Doppler Effect, Stationary source moving observer

In summary, the observer approaching a stationary source emitting waves at frequency f will register the velocity of the waves as v + v0, which is equal to \frac{f}{\lambda}. This means that the observer's velocity is added to the velocity of the waves to determine the overall velocity felt by the observer. This equation is derived from the fact that the velocity of waves is equal to the frequency times the wavelength.
  • #1
max0005
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Homework Statement



My books states, considering a stationary source emitting waves at frequency f, such waves having velocity v, and an observer approaching the source along a linear path at velocity vO we have that: The observer registers the velocity of the waves at [tex]v+v0[/tex]. Up until now all ok, the velocity "felt" by the observer is the sum of the wave's velocity plus his own velocity.

Then the book adds: Which is equal to [tex]\frac{f}{\lambda}[/tex] where [tex]\lambda[/tex] is the wavelength. Can anybody please explain this passage?

Thanks in advance!

max


Homework Equations





The Attempt at a Solution

 
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  • #2
The velocity of the waves is equal to the frequency times the wavelength, i.e. v = f * \lambdaThe velocity felt by the observer is the sum of the wave's velocity and the observer's velocity, i.e. v + vO = (f * \lambda) + v0 Simplifying we get (f * \lambda) + v0 = f * \lambda + v0 Therefore, v + v0 = \frac{f}{\lambda}
 

1. What is the Doppler Effect?

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

2. How does the Doppler Effect affect a stationary source and moving observer?

In this scenario, the source of the wave is not moving, but the observer is. The Doppler Effect causes the frequency of the wave to appear higher to the observer as it approaches and lower as it moves away. This is known as the "blue shift" and "red shift," respectively, in the context of light waves.

3. What factors can influence the magnitude of the Doppler Effect?

The magnitude of the Doppler Effect is influenced by the speed of the source and observer, as well as the speed of the wave itself. Additionally, the angle at which the wave approaches the observer can also affect the magnitude of the effect.

4. How is the Doppler Effect used in real-world applications?

The Doppler Effect has many practical applications, such as in weather radar systems to track the movement of storms, in medical imaging to measure blood flow, and in astronomy to determine the velocity and distance of stars and galaxies.

5. How is the Doppler Effect different from the Doppler Shift?

The Doppler Shift is a more general term that encompasses both the Doppler Effect and the relativistic Doppler Effect. The relativistic Doppler Effect takes into account the effects of time dilation and length contraction in the context of Einstein's theory of relativity. The classical Doppler Effect only applies to non-relativistic speeds and is often used in everyday situations involving sound and light waves.

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