Doppler Frequency Equation Question

[Nathan777]

In my physics books it gives an equation of frequency for a moving observer as

f'= v'/λ =v+u/λ. Since λ=v/f it was converted to f'=v+u/(v/f) = (v+u/v)f

I understand this much of the equation, but the final Algebraic factoring that I don't get is they said this equation is f'= (1+u/v)f

I just don't get how v+u/v was changed to 1+u/v.

Any explanation here would be helpful.

Thanks.

 

[tiny-tim]

Hi Nathan777!

You've left out the brackets!

(Also, your dimensions obviously don't match: you can't add things of different dimensions, ie different units, eg you can't add a v to a u/λ. )

It should be written …

f'= v'/λ =(v+u)/λ. Since λ=v/f it was converted to f'=(v+u)/(v/f) = ((v+u)/v)f = (1 + u/v)f​