Doppler Effect Equations

In summary, the conversation discusses a struggle with rearranging equations for solving Doppler Effect problems. The issue lies in manipulating the equations to isolate certain variables, specifically dealing with the plus-or-minus sign. The speaker provides an example and suggests separating the equation into plus and minus forms, isolating the desired variable in each, and then combining the two equations into one with a plus-or-minus. They also remind the listener to consider the meaning of the symbol when working with it.
  • #1
bbfcfm2000
10
0
I know which equations to use for solving Doppler Effect problems, so figuring out which is the observer and which is the source and which is moving or stationary is not the problem, the problem I am having is in solving the actual formulas... This question might belong in the math help section but I thought it was best to post this in the physics area because it does deal with a physics topic.

Anyway, I attached the equations as graphics (maybe somebody knows how to LATEX these?). I am looking for some help in rearranging these equations to solve for each of the variables, V,Vs,Vo,Fo,Fs.

Can somebody please help?

Thanks!
 

Attachments

  • Doppler EQ - Moving Observer.gif
    Doppler EQ - Moving Observer.gif
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  • Doppler EQ - Moving Source.gif
    Doppler EQ - Moving Source.gif
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  • #2
[tex]f_{o}=f_{s}\left({1\pm \frac{V_{o}}{V}}\right)[/tex]

[tex]f_{o}=f_{s}\left({\frac{1}{1\pm \frac{V_{s}}{V}}}\right)[/tex]

As I understand it, you are having trouble manipulating the equations to isolate certain variables. I suspect it is the plus-or-minus that is giving you trouble. Let's do an example. Let's isolate V in the first equation.

[tex]f_{o}=f_{s}\pm \frac{f_{s}V_{o}}{V}}[/tex]
[tex]Vf_{o}=Vf_{s}\pm f_{s}V_{o}[/tex]
[tex]Vf_{o}-Vf_{s}=\pm f_{s}V_{o}[/tex]
[tex]V(f_{o}-f_{s})=\pm f_{s}V_{o}[/tex]
[tex]V=\pm \frac{f_{s}V_{o}}{f_{o}-f_{s}}[/tex]

Hope that helps. Keep in mind that if you encounter problems handling a [itex]\pm[/itex] sign, just separate the equation into the plus and minus forms, isolate the variable you wish in each equation normally, then unite the two final equations into one with a [itex]\pm[/itex]. Think about what the symbol represents when dealing with it in your work.
 
  • #3


Sure, I'd be happy to help. The equations for solving Doppler Effect problems can be a bit daunting at first, but with some practice and understanding, you'll be able to rearrange them to solve for any variable you need.

First, let's go over the equations. The first equation is for the frequency of the observed wave (Fo), which is equal to the frequency of the source wave (Fs) multiplied by the ratio of the speed of the wave (V) plus the speed of the observer (Vo) over the speed of the wave minus the speed of the source (Vs). This equation is used when the source or observer is moving.

The second equation is for the frequency of the source wave (Fs), which is equal to the frequency of the observed wave (Fo) multiplied by the ratio of the speed of the wave (V) minus the speed of the source (Vs) over the speed of the wave minus the speed of the observer (Vo). This equation is used when the source or observer is stationary.

To rearrange these equations, you will need to use algebraic principles such as isolating the variable you want to solve for and using inverse operations (e.g. if a variable is multiplied, divide to isolate it). It may also be helpful to plug in known values and solve for the unknown variable to get a better understanding of how the equations work.

For example, if you want to solve for the speed of the wave (V), you can rearrange the first equation to be V = (Fo - Fs) * (Vo + Vs) / (Fo + Fs). This would give you the speed of the wave in terms of the frequencies and speeds of the source and observer.

If you're still having trouble, don't hesitate to ask for more specific help or clarification. It's also a good idea to practice using these equations with different scenarios and values to get more comfortable with them. Good luck!
 

1. What is the Doppler Effect Equation?

The Doppler Effect Equation is a mathematical formula that describes the change in frequency or wavelength of a wave due to relative motion between the source of the wave and the observer.

2. How is the Doppler Effect Equation used?

The Doppler Effect Equation is used to calculate the observed frequency or wavelength of a wave when there is relative motion between the source and observer. It is commonly used in physics, astronomy, and meteorology to study the movement of objects in space or the behavior of waves in different mediums.

3. What are the variables in the Doppler Effect Equation?

The variables in the Doppler Effect Equation are the observed frequency (f), the original frequency (f0), the speed of the wave (v), the speed of the source (vs), and the speed of the observer (vo). These variables can be represented in different units, such as meters per second or hertz, depending on the specific situation.

4. How does the Doppler Effect Equation relate to sound waves?

The Doppler Effect Equation can be applied to sound waves, as they are a type of wave that can experience a change in frequency due to relative motion. This is why we perceive a change in pitch when an ambulance or train passes by us, as the sound waves are being affected by the motion of the source and observer.

5. Are there any limitations to the Doppler Effect Equation?

The Doppler Effect Equation assumes that the source and observer are moving in a straight line and that the speed of the wave is constant. It also does not take into account other factors that may affect the observed frequency, such as interference or changes in the medium. Therefore, it is a simplified model and may not accurately represent all real-life situations.

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