Doppler Shift and Velocity Relationship

Therefore, the Doppler shift is directly proportional to the velocity of the source and detector. This relationship is commonly used in applications such as radar and sonar. In summary, the frequency shift of an electromagnetic wave due to the relative velocity between the source and detector, known as Doppler shift, is proportional to the velocity. For small velocities, this relationship simplifies to a proportionality between the frequency shift and the velocity. This is often used in radar and sonar applications.
  • #1
atmostudent
1
0
1. Whenever we talk about a single frequency characterizing an electromagnetic wave, we are tacitly assuming that the source and the detector are stationary relative to one another. However, if the distance between the two is changing in velocity, V, then the frequency of radiation, ν1 emitted by the source will be different than the frequency ν2 observed by the detector. In particular, the frequency shift ∆ν = ν1 - ν2 is approximately proportional to the velocity, a phenomenon known as Doppler shift.
A.) Derive the precise relationship between ∆ν and velocity V, by considering the time lapse, ∆t, between two successive waves crests reaching the detector with speed c.

B.) For the case that V << c, show that your solution to 3A simplifies to a proportionality between ∆ν and V.


I was thinking for A.) maybe something along the lines of

V(∆t) = ∆ν/c

using V = v * wavelenght and

wavelength = c/v
 
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  • #2
to solve for ∆ν = Vc/v ? For B.) If V << c, then the ratio V/c is very small and can be approximated to 0. This means that ∆ν = Vc/v becomes ∆ν = 0, which is a proportionality between ∆ν and V.
 

1. What is the Doppler Effect?

The Doppler Effect is the perceived change in frequency of a wave caused by the relative motion between the source of the wave and the observer. This effect is commonly observed with sound waves, such as the change in pitch of an ambulance siren as it passes by.

2. How is the Doppler Shift calculated?

The Doppler Shift is calculated using the equation: Δf = f0 * (v/c), where Δf is the change in frequency, f0 is the original frequency, v is the velocity of the source or observer, and c is the speed of the wave in the medium.

3. What is the difference between the Doppler Effect and the Doppler Shift?

The Doppler Effect refers to the perceived change in frequency of a wave, while the Doppler Shift refers to the actual change in frequency. The Doppler Effect is dependent on the relative motion between the source and observer, while the Doppler Shift is a measurable quantity.

4. What are some real-world applications of the Doppler Shift?

The Doppler Shift is used in various fields, such as astronomy to measure the speed and distance of celestial objects, meteorology to track the movement of storms, and medical imaging to detect and monitor blood flow.

5. How does the Doppler Shift problem affect communication systems?

The Doppler Shift can cause distortion or loss of signal in communication systems, especially in mobile or satellite communication. To compensate for this effect, communication systems use techniques such as frequency modulation or adaptive equalization.

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