Doppler Effect Definition
In 1842, Austrian physicist Christian Doppler discovered that frequency of wavelengths tends to change with the movement of wave source in relation to an observer. If that sounds too complex, in convenient terms you can ask what is the Doppler Effect simple explanation?
Doppler Effect is the increase or decrease in light, sound or other waves when the source and observer move towards or away from each other. This effect gives rise to not just a crucial theory of physics but also helps in mathematical calculation of waves and their frequencies. Before proceeding to Doppler Effect derivation, let us learn more about it through some examples.
Example 1
Suppose a frog sits in the middle of a lake. It is moving its leg in a way to cause ripples or waves on this water’s surface. These waves arise from this frog’s position and move outward toward the edges of this lake in concentric circles. Two observers, ‘A’ and ‘B’ are standing at the left and right sides of this lake, respectively.
[Image will be Uploaded Soon]
Figure 1.0 The circles in this image represent the waves moving outward from the frog’s position.
At the position above, both observers will find that the waves reach them at similar frequencies, considering that the frog is equidistant from them. However, the frequency of waves, observable to ‘A’ and ‘B’ will start differing as soon as the frog moves toward observer B.
[Image will be Uploaded Soon]
Figure 1.1 The waveform changes for both observers with the movement of the frog (source of the waves).
At this position, wave frequency for observer B is higher than it is for observer A. B experiences higher frequency because the wave source moves toward it. Similarly, ‘A’ observes lower wave frequency as the wave source moves away from it. This is what the Doppler Effect defines.
Doppler Effect Derivation Class 11 for Moving Source and Stationary Observer
[Image will be Uploaded Soon]
Figure 2.0 Wave source moving toward an observer.
Wave velocity c = λS/T
In this equation, λS defines the source’s wavelength.
c is the wave velocity
T is the time for the wave to move one wavelength distance.
For the Doppler Effect derivation, we can say that
T = λS/c (eq.1)
Now, consider that the source is moving with velocity ‘vS’ towards the stationary observer. In T time, this source can travel d distance,
Thus, d = vST (eq.2)
Suppose the source moves in direction x, and due to the shortening wavelength, λO is the wavelength reaching the observer.
λO = λS – d (eq.3)
Now, substitute the value of T from eq.1 into eq.2.
d = vSλS/c
Substitute this value of d into eq.3
λO = λS – (vSλS/c)
λO = λS (1 – vS/c)
Keep in mind that the sign of vS changes as the source moves away from the observer. Everything else in this formula remains the same.
Example 2
Consider that observer A is riding a bike and moving away from a stationary ambulance whose siren is switched on. At first, pitch and sound of its siren are different to observer A when he is closer to the sound’s source. As he moves away, sound and pitch changes, thanks to the Doppler Effect.
Notice that in this example, source of wave remains stationary, but an observer moves away from it.
Doppler Effect Derivation for Moving Observer and Stationary Source
[Image will be Uploaded Soon]
Determining observed frequency is easy since it is the combination of observer velocity and wave velocity divided by actual wavelength.
fO = (c – vO)/λS
fO refers to the frequency observed, and vO is the velocity of the observer.
But, fO = c/λO
Thus, c/λO = (c – vO)/λS
Now, reciprocate both sides, we get
λO/c = λS/(c – vO)
Multiplying by c,
λO = λS/[(c − vO)/c]
Thus, λO = λSc/(c − vO)
If you need further assistance, consult our derivation of Doppler Effect equations pdf, available online. You can also attend our live classes online and get ahead on your preparations. Now you can even download our Vedantu app for further convenience.
FAQs on Doppler Effect Derivation
1. What is the Doppler effect according to the CBSE Class 11/12 syllabus?
The Doppler effect is the apparent change in the frequency of a wave in relation to an observer who is moving relative to the wave source. As per the NCERT syllabus for 2025-26, this is a key concept in Wave Optics. For example, the pitch of a siren sounds higher as it approaches you and lower as it moves away. This is not a change in the siren's actual sound frequency, but in how you perceive it due to the relative motion.
2. What is the general formula used to calculate the Doppler effect for sound?
The general formula for the apparent frequency (f') due to the Doppler effect in sound is:
f' = f [ (v ± vₒ) / (v ∓ vₛ) ]
Where:
- f' is the apparent frequency heard by the observer.
- f is the actual frequency of the source.
- v is the speed of sound in the medium.
- vₒ is the speed of the observer.
- vₛ is the speed of the source.
The signs are chosen based on the direction of motion: use the top sign in the numerator/denominator for movement towards each other and the bottom sign for movement away from each other.
3. How is the Doppler effect formula derived when the source moves towards a stationary observer?
When a source moves towards a stationary observer, it 'chases' its own sound waves. This compresses the wavefronts, effectively shortening the wavelength. The new, apparent wavelength (λ') is the original wavelength (λ) minus the distance the source travelled in one time period (T), which is vₛT.
So, λ' = λ - vₛT.
Since λ = v/f and T = 1/f, we can substitute to get λ' = (v - vₛ)/f.
The apparent frequency f' is v/λ', which leads to the derivation: f' = v / [(v - vₛ)/f] = f [v / (v - vₛ)].
4. What are the key real-world applications of the Doppler effect?
The Doppler effect has several important applications across different fields:
- Meteorology: Doppler radar is used to track storms by measuring the motion of raindrops and predicting weather patterns.
- Astronomy: Astronomers use the 'redshift' (a Doppler effect for light) of distant galaxies to confirm that the universe is expanding.
- Medical Imaging: Echocardiograms use the Doppler effect to measure the speed and direction of blood flow in the heart.
- Law Enforcement: Police use radar guns that bounce microwaves off a moving vehicle to measure its speed based on the frequency shift of the reflected waves.
5. Does the Doppler effect change the actual frequency of the source?
No, this is a common misconception. The Doppler effect does not change the actual frequency emitted by the source. The source continues to vibrate and produce waves at a constant frequency. The effect is entirely about the perceived frequency by the observer, which changes only because the relative motion between the source and observer alters the rate at which wave crests arrive.
6. What is the fundamental difference between the Doppler effect for sound and for light?
The primary difference lies in the medium. Sound requires a medium (like air) to travel, so its Doppler effect formula depends on the velocities of the source and observer relative to that medium. Light, an electromagnetic wave, does not require a medium. Therefore, the Doppler effect for light depends only on the relative velocity between the source and the observer, a key principle of special relativity.
7. What is the Relativistic Doppler effect and when is it used?
The Relativistic Doppler effect is the version of the effect that applies to electromagnetic waves, like light, especially when the source and observer are moving at speeds comparable to the speed of light (c). Unlike the classical formula for sound, this derivation accounts for time dilation from special relativity. It must be used in high-velocity scenarios, such as in astrophysics or particle physics, where classical formulas would give inaccurate results.
8. How does a bat use a 'double Doppler effect' to hunt and navigate?
A bat's echolocation is a sophisticated two-step application of the Doppler effect.
1. First, the bat emits a sound pulse. As the bat flies towards a stationary object (like a moth), the moth receives the sound at a higher frequency.
2. The sound then reflects off the moth, which now acts as a stationary source emitting this higher frequency sound. As the bat (a moving observer) flies towards this reflected sound, it perceives an even higher frequency. This 'double Doppler shift' provides the bat with precise information about the relative speed of its prey.
