How do you finish rearranging the Doppler shift formula

[McWilliams]

Homework Statement

i am using the Doppler shift formula Fs=F0(1/1+-(vsource/c) i can rearrange it to an extent but when i use it to find my answer i i need to divide it by two in order to do it, every time. I would just like to understand why this is, or if i am doing it completely wrong.

The Attempt at a Solution

((Fs/F0)-1)*V(sound)=Vsource
but if i turn it into 2Vsource it comes out that i will get the right answer when i divide it by two to get vsource, so please explain why there is a two there.

Please and thank you for your help.

 

[tms]

((Fs/F0)-1)*V(sound)=Vsource

If I understand your symbols, I think you've got the ratio of the frequencies upside down.

 

[McWilliams]

Yes, thank you, they were reversed, that created my formula to be positive instead of a negative end number, but i still need to divide Vsource by 2 in order to get the correct answer.

 

[tms]

Yes, thank you, they were reversed, that created my formula to be positive instead of a negative end number, but i still need to divide Vsource by 2 in order to get the correct answer.

Show your work, then.

 

[Nickie]

I would like to clarify that the Doppler shift formula is typically written as Fs = F0 * (1 +/- (vsource/c)). The 'c' in the formula represents the speed of light, not the speed of sound. Additionally, the '1' in the parentheses should be squared to represent the square root of the denominator. With these corrections, the formula should look like this: Fs = F0 * (1 +/- (vsource/c))^2.

Now, to address your question about the '2' in the formula, it is actually not necessary. In some cases, it may appear in the formula if you are using certain units (such as in the case of using kilometers per hour for velocity instead of meters per second). However, in most cases, the '2' should not be there.

To rearrange the formula, you can start by dividing both sides by F0: (Fs/F0) = (1 +/- (vsource/c))^2. Then, you can take the square root of both sides: sqrt(Fs/F0) = 1 +/- (vsource/c). Finally, you can subtract 1 from both sides and multiply by c to get the final formula: vsource = c * (sqrt(Fs/F0) - 1). This should give you the correct answer without needing to divide by 2.

In general, it's important to carefully check the units and variables in the formula to make sure they are consistent and accurate. I hope this explanation helps you understand the rearrangement of the Doppler shift formula.