Doppler EffectThe change in the frequency of a wave received by an observer (detector) compared to the frequency with which it was emitted is known as the Doppler Effect (in honor of the Austrian physicist, Christian Doppler, who did pioneering work on the topic). The Doppler Effect (also called Doppler shift) takes place whenever there is relative motion between emitter (or source) and receiver (or observer, or detector).

We can use wavefront diagrams to understand the Doppler effect. If there is no relative motion between source and observer, then the observer receives as many wavefronts per second as the emitter emits; thus the observer measures the same frequency as emitted by the source

The wavefronts are called condensations in the diagram. As long as there is no relative motion between source and observers, the two observers on either side receive waves at the same frequency and wavelength.

Picture is take from Cutnell and Johnson - Physics 8e.

Doppler Effect – No relative motion

Doppler Effect– Stationary Source

• CASE 1: Observer moves towards source.

The velocity of the wave w.r.t the moving observer is

To the moving observer, the approaching waves have a speed of instead of . Using the relationship between , , and we write an expression for the modified frequency as

Picture Source:Physics, 4e by James L Walker.

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Doppler Effect– Stationary Source

• CASE 1 contd: Observer moves towards source. From previous slide

In the above expression, since the wavelength, the distance between the wavefronts, remains the same at all times as the observer moves towards source. Substituting , and , yields

Doppler Effect– Stationary Source

• CASE 2: Observer moves away from source.

The velocity of the wave w.r.t the moving observer is

To the moving observer, the approaching waves have a speed of instead of . Using the relationship between , , and we write an expression for the modified frequency as

Picture Source:Physics, 4e by James L Walker.

+𝑥

Doppler Effect– Stationary Source

• CASE 2 contd: Observer moves away form the source. From previous slide

The calculations is exactly as in case 1 with the signs replaced with signs.

• We can combine the two stationary source cases as

Doppler Effect– Moving Source

• CASE 3: Source moves towards observer. We let be the speed of the source and be the speed of the wave. In a time interval of one period, , the wave has traveled through a distance while the source has moved a distance towards the observer.

The observer at the right measures a shorter wavelength – hence a higher frequency as the source approaches; while the observer at the left measures a longer wavelength – hence a smaller frequency as the source moves away.

Picture from Cutnell and Johnson

Doppler Effect– Moving Source• CASE 3 contd: Source moves towards observer.

At , (for the wave); while (from observer’s frame of reference)

In the above, , and

Picture Source:Physics, 4e by James L Walker.

Doppler Effect– Moving Source

• CASE 4: Source moves away from observer. The observer at the left measures a longer wavelength given by . Thus

• Combining cases 3 and 4:

Doppler EffectCombining all four cases

We can combine the four equations developed in the four cases discussed into one general-purpose equation:

where,• observer (detector) frequency• source frequency• speed of the observer/detector• speed of the source.