The [Doppler effect](https://en.wikipedia.org/wiki/Doppler_effect) formula is $$f = \frac{(v\pm v\_r)}{(v\mp v\_s)}f\_0$$ where $f$ and $f\_0$ are the observed and emitted frequency, respectively, and $v, v\_r$ and $v\_s$ the speed of the waves, receiver and source, respectively (all relative to the medium.) The numerator has $+$ if the receiver moves towards the source, and the denominator has $-$ if the source moves towards the receiver.

Now, assume the receiver and the source are approaching each other. My intuition tells me that there should be no physical difference whether it is the source which is moving towards the receiver, or vice versa. Actually, the only difference between these cases shall be the coordinate system chosen. But the equation above suggests otherwise because one velocity is in the denominator and the other one in the numerator.

For example, take $v=2$ and receiver and source approaching each other at a speed $u = 1$ (disregarding units.) This, I may say, happens because either $v\_s = 0$ and $v\_r = 1$ (towards the source), or $v\_s = 1$ (towards the receiver) and $v\_r = 0$. In the first case, we get $$ f = \frac{2+1}{2} f\_0 = 1.5 f\_0 $$

In the second case: $$ f' = \frac{2}{2-1} f\_0 = 2 f\_0 $$

Where does this asymmetry come from? Or why is my intuition wrong?