# Rearranging the doppler effect formula to solve for Vs

• hellokitty
In summary, the conversation is about the Doppler Effect and the difficulties the speaker is having in solving the equations related to this topic. They are specifically seeking help in rearranging the formula to solve for Vs. The conversation also includes a Latex version of the formula and a request for a step-by-step solution to the problem.
hellokitty
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 me arrange the formula where I can solve for Vs??

#### Attachments

• untitled.bmp
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Here's a latex version of that formula (which applies when the observer is stationary but the source moves):

$$f_o = f_s \frac{v}{v \pm v_s} = f_s \frac{1}{1 \pm v_s/v}$$

Do you have an example of the kind of problem that is giving you trouble?

the problem is asking to solve for Vs from the formula that I have attached. But I do not know how to rearrange it to where I can solve for Vs. I have everything else in the formula but I do not know how to rearrange it...

Do it step by step:

$$f_o = f_s \frac{1}{1 \pm v_s/v}$$

$$\frac{f_o}{f_s} = \frac{1}{1 \pm v_s/v}$$

$$\frac{f_s}{f_o} = 1 \pm v_s/v$$

You take it from here.

## 1. What is the Doppler Effect formula for solving for Vs?

The Doppler Effect formula for solving for Vs is: Vs = (f0 * v) / (v +/- vs)
Where f0 is the original frequency, v is the speed of sound, and vs is the velocity of the source.

## 2. How do I rearrange the formula to solve for Vs?

To rearrange the formula, first multiply both sides by (v +/- vs). This will give you: Vs * (v +/- vs) = f0 * v.
Next, distribute Vs to both terms within the parentheses: Vs * v +/- Vs * vs = f0 * v.
Then, subtract Vs * v from both sides: +/- Vs * vs = f0 * v - Vs * v.
Finally, divide both sides by +/- vs to isolate Vs: Vs = (f0 * v) / (v +/- vs).

## 3. What is the difference between the plus and minus signs in the formula?

The plus sign (+) is used when the source is moving towards the observer, and the minus sign (-) is used when the source is moving away from the observer. This is because the sign represents the direction of the source's velocity relative to the observer.

## 4. Can the formula be used for any type of wave?

Yes, the formula can be used for any type of wave, as long as the speed of the wave is known and the source is moving relative to the observer. This includes sound waves, light waves, and other types of electromagnetic waves.

## 5. How can I use the formula to calculate the velocity of a moving source?

To use the formula to calculate the velocity of a moving source, you will need to know the original frequency of the wave, the speed of the wave, and the observed frequency. Plug these values into the formula, and solve for Vs.

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