Understanding Doppler Formula: Solving for Vs and Equivalencies

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    Doppler Formula
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The discussion centers on the equivalence of two forms of the Doppler formula, f1=f2 (Vw/Vw-Vs) and f1=f2/(1+Vs/Vw). Participants are trying to understand how to derive one equation from the other and specifically how to solve for Vs in the first equation. It is noted that replacing Vs with -Vs makes the equations equivalent, but further clarification is sought on the steps to transition between the two forms. One suggestion involves dividing both the numerator and denominator by Vw, but confusion arises regarding the manipulation of terms. The conversation highlights the need for a clearer explanation of the mathematical transformations involved.
chiuda
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doppler formula help please!:)

Hello, i see the doppler formula in 2 different forms one being f1=f2 (Vw/Vw-Vs) and the other f1=f2/(1+Vs/Vw)

f1= Doppler frequency
f2= Source frequency
Vw= Speed of sound
Vs= Speed of source

the problem i am having is understanding how these are equivalent? how fit they get from one to the other? And how would you solve for Vs in the first doppler equation stated? any help would be greatly appreciated :)
 
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hello chiuda! :smile:

if you replace Vs by -Vs, they're the same! :wink:​
 


yes i understand that part but let's say the 2nd eqn was already -vs how does one get from the first equation to the second one? it would be very appreciated if all the steps could be shown thank you :)
 


Try dividing up and bottom by Vw.
 


then i would have f2*(1-Vs/Vw) which is not the same as f2/ (1-Vs/Vw) :S
 
chiuda said:
Hello, i see the doppler formula in 2 different forms one being f1=f2 (Vw/Vw-Vs) and the other f1=f2/(1+Vs/Vw)
chiuda said:
… let's say the 2nd eqn was already -vs how does one get from the first equation to the second one?
chiuda said:
then i would have f2*(1-Vs/Vw)

how do you get that? :confused:
 
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