the same directions, there won’t be relative motion between them and thus, the Doppler effect will not be observed.

Q5. Why does the Doppler effect occur?

Ans. When the source is moving, the successive wave crests emitted by it are spaced closer together in the front than in the back. Thus, the frequency appears to be altered.