Confusion in Doppler shift equation?

In summary, the conversation is about the Doppler shift equation for a moving observer and stationary source. The question is regarding a specific step involving the algebraic manipulation of the equation. The solution is to solve for Δt0 in the first equation shown in the attached image. The previous line shows that Δt0 is equal to Δt_s plus vΔt0 over u, and the next step is to algebraically manipulate the equation to solve for Δt0. The poster also asks for clarification on whether Δt0 is represented as 1 in the equation.
  • #1
Tim541541
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I'm just trying to build Doppler shift equation for Moving observer and stationary source. I have an problem in a step. I'm attaching a screen-shot please check it and tell me where to this step ( 1 - v/u)^-1 comes from ?

Thanks in advance.
 

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  • #2
The previous line is ##\Delta{t}_0=\Delta{t}_s+\frac{v\Delta{t}_0}{u}##. It's just algebra from there.
 
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  • #3
Solve for Δt0 in the first equation at the attached image.
 
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  • #4
Nugatory said:
The previous line is ##\Delta{t}_0=\Delta{t}_s+\frac{v\Delta{t}_0}{u}##. It's just algebra from there.
Thank you Nugatory for reply. Can you tell me is that delta t sub o will be mentioned as 1 here ? Actually i just really want to understand algebra behind it.
 
  • #5
Tim541541 said:
Thank you Nugatory for reply. Can you tell me is that delta t sub o will be mentioned as 1 here ? Actually i just really want to understand algebra behind it.
I'm sorry, but I don't understand what you mean by "will be mentioned as 1 here"... The algebra is, as Erland says above, just solving for ##\Delta{t}_0##.
 

1. What is the Doppler shift equation?

The Doppler shift equation is a mathematical formula used to calculate the change in frequency of a wave, such as light or sound, due to relative motion between the source of the wave and the observer.

2. How does the Doppler shift equation relate to confusion?

The Doppler shift equation can lead to confusion when trying to apply it in certain scenarios, such as when the relative motion between the source and observer is not directly towards or away from each other. This can result in incorrect calculations and confusion in interpreting the results.

3. What factors can affect the accuracy of the Doppler shift equation?

There are several factors that can affect the accuracy of the Doppler shift equation, such as the relative velocity between the source and observer, the speed of the wave, and the angle of approach between the two. Additionally, factors such as the medium through which the wave is traveling and any interference can also impact the accuracy of the equation.

4. How does the Doppler shift equation apply to different types of waves?

The Doppler shift equation can be applied to various types of waves, including electromagnetic waves like light and radio waves, as well as mechanical waves like sound. However, the specific formula and variables used may differ depending on the type of wave being analyzed.

5. Can the Doppler shift equation be used in real-world applications?

Yes, the Doppler shift equation is commonly used in various real-world applications, such as in radar technology, astronomy, and medical imaging. It is also used in everyday scenarios, such as calculating the change in pitch of a siren as a vehicle approaches or moves away.

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