# Doppler shift equation results in inconsistencies

The non-Relativistic Doppler shift equation is $f = \left( \frac{c + v_\text{r}}{c + v_\text{s}} \right) f_0$ where c is the speed of the medium (346.4 m/s for sound at 25 C temperature). I tried calculating the Doppler shift for the case when the source was moving towards the observer, and the case where the observer is moving with the same velocity towards the source, but I get different answers by about 0.75 m/s. Why does the frame I choose make a difference?

http://www.wolframalpha.com/input/?i=200*%28346.4+%2B+20%29%2F%28346.4+-+0%29

I am running the calculation for a wave with 200Hz frequency and a source(or an observer) moving with 20 m/s. $v_s$ is velocity of the source and $v_r$ is the velocity of the observer.

Sound waves propagate at 340 m/s relative to the medium (air). In both cases, the relative motion of the source and receiver are the same, but the relative motions of the source and receiver with respect to the medium are different. This is what breaks the symmetry of your two setups, and why you're getting different answers.

It may help to look at a derivation of the doppler shift to better understand how that difference plays a role. Here is one direvation I came across while searching. There may be better ones.

• I understand how the fact that the velocities in the equation are with respect to the medium makes a difference in the math, but I still don't "feel" any physical difference. Is it possible that you try to explain it from a physical point of view or re-word it for me if it was already included in your answer? Jul 9, 2014 at 22:49
• Any attempt by me would just be rehashing a derivation with pictures. Take a look around on the internet, or in your textbook. If you have a specific conceptual question on this I or others may be able to help.
– BMS
Jul 10, 2014 at 1:23
• Ok here's a situation that conveys where I am confused: imagine a blindfolded man who's seated in a remote controlled wheelchair 50 meters from an ambulance. Suppose the ground is so smooth the man wouldn't know it if he started moving, and supposed the man also has an airtight mask on so he wouldn't feel any air brushing on his face. And let us make the man sleep through the acceleration of the chair so he wouldn't know he started moving. The man suddenly hears the siren's frequency rise. How does the man know if he's approaching the ambulance or if the ambulance is approaching him? Jul 10, 2014 at 8:50