# Doppler shift and relative velocity

I have come across Doppler shift equation. If we consider the source to be moving toward the observer at a speed $V$ and observer moving toward the source with a speed $U$, for the calculation of the apparent frequency, can't we think of the observer to be at rest from his frame and think that the source is moving with a speed $V+U$?

I have tried to solve a problem doing this but the answers i get are different.

• For what kind of signals? If there is a physical medium, then the situations are not symmetric. Dec 15, 2016 at 7:17

No, assuming you are talking about sound waves, you can't add the velocities of the source and the observer in the equation for effective frequency: $$f_{\text{eff}}=\frac{v'}{\lambda'}$$
The reason is that a source moving toward the observer raises the frequency heard by the observer by decreasing the wavelength of the sound in the denominator (because it is "chasing" its own wave), $$\lambda'=\frac{(v_{\text{sound}}-{V})}{f},$$ but an observer moving toward the source increases the frequency heard by increasing the relative velocity between him and the sound wave in the numerator. $$v'=v_{\text{sound}}-U$$ (where $$U$$ is negative when toward the source).